Circle the Square

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Liddz
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re: Circle the Square

Post by Liddz »

Another correct value of Pi debate:
Golden Pi = 4/√φ = 3.144605511029693144 is the correct value of Pi and this fact can be proven by almost anybody that has sufficient knowledge of the principles of the Kepler right triangle including the creation of a circle with a circumference equal in measure to the perimeter of a square.

The correct value of the Golden ratio will determine the correct value of both the square root of the Golden ratio and Pi.

Traditional Pi 3.141592653589793 is also false because it is based upon a false value for the Golden ratio for example traditional Pi 3.141592653589793 can also be gained from 4 divided by the square root of 1.621138938277405 = 1.273239544735163. The ratio 1.621138938277405 can be gained in Trigonometry through the formula Cosine (35.84839254086685) multiplied by 2.

The ratio 1.621138938277405 is a very poor approximation of the real Golden ratio of 1.618. The correct value for the Golden ratio is Cosine (36) multiplied by 2 = 1.618033988749895 and the correct value for the square root of the Golden ratio is 1.27201964951406. 16 divided by traditional Pi 3.141592653589793 squared = 9.869604401089357 results in the False value of the Golden ratio 1.621138938277405, while 16 divided by Golden Pi 3.144605511029693 squared = 9.888543819998317 = 1.618033988749895. Remember that 1.618033988749895 is the real Golden ratio and NOT 1.621138938277405.

We do not even need to use any of the Pi values to determine the diameter of a circle or the circumference of a circle instead we can use the Square root of the Golden ratio = 1.27201964951406. If we multiply 1 quarter of the circle's circumference by 1.27201964951406 then the result is the correct measure for the circle's diameter. If we already know the length of the circle's diameter but we do not yet know the measure for the circle's circumference then all we have to do is divide the measure of the circle's diameter by 1.27201964951406 and the result will be 1 quarter of the circle's circumference.

Multiply 1 quarter of the circle's circumference by 4 and obviously we have the value for the circumference of the circle. If we use 1.27201964951406 to get the length of the circle's diameter or the measure for the circle's circumference and then we divide the measure for the circle's circumference by the measure for the circle's diameter I guarantee you the result is 3.144605511029693.

The Kepler right triangle has so much wisdom encoded in it.

The Kepler right triangle is proof that 3.144605511029693 is the correct value for Pi.

3.141592653589793 as Pi has already been proven to be false by the aid of computer software that demonstrate that the curve of a circle can never be filled completely by polygons so the assumption that the gaps in the circle’s curve will disappear is false and thus proves that the multiple Polygon method for deriving a value of Pi is flawed because the multiple polygon method can only give us approximations for Pi while the Kepler right triangle gives us the exact value of Pi and that is 3.144605511029693.

For example if the second longest edge length of a Kepler right triangle is the same length as the diameter of a circle then shortest edge length of the Kepler right triangle is equal to 1 quarter of the circle’s circumference. So if the shortest edge length of the Kepler right triangle is multiplied by 4 and the result divided by the second longest edge length while we use 1.27201964951406 then we can get the correct value of Pi and again that is 3.144605511029693.

The Kepler right triangle is also the key to squaring the circle with equal perimeters and also equal areas. So almost anybody can get the right value of Pi by just constructing a Kepler right triangle and also a pocket calculator.

Remember that the hypotenuse of a Kepler right triangle divided by the shortest edge length produces the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895, while the second longest edge length of a Kepler right triangle divided by the shortest edge length produces the square root of the Golden ratio 1.27201964951406.

Pi can be also be calculated from a Kepler right triangle if the measure for the perimeter of the square that is located on the shortest edge length of the Kepler right triangle is divided by the measure for the second longest edge length of the Kepler right triangle.

Pi can also be gained if the measure of the perimeter of the square that is located on the second longest edge length of a Kepler right triangle is divided by the hypotenuse of the Kepler right triangle.

Traditional Pi = 3.141 can also be gained from a Kepler right triangle that has a hypotenuse with a measure of 34 while the shortest edge length of this Kepler right triangle is 21 and the second longest edge length of the Kepler right triangle has a measure that is equal to the square root of 715. 34 and 21 are both numbers that can be found among the Fibonacci sequence that progresses towards the Golden ratio Phi of Cosine (36) multiplied by 2 = 1.618033988749895 when any of the numbers that are next to each other in the Fibonacci sequence are divided by each other resulting in an approximation for the Golden ratio-Phi of Cosine (36) multiplied by 2 = 1.618033988749895.

34 divided by 21 = 1.619047619047619. 1.619047619047619 is an approximation for the Golden ratio –Phi of Cosine (36) multiplied by 2 = 1.618033988749895. 21 multiplied by 4 = 84. 84 divided by the square root of 715 = 3.141421886428416. 3.141421886428416 multiplied by the square root of 715 = 84. The real value of Pi = 3.144605511029… and can be gained from a Kepler right triangle that has a hypotenuse that has a measurement of 9227465, while the shortest edge length of this Kepler right triangle is 5702887 and the measurement for the second longest edge length of this Kepler right triangle is 7254184.322958371.

9227465 and 5702887 are numbers that are both featured among the Fibonacci sequence that moves towards the Golden ratio-Phi of Cosine (36) multiplied by 2 = 1.618033988749895 when any of the numbers that are next to each other in the Fibonacci sequence are divided by each other resulting in an approximation for the Golden ratio-Phi of Cosine (36) multiplied by 2 = 1.618033988749895. 9227465 divided by 5702887 = the Golden ratio-Phi of Cosine (36) multiplied by 2 = 1.618033988749895.

5702887 multiplied by 4 = 22811548.
22811548 divided by 7254184.322958371 = 3.144605511029681. 3.144605511029681 multiplied by 7254184.322958371 = 22811548.

3.144605511029…….. is the true real value of Pi.

Traditional Pi 3.141592653589793 has been proven to be Transcendental in addition to being irrational. Traditional Pi 3.141592653589793 is Transcendental because Traditional Pi 3.141592653589793 does not fit any polynomial equations. Squaring the circle with equal surface areas becomes possible and easy after traditional Pi 3.141592653589793 has been rejected and replaced with other values of Pi that are NOT transcendental. Golden Pi = 3.144605511029693 is irrational but Golden Pi is NOT transcendental because Golden Pi = 3.144605511029693 is the only value of Pi that fits the following polynomial equation:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693.

x4 + 16x2 – 256 = 0.


THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION: 4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

x4 + 16x2 – 256 = 0.

https://www.tiger-algebra.com/drill/x~4-16x~2-256=0/

Wolfram Alpha proof that the real Pi is NOT transcendental:

• https://www.wolframalpha.com/input/?i=x ... +256+%3D+0


• https://www.wolframalpha.com/input/?i=4%2F√φ


• Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html

• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html

• 2/Sqrt[Sqrt[GoldenRatio]]

2/√√φ = the square root of 3.144605511029693144.

(Square root of Pi = 2 divided by 1.127838485561682 = 1.773303558624324)

http://www.wolframalpha.com/input/?i=2% ... 8%9A%CF%86

(-256 + 16 x^4 + x^8)

(x8 + 16x4 – 256)

http://www.wolframalpha.com/input/?i=-2 ... DShow+less


The Non Transcendental, Exact Value of π and the Squaring of the Circle 1: https://www.youtube.com/watch?v=ccxVW2M ... 1876258142

The Non Transcendental, Exact Value of π and the Squaring of the Circle 3: https://www.youtube.com/watch?v=-QCtnZjZIsw

• Kepler right triangle information:

https://houseoftruth.education/en/teach ... at-pyramid

https://www.goldennumber.net/triangles/

https://en.wikipedia.org/wiki/File:Kepl ... uction.svg

The real value of Pi = 4/√φ on Facebook:

https://m.facebook.com/TheRealNumberPi/

Website for the real value of pi = 4/√φ: www.measuringpisquaringphi.com

Download for free and keep and read The book of Phi volume 8: The true value of Pi = 3.144, by Mathematician and author Jain 108:

https://lists.gnu.org/archive/html/help ... jmqrL6.pdf

Download for free and keep and read The book of Phi volume 9: The true value of Pi = 3.144, by Mathematician and author Jain 108:

https://drive.google.com/file/d/1cIEvbb ... sp=sharing
Liddz
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Dabbler
Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

PI MEASUREMENT CONFIRMED TO BE 3.1446:


The Great Pi conspiracy part 1: http://www.veteranstoday.com/2015/02/05/pi/

The Great Pi conspiracy part 2: http://www.veteranstoday.com/2015/10/06/pi2/


THE FOLLOWING VIDEOS HAVE BEEN SEEN MANY TIMES WHERE THE CURVATURE OF A CYLINDER WITH A DIAMETER OF 1 METER IS MEASURED AND THE PI CIRCUMFERENCE IS REVEALED TO BE 3.1446 AND NOT 3.1415 OR 3.1416

Pythagorean theorem: https://en.wikipedia.org/wiki/Pythagorean_theorem

YouTube downloader, download videos from YouTube and watch them later and keep the videos: YouTube downloader for Windows:

https://ytd-video-downloader-free.en.so ... m/download

YouTube downloader for Mac:

https://www.macxdvd.com/free-youtube-vi ... myoutubedl

Felder group: FORMAT-4® - profit H08 - CNC machining center:

https://www.youtube.com/watch?v=EkOYPmYUAKU




Videos for the true value of Pi: 3.144605511029: Introduction to finding the real value of Pi:

https://www.youtube.com/watch?v=1DawMQ1LV6Q

Physical measurement for the real value of Pi part 1:

https://www.youtube.com/watch?v=iVNrhqLN110

Physical measurement for the real value of Pi part 2:

https://www.youtube.com/watch?v=Ck_pe81qZ9Q

Physical measurement for the real value of Pi part 3:

https://www.youtube.com/watch?v=fATlIzht7VI

Physical measurement for the real value of Pi part 4:

https://www.youtube.com/watch?v=DSAK6XcdVuI

Physical measurement for the real value of Pi part 5:

https://www.youtube.com/watch?v=KFGww0z6HRw

Physical measurement for the real value of Pi part 6:

https://www.youtube.com/watch?v=KTJsCzHLsEo

Physical measurement for the real value of Pi part 7:

https://www.youtube.com/watch?v=ehjANdRlktw







Pi Math Proof: http://measuringpisquaringphi.com/pi-math-proof/

Proof 7 Part 2 Pi Math Proof:

https://www.youtube.com/watch?v=ohFXjnPOOnw&t=4s

Kepler right triangle math proof for Pi;

https://www.youtube.com/watch?v=nvja8rGCbzY&t=123s

Fixing Correcting the problems caused by using traditional Pi:

https://www.youtube.com/watch?v=X1ZAtn6g-Vg

Geo Proof 1 Brand: https://www.youtube.com/watch?v=FBKl62-13SQ&t=52s

Geo Proof 2 Brand: https://www.youtube.com/watch?v=E1KUSEfr46k&t=12s

Geo Proof 4 Brand: https://www.youtube.com/watch?v=d22iTENHGwU&t=69s

Geo Proof 6 Brand: https://www.youtube.com/watch?v=VVwJ4J4pUFQ

5 more squared circle mathematical constants:

https://www.youtube.com/watch?v=BYlEvYflOps&t=6s

The real value of Pi = 4/√φ on Facebook:

https://m.facebook.com/TheRealNumberPi/

Website for the real value of pi = 4/√φ: MEASURING PI SQUARING PHI:

www.measuringpisquaringphi.com

Download for free and keep and read The book of Phi volume 8: The true value of Pi = 3.144, by Mathematician and author Jain 108:

https://lists.gnu.org/archive/html/help ... jmqrL6.pdf

Download for free and keep and read The book of Phi volume 9: The true value of Pi = 3.144, by Mathematician and author Jain 108:

https://drive.google.com/file/d/1cIEvbb ... sp=sharing

The Non Transcendental, Exact Value of π and the Squaring of the Circle 1:

https://www.youtube.com/watch?v=ccxVW2M ... 1876258142


Pi by phi quadrature: https://www.youtube.com/watch?v=CRkIKSkVzPA

Measuring Pi squaring phi: www.measuringpisquaringphi.com

More information about Pi, Archimedes boundary limit claim is a DOGMA. :


https://translate.google.com/translate? ... rev=search


I have found the EXACT VALUE OF PI = 4/√φ = 3.1446.

3.1446 IS THE EXACT 100% REAL VALUE OF PI.


PURCHASE A ROLLING CIRCLE CUTTER WITH A RADIUS OF 50 CENTIMETERS:

https://www.ebay.com/itm/NT-Cutter-Larg ... 1#viTabs_0


PURCHASE A GOLDEN CIRCLE CUTTER WITH A 200-CENTIMETER DIAMETER FOR £65:

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BRISTOL BOARD THAT IS LARGER THAN AO. MEASURMENT FOR BRISTOL BOARD = 3050MM X 1220MM:

https://www.amazon.co.uk/White-Foamex-S ... 8QZ5N&th=1


BEAM COMPASS WITH A RADIUS THAT IS LARGER THAN 500MM:

https://www.londongraphics.co.uk/ecobra ... te-compass

Pi Tape Easy read: http://www.pitape.co.uk/products.asp#Easy_Read

Pi tape standard: http://www.pitape.co.uk/products.asp

Pi tape pricing: http://www.pitape.co.uk/pdf/PiTapeEuroPriceList.pdf


SOFT 5 METER PLUS ENGINEERING TAPE 1:

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5 PLUS METER HARD ENGINEERING TAPES:

ELECTRONIC 5-METER HARD ENGINEERING TAPE 1:

https://www.amazon.co.uk/Tacklife-Screw ... e+Measures

ELECTRONIC 5-METER HARD ENGINEERING TAPE 2:

https://www.amazon.co.uk/dp/B07GNL7KKB/ ... B07GS423BG

VARIOUS 5-METER HARD TAPE MEASURES WITH METAL BLADES:

https://www.thetapestore.co.uk/tapes-ru ... e-measures
Liddz
Dabbler
Dabbler
Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

Traditional Pi = 3.141592653589793 is false and is the result of the perimeter of a regular polygon with more than a trillion edges divided by the diagonal of the polygon that has a perimeter with more than a trillion edges.

Perimeter of the regular polygon = 1000,000,000,000,000,000,000,000,000,000,000,000,000,000.
That is 1 Plus 42 zeros.


Commas removed = 1000000000000000000000000000000000000000000.
Diagonal of a regular polygon with 1000,000,000,000,000,000,000,000,000,000,000,000,000,000 edges = the ratio 3.183098861837902e + 82.
1000,000,000,000,000,000,000,000,000,000,000,000,000,000
divided by 3.183098861837902e + 82 =
3.14159265358979769496178102.


Traditional pi with 24 decimal places = 3.141,592,653,5897,976,949,617,8102
Traditional pi with 15 decimal places = 3.141,592,653,589,793.

Regular Polygon calculator. Please remember to use a minimum of 15 digits to be accurate:
http://www.1728.org/polygon.htm

Regarding the chords and arcs of circles:

A chord is a straight line. The edge of a polygon is a chord.
An arc is a curve. The total arc length of a circle is the full curvature around the circle.

If an arc is attached to a chord in a circle then the length of the arc is longer than the length of the chord.

It is known that the curvature of a circle is longer than the chord length for the perimeter of a polygon that is contained inside of the circle and this knowledge makes it evident that the numerical value for the perimeter of a polygon is always the same as the numerical value for the division of the curvature of the circle that contains the polygon.

If the circumference of a circle is divided into 3 equal parts then the circumference of the circle will contain both 3 chords and 3 arcs and the length of 1 of the arcs will be longer than 1 of the 3 chords that make up the circumference of the circle.

If the circumference of a circle is divided into 8 equal parts then the circumference of the circle will contain both 8 chords and 8 arcs and the length of 1 of the arcs will be longer than 1 of the 8 chords that make up the circumference of the circle.

If the circumference of a circle is divided into 12 equal parts then the circumference of the circle will contain both 12 chords and 12 arcs and the length of 1 of the arcs will be longer than 1 of the 12 chords that make up the circumference of the circle.

The curvature of the circle when divided into equal divisions has the same numerical value as the perimeter of a polygon that is contained inside of the circle.

If a polygon is inscribed inside of a circle then the diagonal of the polygon and the diameter of the circle will have the same measure but the total curvature around the circle will be longer in measure than the perimeter of the polygon that is contained inside of the circle.

The correct definition for pi is the ratio for the circumference of a circle divided by the diameter of a circle.

Traditional pi = 4 divided by the square root of = 1.621138938277405 = 3.141592653589793 is false and does not come from the ratio for the circumference of a circle divided by the diameter of a circle.

The correct value for pi cannot be derived from dividing the perimeter of a polygon with a trillion edges by the diagonal of the polygon with a trillion edges.

The measure for the curvature of a circle divided by the diameter of the circle produces the correct value for pi = 4 divided by the square root of the golden ratio = 4/√φ = 3.144605511029693144.

To discover the value for the curvature of a circle divided by the diameter of a circle a circle with a 1 meter diameter should be created and the number of times the 1 meter –diameter can be multiplied around the curvature of the circle must be measured and recorded to confirm the correct value of pi.

The measure for the curvature of the circle with a 1-meter diameter must be divided by the 1-meter diameter to confirm the correct value for pi.

Measurements from multiplying a 1-meter diameter for a circle around the curvature of a circle has already been recorded and the
correct value for pi have been confirmed to be 3.1446 and not 3.141.

To get the rest of the digits for the true value of pi = 3.1446 a kepler right triangle can be used to create a square that has a perimeter that is equal in measure to the curvature of a circle.

If the second longest edge length for a Kepler right triangle is used as the diameter for a circle then the perimeter of the square that is located upon the shortest edge length for the Kepler right triangle can be confirmed to be the same measure as the curvature of the circle that has a diameter equal in measure to the second longest edge length for the Kepler right triangle.

When the perimeter of the square that is located on the shortest edge length for the Kepler right triangle is divided by the diameter of the circle that is equal in measure to the second longest edge length for the Kepler right triangle the correct value for pi = 4/√φ = 3.144605511029693144 is further proven and then the correct value for pi = 4/√φ = 3.144605511029693144 is multiplied by the diameter of the circle that is equal in measure to the second longest edge length for the Kepler right triangle the result is that the curvature of the circle is confirmed to be the same measure as perimeter of the square that is located on the shortest edge length for the Kepler.

The arc length of the circle is the same measure as the perimeter of the square because the square root of the golden ratio = 1.2720196495141 can allow the curvature of a circle to be placed on a straight line by using just compass and straight edge.

The Square root of the Golden ratio can be used to transfer the total curvature of a circle to a straight line. The Square root of the Golden ratio = 1.2720196495141 can turn curves into straight lines and straight lines back into curves.

The square root of the golden ratio = 1.2720196495141 can be used to transform curves into straight lines and straight lines into curves.

The claim that the perimeter of the square is the same measure as the arc length of the circle due to the measure of the arc length of the circle being derived with the use of the square root of the golden ratio = 1.272019649514069 can be confirmed if a circle with a 1-meter diameter is created and the diameter of the circle is multiplied around the curvature of the circle confirming that the correct value for pi must be 3.1446.

The Kepler right triangle also confirms that ratio for a circle’s circumference divided by a circle’s diameter is 3.1446.


THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal polynomial:

x4 + 16x2 – 256 = 0.



More dissing of fake Pi:

If you do NOT know what Pi is due to the fact that you have NEVER divided the circumference of a circle by the diameter of a circle then you cannot honestly create boundary limit claims for Pi.

To discover Pi you must divide the measure for the circumference of a circle by the measure for the diameter of a circle or alternatively to discover Pi you must divide the area of a circle by the area of the square that is located on the radius of the circle.

You cannot inscribe circles inside of Polygons and circumscribe circles around Polygons to achieve the circumference of a circle because there is forever a gap between the edges of the polygon that is contained inside of the circle and the curvature of the circle.

The area under the curvature of the circle NEVER disappears regardless of the amount of polygons that are constructed inside of the circle and also around the circle.

It is impossible for a polygon to become a circle because polygons have angles while circles do NOT have any angles.

There is NO such thing as a polygon with an infinite amount of edges. It is impossible for a Polygon with an infinite amount of edges to exist because a Polygon is known and identified by the number of edges that a Polygon has for example a Decagon is known for having 10 edges of equal measure.

Infinity cannot be fully counted.

Anything that can be fully counted is NOT infinite.





The True Value of Pi revealed = 4/√φ = 3.144605511029693144:

https://www.youtube.com/watch?v=AHAOn7UfXt8

The Pi that is equal to 3.141592653589793 that you are using is wrong - ULTIMATE PROOF part 1:

https://www.youtube.com/watch?v=UFh2Imm6Lrk

The Pi that is equal to 3.141592653589793 that you are using is wrong - ULTIMATE PROOF part 2:

https://www.youtube.com/watch?v=PtCyUUBomtM

Proof of Pi = 3.14466 in EQUILATERAL triangle:

https://www.youtube.com/watch?v=AEqzCMKY7lg

Pi: 3.1416 vs. 3.1446:

https://www.youtube.com/watch?v=K1HBn4PV4EE
Liddz
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Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

Proof that the shortest edge length of a Kepler right triangle is equal in measure to the circumference of a circle with a diameter that is equal in measure to 1 quarter of the second longest edge length of the Kepler right triangle:

The shortest edge length of the Kepler right triangle is 12.

If the hypotenuse of a Kepler right triangle is divided by the measure for the shortest edge length of the Kepler right triangle the result is the Golden ratio of cosine (36) multiplied by 2 = Phi = 1.618033988749895.

The shortest edge length of the Kepler right triangle is 12.

12 multiplied by the Golden ratio of cosine (36) multiplied by 2 = Phi = 1.618033988749895 = 19.41640786499874.

The hypotenuse of a Kepler right triangle that has its shortest edge length equal to 12 is equal to 12 times the Golden ratio = 19.41640786499874.

Apply the Pythagorean theorem to the hypotenuse of the Kepler right triangle and the shortest edge length of the Kepler right triangle to get the measure for the second longest edge length of the Kepler right triangle.

19.41640786499874 squared = 376.996894379984929.

12 squared = 144.

376.996894379984929 subtract 144 = 232.996894379984929.

The square root of 232.996894379984929 = 15.26423579416883.

The second longest edge length of the Kepler right triangle that has its shortest edge length equal to 12 is equal to 15.26423579416883.

15.264235794168832 divided by 4 = 3 times the square root of the Golden ratio 3.816058948542208 the diameter of the circle.

15.264235794168832 divided by the square root of the Golden ratio = 1.272019649514069 = 12.

The shortest edge length of the Kepler right triangle has been divided into 12 equal units of measure and is the same measure as the circumference of a circle with a diameter that is equal in measure to 1 quarter of the second longest edge length of the Kepler right triangle.

12 is the numerical value for both the circumference of the circle and the shortest edge length of the Kepler right triangle that has its hypotenuse equal to 12 times the Golden ratio = 19.41640786499874 while the second longest edge length of the Kepler right triangle is equal to 15.264235794168832.

Circumference of circle and the shortest edge length of the mentioned Kepler right triangle are both equal to 12.

1 quarter of the second longest edge length of the Kepler right triangle and the diameter of the circle are both equal to 3 times the square root of the Golden ratio = 3.816058948542208.

The Golden ratio = the square root of 5 divided by 2 = 1.618033988749895 or alternatively Cosine (36) multiplied by 2 = 1.618033988749895.

The square root of the Golden ratio = 1.272019649514069.

The square root of the Golden ratio = 1.272019649514069 multiplied by 3 = the ratio 3.816058948542207.
The ratio 3.816058948542207 is 3 times the square root of the Golden ratio and also 1 quarter of the second longest edge length of a Kepler right triangle that has its shortest edge length divided into 12 equal units of measure.


12 divided by 3.816058948542208 = Pi = 3.144605511029692.

Remember to multiply the shortest edge length of the Kepler right triangle that is 12 by Cosine (36) multiplied by 2 = The Golden ratio = Phi = 1.618033988749895 to get the measure for the hypotenuse of the Kepler right triangle = the ratio 19.41640786499874 then apply the Pythagorean theorem to the shortest edge length of the Kepler right triangle and the hypotenuse of the Kepler right triangle to get the measure for the second longest edge length of the Kepler right triangle.

The diameter of the circle is equal to 1 quarter of the second longest edge length of the Kepler right triangle.

The shortest edge length of the Kepler right triangle is equal in measure to the circumference of the circle that has a diameter that is equal in measure to 1 quarter of the second longest edge length of the Kepler right triangle.

Divide the measure of the shortest edge length of the Kepler right triangle by the measure for 1 quarter of the second longest edge length of the Kepler right triangle to get Pi = 3.144605511029.


Pi can also be calculated from the diagram of a circle contained inside of a square if the width of the square is the same measure as the diameter of the circle because if the perimeter of a square is divided by the square root of the Golden ratio = 1.272019649514069 then the result is the measure for the circumference of a the circle that has a diameter that is the same measure as the width of the square.

Example:

The width of the square = 3 times the square root of the Golden ratio = 3.816058948542208.

Diameter of the circle that is contained inside of the square = 3 times the square root of the Golden ratio = 3.816058948542208.

3 times the square root of the Golden ratio = 3.816058948542208 multiplied by 4 = the ratio 15.264235794168832.

Perimeter of square that contains the circle that has a diameter that is the same measure as the width of the square = the ratio 15.264235794168832.

12 times the square root of the Golden ratio = the ratio 15.264235794168832 divided by the square root of the Golden ratio = 1.272019649514069 = 12.

12 is the measure for the circumference of the circle that has a diameter that is the same measure as the width of the square.

12 divided by 3 times the square root of the Golden ratio = 3.816058948542208 = Pi = 3.144605511029693144.

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINKS,

Example of proof 1:

https://drive.google.com/file/d/1eS-HGA ... sp=sharing

Example of proof 2:


https://drive.google.com/file/d/10RjD1J ... sp=sharing

Example of proof 3:

https://drive.google.com/file/d/1bxiXiJ ... sp=sharing

Geometric diagram scan:

https://drive.google.com/file/d/1XeYiSO ... sp=sharing
Liddz
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Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

Pi can also be calculated from a square and a circle with the same surface area because if the edge of a square is multiplied by √√φ = 1.127838485561682 then the result is the diameter of a circle with the same surface area as the square and if the perimeter of a square is divided by √√φ = 1.127838485561682 the result is the circumference of a circle with the same surface area as the square. Circumference of circle divided by diameter of circle = π = 3.144605511029693144.

Also you do NOT need Pi to create a circle and a square with the same surface area instead you MUST use √√φ = 1.127838485561682: http://www.wolframalpha.com/input/?i=&# ... 8730;φ


The creation of a circle and a square with the same surface area can also be used to find Pi:

If only the surface area for a circle is known and the desire is to know both the measure of the circumference and the diameter of the circle a solution for finding the measure for the diameter of the circle is to multiply the square root for the surface area by the ratio 1.127838485561682. To find the measure for the circumference of a circle when only the surface area of a circle is known a solution is to multiply the square root of the circle's surface area by 4 then divide the result of multiplying the square root of the circle's surface area by 4 by the ratio 1.127838485561682.Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

If only the surface area for a circle is known and the desire is to know both the measure of the circumference and the diameter of the circle a solution for finding the measure for the diameter of the circle and the circumference of the circle is to divide the square root for the surface area of the circle by the ratio 1.127838485561682 resulting in quarter of the circle’s circumference. If 1 quarter of a circle’s circumference is multiplied by the square root of the Golden ratio = 1.272019649514069 the result is the diameter for the circle. Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.


For example.

The edge of square is equal to 3.383515456685047.

3.383515456685047 divided by 3 = √√φ = 1.127838485561682.


3.383515456685047 multiplied by √√φ = 1.127838485561682 =

3.816058948542207 the diameter of a circle with the same surface area as the square with a width equal to 3.383515456685047.

3.383515456685047 multiplied by 4 = 13.534061826740188 the perimeter of the square.

13.534061826740188 divided by √√φ = 1.127838485561682 = 12 the circumference of a circle with the same surface area as the square with a width equal to 3.383515456685047.

12 divided by 3.816058948542207 = Pi = 3.144605511029693.


Quadrature of the circle constants again:

The Golden ratio Phi = Cosine (36) multiplied by 2 = 1.618033988749895.

The square root of Phi = 1.272019649514069.

1.272019649514069 squared = 1.618033988749895.

The square root of the square root of Phi = 1.127838485561682.

1.127838485561682 squared = 1.272019649514069.

The true value of Pi = 4 divided by 1.272019649514069 = 3.144605511029693144.

The square root of Pi = 2 divided by 1.127838485561682 = 1.773303558624324.

2 divided by the square root of Golden Pi = 1.773303558624324 = 1.127838485561682.

Please remember that the ratio 1.127838485561682 is the square root of the ratio
1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

1.773303558624324 squared = 3.144605511029693144.



The ratio for the diameter of a circle divided by 1 quarter of the circle's circumference is the square root of the Golden ratio = 1.272019649514069 because if a circle with a 1-meter diameter is created and the diameter of the circle is multiplied around the curvature of the circle confirming that the correct value for Pi MUST be 3.1446. The Kepler right triangle also confirms that ratio for a circle’s circumference divided by a circle’s diameter is 3.1446.

The perimeter of the square that has the same surface area as the circle is also the second longest edge length of a Kepler right triangle and also the longer edge length for a square root of the Golden ratio = 1.272019649514069 rectangle.The mean proportional of the square root of the Golden ratio = 1.272019649514069 rectangle is the same measure as the curvature of the circle, the arc length of the circle, the circumference of the circle.


The real value of Pi = 4/√φ = 3.144605511029693144 can be confirmed by always remembering the ratio of the diameter of a circle divided by 1 quarter of the circle's circumference = the square root of the Golden ratio Phi = 1.272019649514069.

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINKS,

Geometric description:

https://drive.google.com/file/d/1K49xDD ... sp=sharing

Geometric diagram:

https://drive.google.com/file/d/1C-UEOM ... sp=sharing


The true value of Pi = 3.144605511029 is NOT Transcendental:

Pi = 4/√φ = 4 divided by 1.2720196495141 = 3.144605511029.
π = 4/√φ = 3.144605511029693144.


THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal Polynomial:

x4 + 16x2 – 256 = 0.

https://www.tiger-algebra.com/drill/x~4-16x~2-256=0/

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144:

Please copy and paste the following link into your web browser if you cannot click onto the following link:

https://www.wolframalpha.com/input/?i=4 ... lden+ratio

PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144.

Minimal polynomial:

x4 + 16x2 – 256 = 0

https://www.wolframalpha.com/input/?i=x ... +256+%3D+0

3D plot of a graph proving that the real value of Pi is NOT transcendental:

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINK

https://drive.google.com/file/d/1nT0xGI ... sp=sharing

• Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html

• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html
Liddz
Dabbler
Dabbler
Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

To get the correct measure for a circle’s diameter and to prove that Golden Pi = 4/√φ = 3.144605511029693144 is the true value of Pi by applying the Pythagorean theorem to all the edges of a Kepler right triangle when using the second longest edge length of a Kepler right triangle as the diameter of a circle then the shortest edge length of a Kepler right triangle is equal in measure to 1 quarter of a circle’s circumference. Also if the radius of a circle is used as the second longest edge length of a Kepler right triangle then the shortest edge length of a Kepler right triangle is equal to one 8th of a circle’s circumference:


Example 1:

The circumference of the circle is 12 but the measure for the diameter of the circle is not yet known. To discover the measure for the diameter of the circle apply the Pythagorean theorem to both 1 quarter of the circle’s circumference and also the result of multiplying 1 quarter of the circle’s circumference by the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

Divide the diameter of the circle by the square root of the Golden ratio = 1.272019649514069 to confirm that the edge of the square that has a perimeter that is equal to the numerical value for the circumference of the circle is equal to 1 quarter of the circle’s circumference.

Multiply the edge of the square by 4 to also confirm that the perimeter of the square has the same numerical value as the circumference of the circle.

Divide the measure for the circumference of the circle by the measure for the diameter of the circle to discover the true value of Pi.

Multiply Pi by the diameter of the circle to also confirm that the circumference of the circle has the same numerical value as the perimeter of the square.


The second longest edge length of a Kepler right triangle is used as the diameter of a circle in this example. 12 divided by 4 is 3 so the shortest edge length of the Kepler right triangle is 3 and is equal in measure to 1 quarter of the curvature of the circle’s circumference.

The hypotenuse of a Kepler right triangle divided by the shortest edge length of a Kepler right triangle produces the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.


According to the Pythagorean theorem the hypotenuse of any right triangle contains the sum of both the squares on the 2 other edges of the right triangle.

The shortest edge length of the Kepler right triangle is equal to quarter of the circumference of the circle that has its diameter used as the second longest edge length for the Kepler right triangle. The ratio gained from dividing the hypotenuse of a Kepler right triangle by the measure for the shortest edge of the Kepler right triangle is the Golden ratio of Cosine (36) multiplied by 2 = 1.61803398874989. The measure for the hypotenuse of a Kepler right triangle that has its shortest edge length divided into 3 equal units of measure is 3 times the Golden ratio = 4.854101966249685.


3 times the Golden ratio = 4.854101966249685.

4.854101966249685 divided by 3 is the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

The square root of the Golden ratio = 1.272019649514069

4.854101966249685 squared is 23.562305898749058.

3 squared is 9.

23.562305898749058 subtract 9 = 14.562305898749058

The square root of 14.562305898749058 is 3.816058948542208.

Remember that the second longest edge length of the Kepler right triangle is used as the diameter of a circle.

The measure for both the second longest edge length of this Kepler right triangle and the diameter of the circle is 3.816058948542208.

3 times the square root of the Golden ratio = 3.816058948542208.


Remember that the shortest edge length of this Kepler right triangle is 3 and is equal to 1 quarter of a circle’s circumference that has a measure of 12 equal units.

Circumference of circle is 12

Diameter of circle is 3.816058948542208.

Diameter of circle is 3.816058948542208 divided by the square root of the Golden ratio = 1.272019649514069 = 3 the edge of the square.

3 multiplied by 4 = 12.

The perimeter of the square = 12 and is the same measure as the circumference of the circle because the square root of the Golden ratio = 1.272019649514069 can be used to transfer the total arc length of a circle to a straight line. The arc length of the circle is the curvature of the circle.




The perimeter of the square = 12 divided by 3 times the square root of the Golden ratio = 3.816058948542208 = Golden Pi = 3.144605511029693144.

12 divided by 3 times the square root of the golden ratio = Pi = 3.144605511029693144.

4/√φ = Pi = 3.144605511029693144 multiplied by the diameter of the circle = 3.816058948542208 = 12.

The circumference of the circle has the same numerical value as the perimeter of the square.

4/√φ = 3.144605511029693144 is the true value of Pi.

The claim that the perimeter of the square is the same measure as the arc length of the circle due to the measure of the arc length of the circle being derived with the use of the square root of the Golden ratio = 1.272019649514069 can be confirmed if a circle with a 1-meter diameter is created and the diameter of the circle is multiplied around the curvature of the circle confirming that the correct value for Pi MUST be 3.1446. The Kepler right triangle also confirms that ratio for a circle’s circumference divided by a circle’s diameter is 3.1446.


(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINKS,

Squared Scan of 2 Kepler right triangle Golden Pi proof (main proof):

https://drive.google.com/file/d/1zK4WWK ... sp=sharing


Scan of 2 Kepler right triangle Golden Pi proof (Main diagram)

https://drive.google.com/file/d/1zjAUOo ... sp=sharing


Kepler right triangle diagram with squares upon the edges of the Kepler right triangle:

https://drive.google.com/file/d/1iBtXYy ... sp=sharing

Kepler right triangle construction method:

https://drive.google.com/file/d/15DNXB_ ... sp=sharing

PYTHAGOREAN THEOREM:

https://en.wikipedia.org/wiki/Pythagorean_theorem

Golden ratio: https://en.wikipedia.org/wiki/Golden_ratio

THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal Polynomial:

x4 + 16x2 – 256 = 0.

https://www.tiger-algebra.com/drill/x~4-16x~2-256=0/

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144:

Please copy and paste the following link into your web browser if you cannot click onto the following link:

https://www.wolframalpha.com/input/?i=4 ... lden+ratio

PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144.

Minimal polynomial:

x4 + 16x2 – 256 = 0

https://www.wolframalpha.com/input/?i=x ... +256+%3D+0

3D plot of a graph proving that the real value of Pi is NOT transcendental:

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINK

https://drive.google.com/file/d/1nT0xGI ... sp=sharing

• Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html

• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html
Liddz
Dabbler
Dabbler
Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

Some of the properties of the Kepler right triangle:

The measuring angles for the hypotenuse of a Kepler right scalene triangle are 51.82729237298776 degrees and 38.17270762701224 degrees in Trigonometry.

51.82729237298776 degrees is gained when the ratio 1.272019649514069 is applied to the inverse of the Tangent function in Trigonometry.

38.17270762701226 degrees is gained when the ratio 0.786151377757423 is applied to the inverse of the Tangent function in Trigonometry.

If the hypotenuse of a Kepler scalene right triangle is divided by the shortest edge length of the Kepler scalene right triangle then the resulting ratio is the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

1.27201964951406 is the ratio gained from dividing the second longest length of a Kepler scalene right triangle by the shortest edge length of the Kepler right scalene triangle.

1.27201964951406 is also the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

The Kepler right triangle is the solution to:

1. Discovering the correct value for Pi = 4/√φ = 3.144605511029693144.

2. Creating a circle and a square with the same surface area by using just compass and straight edge.

3. Creating a circle and a square with equal perimeters by using just compass and straight edge.


4. Creating an Equilateral triangle and a circle with equal perimeters by using just compass and straight edge.


5. Creating an Equilateral triangle and a circle with he same surface area by using just compass and straight edge.


6. Creating a Pentagon and a circle with equal perimeters by using just compass and straight edge.


7. Creating a Pentagon and a circle with the same surface area by using just compass and straight edge.


8. Creating a Cube and a sphere with the same surface area by using just compass and straight edge.


9. Creating a Cube and sphere with the same volume.

10.Creating a Phi Pyramid and a sphere with the same surface area by using just compass and straight edge.


11.Creating a Phi Pyramid and a sphere with the same volume.

12. Creating a Locun ratio Pyramid and a sphere with the same surface area by using just compass and straight edge.


13. Creating a Locun ratio Pyramid and a sphere with the same volume.

More information about the Kepler right triangle revealed:

The measuring angles for the hypotenuse of a Kepler right scalene triangle are 51.82729237298776 degrees and 38.17270762701224 degrees in Trigonometry.

51.82729237298776 degrees is gained when the ratio 1.272019649514069 is applied to the inverse of the Tangent function in Trigonometry.

38.17270762701226 degrees is gained when the ratio 0.786151377757423 is applied to the inverse of the Tangent function in Trigonometry.

A Kepler right scalene right triangle can allow a circle with a circumference equal to the perimeter of a square to be created. If a circle and a square are created with equal perimeters of measure than half the perimeter of the square divided by the radius of the circle is Pi and if either the perimeter of the square or the circumference of the circle is divided by the diameter of the circle then the resulting ratio is Pi.

Also if a circle and a square are created with equal perimeters of measure and the width of the square is divided by the radius of the circle then the resulting ratio is half of Pi 1.572302755514847. The ratio 1.572302755514847 half of Pi can be gained from 2 divided by the square root of 1.618033988749895 (1.27201964951406).

If the hypotenuse of a Kepler scalene right triangle is divided by the shortest edge length of the Kepler scalene right triangle then the resulting ratio is the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.
1.27201964951406 is the ratio gained from dividing the second longest length of a Kepler scalene right triangle by the shortest edge length of the Kepler right scalene triangle. 1.27201964951406 is also the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.
Please remember that if the second longest edge length of a Kepler right triangle is divided by 1 quarter of the shortest edge of a Kepler right triangle the result is the ratio 4 times the square root of the Golden ratio = 5.088078598056276.

The square root of the Golden ratio = 1.272019649514069. 1.272019649514069 multiplied by 4 = 5.088078598056276.

Please remember that if the hypotenuse a Kepler right triangle is divided by 1 quarter of the second longest edge length of a Kepler right triangle the result is the ratio 4 times the square root of the Golden ratio = 5.088078598056276.

The square root of the Golden ratio = 1.272019649514069. 1.272019649514069 multiplied by 4 = 5.088078598056276.

If a circle and a square are created and the perimeter of the square is the same measure as the circumference of the circle and the circle’s circumference is divided by the circumference of another circle that has a diameter that is the same measure as the width of the square then the result is the square root of the Golden ratio = 1.27201964951406.

If a circle and a square are created with the same surface area and the circumference of the circle is divided by the circumference of another circle that has the same measure as the width of the square then the result is the square root of the square root of the Golden ratio = 1.127838485561682. Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

If the shortest edge length an Illumien right triangle is reduced to 1 then the second longest edge length of the Illumien right triangle is equal to the square root of the square root of the Golden ratio = 1.127838485561682. If the shortest edge length an Illumien right triangle is reduced to 1 then the hypotenuse of the Illumien right triangle is equal to the Locun ratio = the square root of 2.272019649514069 = 1.507322012548768.

If the second longest edge length of an Illumien right triangle is divided by 1 quarter of the shortest edge length of an Illumien right triangle the result is the ratio = 4.511353942246728. The ratio 4.511353942246728 is 4 times the square root of the square root of the Golden ratio = 1.127838485561682.

The ratio 1.127838485561682 multiplied by 4 = 4.511353942246728.

A circle with a radius equal to 4.511353942246729 equal units of measure has a surface area of 64 equal units of measure according to Golden Pi = 4 divided by the square root of Phi = 3.144605511029693. 8 squared = 64.

Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.


Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html


• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html



The square root of Phi = 1.272019649514069:

(-1 - x^2 + x^4) http://www.wolframalpha.com/input/?i=%E2%88%9A%CF%86

The square root of the square root of Phi = 1.127838485561682.

(-1 - x^4 + x^8) http://www.wolframalpha.com/input/?i=&# ... 8730;φ


PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144.

https://www.wolframalpha.com/input/?i=4 ... lden+ratio

Minimal polynomial: x4 + 16x2 – 256 = 0

https://www.wolframalpha.com/input/?i=x ... +256+%3D+0

The knowledge of the square root of the Golden ratio being applicable to the diameter of a circle divided by 1 quarter of the circle's circumference can easily be verified if 2 right angles are created and the vertical right angle is used for the diameter of the circle while the horizontal right angle has 1 quarter of the circle's circumference placed on to it resulting in a Kepler right triangle with the diameter of the circle being the second longest edge length of the Kepler right triangle while the shortest edge length for the Kepler right triangle is equal in measure to 1 quarter of the circle's circumference.


The fact that the result of creating 2 perfect right angles with the vertical right angle being used as the diameter of the circle while the horizontal right angle is used as 1 quarter of the circle's circumference results in a Kepler right triangle is 100% proof that the real value of Pi = 4/√φ = 3.144605511029693144.

Apply the Pythagorean theorem to al the edges of the Kepler right triangle to get the exact measure for the diameter of the circle then divide the circumference of the circle by the diameter of the circle to get Pi = 4/√φ = 3.144605511029693144.

The Kepler right triangle is also featured in the Great Pyramid of Giza and also the Earth and moon ratio according to Pi as 22 divided by 7 = 3.142857142857143.

Pythagorean theorem:

https://en.wikipedia.org/wiki/Pythagorean_theorem


There's something about phi - Chapter 12 - Pythagoras theorem and the golden ratio:

https://www.youtube.com/watch?v=2IemLpxJ5SI

Kepler right triangle: https://www.goldennumber.net/triangles/

Method for constructing a Kepler right triangle:

https://en.wikipedia.org/wiki/File:Kepl ... uction.svg

Drawing a Kepler Triangle (Great Pyramid):

https://www.youtube.com/watch?v=vutUKmWFJ0w

constructing the kepler right triangle:

https://www.youtube.com/watch?v=LFBW9CY9PkQ

GOLDEN GEOMETRY: Draw Phi, the Golden & Kepler's Triangles, and Fibonacci's Spiral (Sacred Geometry):

https://www.youtube.com/watch?v=TCaA5nToTlg

Kepler right triangle in the Great Pyramid of Giza:

https://houseoftruth.education/en/teach ... at-pyramid

How to Draw: Great Pyramid Triangle Using Phi and Sacred Geometry:

https://www.youtube.com/watch?v=YyxNqnIWomE


Pyramid and Squaring the circle:

http://www.dailymotion.com/video/xijbpv ... OG_HTML5=1

The square root for the square of the Golden ratio = sqrt[sqrt(phi)] √√φ = 1.127838485561682 is the key to creating a circle and a square with the same surface area:

http://www.wolframalpha.com/input/?i=&# ... 8730;φ
Liddz
Dabbler
Dabbler
Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

Explaining the causes of the Quadrature of the circle part 1:

First regarding the creation of a circle and a square with equal perimeters meaning the circumference of the circle is equal in measure to the perimeter of the square, the width of the square must be equal to 1 quarter of the circle’s circumference resulting in the perimeter of the square being the same measure as the circumference of the circle. For example if the circumference of the circle is 8 then the edge of the square with a perimeter that is equal to a circle with a circumference of 8 must be 2.

Also if the square and circle share the same center and the circumference of the circle is equal to the perimeter of the square then the radius of the circle must be the longer measure of a 1.272019649514069 ratio rectangle while half the central width of the square must be the shorter measure of a 1.272019649514069 ratio rectangle.

If a circle and square are created with the perimeter of the square being the same measure as the circumference of the circle and the circle and square do NOT share the same center then the diameter of the circle CAN be the longer measure of a 1.272019649514069 ratio rectangle while the edge of the square CAN be the shorter measure of a 1.272019649514069 ratio rectangle but this is NOT compulsory.

In another example the edge of the square is the longer measure of a 1.272019649514069 ratio rectangle while the shorter measure of the 1.272019649514069 ratio rectangle is equal in measure to 1 quarter of the real value of Pi = 3.144605511029693.

Second regarding the creation of a circle and a square with equal areas the radius of the circle must be the longer measure of a 1.127838485561682 ratio rectangle while half the central width of the square must the shorter measure of a 1.127838485561682 ratio rectangle if the circle and square share the same center. If the circle and square do NOT share the same center and the circle and square have the same surface area then the diameter of the circle CAN be the longer measure of 1.127838485561682 ratio rectangle while the edge of the square CAN be the shorter measure of a 1.12783848556 ratio rectangle but this is NOT compulsory.

The relationship between the circle and the square having the same perimeter or the same area is a result of 2 ratios that are related to the Golden ratio of cosine (36) multiplied by 2 = 1.618033988749895 being used and those 2 ratios again are:


• The square root of the Golden ratio also called the Golden root = 1.272019649514069.

The Golden root 1.272019649514069 is the result of either the diameter of a circle being divided by 1 quarter of a circle’s circumference or the radius of a circle being divided by one 8th of a circle’s circumference.

The square root of the Golden ratio = 1.272019649514069 also applies to the perimeter of a square divided by the circumference of a circle with a diameter equal to the width of the square. The square root of the Golden ratio = 1.272019649514069 also applies to the surface area of a square divided by the surface area of a circle with a diameter equal to the width of the square.

The square root of the Golden ratio = 1.272019649514069 also applies to the surface area of a square divided by the surface area of a circle with a circumference equal in measure to the perimeter of the square.
The second longest edge length of a Kepler right triangle divided by the shortest edge length of a Kepler right triangle is the square root of the Golden ratio also called the Golden root = 1.272019649514069. The hypotenuse of a Kepler right triangle divided by the second longest edge length of a Kepler right triangle is the square root of the Golden ratio = 1.272019649514069.

The square root of the Golden ratio = 1.272019649514069 can also be gained if the surface area of circle is multiplied by 16 and then the result of the surface area of a circle being multiplied by 16 is then divided by the circumference of the circle squared. If the measure for the diameter of a circle is multiplied by 4 and the result of multiplying the measure of a circle’s diameter by 4 is divided by the measure for the circumference of a circle the result is also the square root of the Golden ratio also called the Golden root = 1.272019649514069.

4 divided by Golden Pi = 3.144605511029693 = the square root of the Golden ratio = 1.272019649514069.The square root of the Golden ratio = 1.272019649514069 also applies to the calculation of the surface area of a circle when the surface area of a square with a width that is equal to 1 quarter of the circle’s circumference is multiplied by the square root of the Golden ratio = 1.272019649514069. If the surface area of a circle is multiplied by the square root of the Golden ratio = 1.272019649514069 the result is the square root for the diameter of the circle.



• The square root of the Golden root = 1.127838485561682.

The square root of the Golden root 1.127838485561682 can be gained if the diameter of a circle that has the same surface area as a square is divided by the width of the square that has the same surface area as the circle. The square root of the Golden root 1.127838485561682 can also be gained if the radius of a circle that has the same surface area as a square is divided by half the width of the square that has the same surface area as the circle.

The square root of the Golden root 1.127838485561682 can also be gained if a circle and a square with the same surface area are created and the perimeter of the square is divided by the circumference of the circle. The second longest edge length of a Illumien right triangle divided by the shortest edge length of a Illumien right triangle is the ratio The square root of the Golden root = 1.127838485561682.


If a circle and a square are created with equal areas of measure and the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 quarter of the circle’s circumference that has the same surface area as the square and if 1 quarter of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the diameter of the circle.

If the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the diameter of the circle with the same surface area as the square.

If a circle and a square are created with equal areas of measure and half the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 eighth of the circle’s circumference that has the same surface area as the square and if 1 eighth of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the radius of the circle.

If half the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the radius of the circle with the same surface area as the square.

If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the radius or the diameter of a circle that has the same surface area to the already existing square that already has a circle with a circumference that is equal to the perimeter of the square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for the radius or diameter of the circle that has the same surface area to the already existing square that has a perimeter that is equal in measure to the circumference of the already existing circle.

Alternatively If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the edge of a square that has the same surface area as the already existing circle that has a circumference equal in measure to the perimeter of the already existing square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the already existing square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for half the edge of the square or the edge of the square that has the same surface area as the already existing circle that has a circumference that is equal in measure to the perimeter of the already existing square.


Explaining the causes of the Quadrature of the circle part 2:


If the diameter of a sphere is divided by the ratio √√φ = 1.127838485561682 the result is the slant height of a Phi Pyramid with a total surface area that is equal to the surface area of the sphere.

The Phi Pyramid produces the square root of the Golden ratio = 1.272019649514069 when the height of the Phi Pyramid is divided by half the width of the square base of the Phi Pyramid.

The Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 is the result when the slant height of the Phi Pyramid is divided by half the width of the square base of the Phi Pyramid.

Alternatively if the slant height of a Phi pyramid is multiplied by the ratio √√φ = 1.127838485561682 the result is the diameter of a sphere with the same surface area as the total surface area of the Phi Pyramid that produces the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 when the slant height of the Phi Pyramid is divided by half the width of the square base of the Phi Pyramid.

The Phi Pyramid produces the square root of the Golden ratio = 1.272019649514069 when the height of the Pyramid is divided by half the width of the square base of the Phi Pyramid.

The ratio of the diameter of a sphere divided by the height of a Phi Pyramid that has the same total surface area as the sphere = the ratio √√φ = 1.127838485561682 ^ 3 = 1.434632715112648.


√√φ = 1.127838485561682 cubed = 1.434632715112648.

The Phi Pyramid produces the square root of the Golden ratio = 1.272019649514069 when the height of the Phi Pyramid is divided by half the width of the square base of the Phi Pyramid. The Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 is the result when the slant height of the Phi Pyramid is divided by half the width of the square base of the Phi Pyramid.

√√φ = 1.127838485561682.

√24/3/√√ φ = 1.447896292563731.


√24 divided by 3 divided by √√ φ = 1.447896292563731.

√24 = 4.898979485566356 divided by 3 = 1.632993161855452 divided √√φ = the square root of the square root of Phi = 1.127838485561682 = 1.447896292563731.

If a Cube and a sphere are both created with the same surface area then the ratio for the edge of the Cube divided by the radius of the sphere is 1.447896292563731.

2 divided by the square root of Golden Pi = 1.773303558624324 = 1.127838485561682.


Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.


The square root of Phi = 1.272019649514069:

(-1 - x^2 + x^4) http://www.wolframalpha.com/input/?i=%E2%88%9A%CF%86

The square root of the square root of Phi = 1.127838485561682.

(-1 - x^4 + x^8) http://www.wolframalpha.com/input/?i=&# ... 8730;φ
Liddz
Dabbler
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Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

The true value of Pi hidden inside of the Kepler right triangle and the mystical squaring of the circle version 2:

Please use the diagram of the squaring of the circle that has a circumference that is equal in measure to the perimeter of a square by applying the Pythagorean theorem to all the edges of the Kepler right triangle.

Notice that if the shortest edge length of a Kepler right triangle is reduced to 1 then the hypotenuse of the Kepler right triangle is the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895 and the second longest edge length of the Kepler right triangle is equal to the square root of the Golden ratio = 1.272019649514069.

Apply the Pythagorean theorem to all the edges of the Kepler right triangle to confirm that if the hypotenuse of a Kepler right triangle is divided by the shortest edge length of the Kepler right triangle the result is the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

Apply the Pythagorean theorem to the Kepler right triangle to also confirm that if the second longest edge length of the Kepler right triangle is divided by the shortest edge length of the Kepler right triangle the result is the square root of the Golden ratio = 1.272019649514069.

Apply the Pythagorean theorem to the Kepler right triangle to also confirm that if the hypotenuse the Kepler right triangle is divided by the second longest edge length of the Kepler right triangle the result is also the square root of the Golden ratio = 1.272019649514069.

Take a look at the diagram of the squared circle with the circumference of the circle being the same as the perimeter of the square and the circle the square share the same center.
The perimeter of the square is the same measure as the arc length of the circle, the circumference of the circle.

The claim that the perimeter of the square is the same measure as the arc length of the circle due to the measure of the arc length of the circle being derived with the use of the square root of the Golden ratio = 1.272019649514069 can be confirmed if a circle with a 1-meter diameter is created and the diameter of the circle is multiplied around the curvature of the circle confirming that the correct value for Pi MUST be 3.1446. The Kepler right triangle also confirms that ratio for a circle’s circumference divided by a circle’s diameter is 3.1446.

An Octagon is a regular 8-sided polygon.

The arc length of a circle is longer than the chord length of a circle but both the total arc length of a circle and the total chord length of a circle always have the same numerical division for example if the total arc length of a circle is divided into 8 equal parts then the total chord length of the circle will also be divided into 8 equal parts. The arc length of a circle is longer than the chord length of a circle but both have the same numerical divisions and the same numerical value.

Please take a look at the diagram of the circle and the square with equal perimeters with the circle and the square sharing the same center. The second longest edge length of a Kepler right triangle is the radius of the circle. The shortest edge length of the Kepler right triangle is equal to 8th of the circle’s circumference while the hypotenuse of the Kepler right triangle is equal in measure to the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895. The second longest edge length of the Kepler right triangle is equal in measure to the square root of the Golden ratio = 1.272019649514069 and is used as the radius of the circle.

The center width of the square that has a perimeter that is equal in measure to the circumference of the circle is the base width of an isosceles triangle that is made from 2 Kepler right triangles. The shape of this isosceles triangle appears similar to the shape of the Great Pyramid of Giza because the 2 slope angles are both 51.82729237298774 degrees. ATAN (1.272019649514069) = 51.82729237298774 degrees.

Remember that the radius of the circle is the second longest edge length of a Kepler right triangle and is equal in measure to the square root of the Golden ratio = 1.272019649514069 and that means that the diameter of the circle that is the same measure as the perimeter of the square is 2 times the square root of the Golden ratio = 1.272019649514069.

The square root of the Golden ratio = 1.272019649514069 multiplied by 2 = 2.544039299028138.
Both the perimeter of the square and the circumference of the circle are 8 equal units of measure.

The perimeter of the square is the same measure as the circumference of the circle .The curvature of the circle is the same measure as the perimeter of the square.

The radius of the circle is the second longest edge length of a Kepler right triangle and is equal in measure to the square root of the Golden ratio = 1.272019649514069.

The diameter of the circle is equal in measure to 2 times the square root of the Golden ratio = 1.272019649514069 = 2.544039299028138.

To discover Pi the circumference of a circle MUST be divided by the measure for the diameter of the circle.

8 divided by 2 times the square root of the Golden ratio = 2.544039299028138 = 4/√φ = 3.144605511029693144.

THE TRUE VALUE OF PI = 3.144605511029693144.

FROM THE GEOMETRY OF THE SQUARED CIRCLE WE CAN DISCOVER THAT THE TRUE VALUE OF PI CAN BE REDUCED TO 4 DIVIDED BY THE SQUARE ROOT OF THE GOLDEN RATIO = 3.144605511029693144.

4 DIVIDED BY 1.272019649514069 = 3.144605511029693144.

4 DIVIDED BY THE SQUARE ROOT OF THE GOLDEN RATIO = 1.272019649514069 = 3.144605511029693144.

4/√φ = 3.144605511029693144.

THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal polynomial:

x4 + 16x2 – 256 = 0.
How to create a circle that has a circumference that is equal to the perimeter of a square by using compass and straight edge.

The construction of a circle that has a circumference that is equal to the perimeter of a square is a good method for discovering the true value of pi = 4/√φ = 3.144605511029693144 by applying the Pythagorean theorem to all the edges of the Kepler right triangle that is discovered when we square the circle with equal perimeters. Divide the perimeter of the square or the circumference of the circle by the diameter of the circle to discover the true value of Pi.

Method 1: Beginning with the circle:

The circle and the square share the same center in this example.

To create a circle and square with equal perimeters meaning that the perimeter of the square has the same measure as the curvature of the circle, the arc length of the circle, the circumference of the circle the radius of the circle MUST be used as second longest edge length for a Kepler right triangle. The shortest edge length of the Kepler right triangle is equal to half the width of the square.

The perimeter of the square is the same measure as the circumference of the circle due to the perimeter of the square being created with the use of the square root of the Golden ratio = 1.272019649514069 because the square root of the Golden ratio = 1.272019649514069 can be used to turn curves into straight lines and lines into curves. The square root of the Golden ratio allows the curvature of a circle to be placed on a straight line with just the use of compass and straight edge.

Method 2: Beginning with the circle:

The circle and the square do NOT share the same center in this example.

To create a circle and square with equal perimeters meaning that the perimeter of the square has the same measure as the curvature of the circle, the arc length of the circle, the circumference of the circle the diameter of the circle MUST be used as the second longest edge length of a Kepler right triangle while the shortest edge length of the Kepler right triangle is equal to 1 quarter of the circle’s circumference.

Method 3: Beginning with the square:

The circle and the square share the same center in this example.

Construct a square and the center width of the square is divided into 2 Golden ratio Cosine (36) multiplied by 2 = 1.618033988749895 rectangles.

The 2 center halves of the square are the shorter edges of the 2 Golden ratio Cosine (36) multiplied by 2 = 1.618033988749895 rectangles. Swing the furthest from the center of the square for the longer edges of any of the 2 Golden ratio rectangles that have their shorter edges as half the center width of the square towards the vertical center line that emanates from the center of the square.

The result of the construction of an isosceles triangle that has its base width as the same as the center width of the square and the height of the isosceles triangle is the radius of a circle that has a circumference that is equal to the perimeter of the square. The radius of the circle is the second longest edge length of 2 Kepler right triangles that have been joined together to create an isosceles triangle that has a shape that is similar to the Great Pyramid of Giza.

Method 4: Beginning with the square:

The circle and the square do NOT share the same center in this example.

Construct a Kepler right triangle and the perimeter of the square that is located on the shortest edge length of the Kepler right triangle has the same numerical value as the circumference of a circle with a diameter that is equal in measure to the second longest edge length of the Kepler right triangle. Because the perimeter of the square that is located on the shortest edge length of the Kepler right triangle has the same numerical value as the circumference of the circle we can divide the perimeter of the square that is located on the shortest edge length of the Kepler right triangle by the measure of the second longest edge length of the kepler right triangle to discover the true value of Pi = 4/√φ = 3.144605511029693144.
Liddz
Dabbler
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Posts: 20
Joined: Fri Dec 13, 2019 2:35 am
Location: United Kingdom

re: Circle the Square

Post by Liddz »

How to create a circle and a square with the same surface area by using compass and straight edge part 1.

A Kepler right triangle is half of a square root of the Golden ratio = 1.272019649514069 rectangle.
The mean proportional of a rectangle is the square root for the surface area of a rectangle.

The surface area of a rectangle can be calculated if the shorter edge of the rectangle is multiplied by the longer edge of the rectangle.

The mean proportional of a square root of the Golden ratio = 1.272019649514069 rectangle is the same measure as the diameter of a circle with the same surface area as the square that is located on the shorter edge of the square root of the Golden ratio = 1.272019649514069 rectangle.

The mean proportional of a rectangle that has its longer edge equal to the shortest edge length of a Kepler right triangle while the shorter edge of the rectangle is equal to 1 quarter of the second longest edge length of the Kepler right triangle is equal to the radius of a circle that has the same surface area as the square that us located on the shortest edge length of the Kepler right triangle.

The construction process of a circle and a square with the same surface area:

Construct a Kepler right triangle because the second longest edge length of a Kepler right triangle is the longer edge of a square root of the Golden ratio = 1.272019649514069 rectangle, while the shortest edge of the Kepler right triangle is the shorter edge of the square root of the Golden ratio = 1.272019649514069 rectangle and the hypotenuse of the Kepler right triangle is the diagonol of the square root of the Golden ratio = 1.272019649514069 rectangle.

A Kepler right triangle is half of a square root of the Golden ratio = 1.272019649514069 rectangle.

The mean proportional of a rectangle is the square root for the surface area of a rectangle.

The surface area of a rectangle can be calculated if the shorter edge of the rectangle is multiplied by the longer edge of the rectangle.

If an individual can construct a Kepler right triangle by using compass and straight edge then that individual can square the circle. We do NOT need to know anything about Pi to create a circle and a square with the same surface area. We must learn about the Golden ratio = Cosine (36) multiplied by 2 = 1.618033988749895 and the square root of the Golden ratio = 1.272019649514069 and also the square root of the square root of the Golden ratio = 1.127838485561682 if we want to create a circle and a square with the same surface area.

If a circle and a square are created with equal areas of measure and the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 quarter of the circle’s circumference that has the same surface area as the square and if 1 quarter of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the diameter of the circle .

If the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the diameter of the circle with the same surface area as the square.

If a circle and a square are created with equal areas of measure and half the width of the square of the square is divided by the ratio 1.127838485561682 the result is equal to 1 eighth of the circle’s circumference that has the same surface area as the square and if 1 eighth of the circle’s circumference is multiplied by the ratio 1.272019649514069 the result is the measure for the radius of the circle.

If half the width of the square is multiplied by the ratio 1.127838485561682 the result is the measure for the radius of the circle with the same surface area as the square.

If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the radius or the diameter of a circle that has the same surface area to the already existing square that already has a circle with a circumference that is equal to the perimeter of the square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for the radius or diameter of the circle that has the same surface area to the already existing square that has a perimeter that is equal in measure to the circumference of the already existing circle.

Alternatively If a circle and a square have been created with the circumference of the circle being equal in measure to the perimeter of the square and the desire is to gain the measure for the edge of a square that has the same surface area as the already existing circle that has a circumference equal in measure to the perimeter of the already existing square a solution is to divide the radius or the diameter of the circle that has a circumference equal to the perimeter of the already existing square by the square root of the square root of Phi = 1.127838485561682 resulting in the measure for half the edge of the square or the edge of the square that has the same surface area as the already existing circle that has a circumference that is equal in measure to the perimeter of the already existing square.

2 divided by the square root of Golden Pi = 1.773303558624324 = 1.127838485561682.

Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.


How to create a circle and a square with the same surface area by using compass and straight edge part 2.

Method 1: Beginning with the square:

The circle and the square share the same center in this example.

To create a circle and a square with the same surface area using compass and straight edge half the edge of the square can be the shortest edge length of a Kepler right triangle when the circle and the square share the same center. Use half the edge of the square that is also the shortest edge length of a Kepler right triangle plus the second longest edge length of the Kepler right triangle as the diameter of a semi-circle and the radius of the circle that has the same surface area as the square will originate from the center of the square and touch the circumference of the semi-circle that has a diameter that is made from the combined measures of both half the width of the square and the second longest edge length of the Kepler right triangle.

Please remember that the shortest edge length of the Kepler right triangle is also half the edge of the square that has the same surface area as the circle.

The circle and the square share the same center and that means that the second longest edge length of the Kepler right triangle will also emanate from both the center of the square and the center of the circle.

To confirm that the circle and the square have the same surface area use half the center width of the square plus 1 quarter of the second longest edge length of the Kepler right triangle that emanates from both the center of the circle and the center of the square as the diameter of a semi-circle that has a circumference that touches the center of the radius of the circle that has the same surface area s the square.

Method 2: Beginnig with the square:

The square and the circle do NOT share the same center in this example.

Construct a square and the edge of the square is also the shortest edge length of a Kepler right triangle. Use the second longest edge length of the Kepler right triangle plus the edge of the square that is on the same line as the second longest edge length of the Kepler right triangle as the diameter of a semi-circle. From the edge of the square that is also the shortest edge length of the Kepler right triangle a vertical line MUST emanate from the point that is between the edge of the square and the second longest edge length of a Kepler right triangle.

The vertical line that emanates from the point that is between the edge of the square and the second longest edge length of a Kepler right triangle MUST touch the circumference of the semi-circle that has a diameter that is made from the combined measures of the edge of the square plus the second longest edge length of the Kepler right triangle.

The vertical line that emanates from the point that is between the edge of the square and the second longest edge length of the Kepler right triangle is the diameter of the circle that has the same surface area as the square.

To confirm that the circle and the square have the same surface area use the edge of the square plus 1 quarter of the second longest edge length of the Kepler right triangle that has its shortest edge length as the edge of the square as the diameter of a semi-circle that has a circumference that touches the center of the circle that has the same surface area as the square.

Method 3: Beginning with the circle:

The circle and the square share the same center in this example.

Use the radius of the circle as the second longest edge length of a Kepler right triangle causing the shortest edge length of the Kepler right triangle to be equal in measure to 1 eighth of the circumference of the circle. Use the radius of the circle plus 1 eighth of the circumference of the circle as the diameter of a semi-circle to get half the edge of a square that has the same surface area as the circle. Half the edge of the square that has the same surface area as the circle emanates from the center of the circle and touches the circumference of the semi-circle that has a diameter that has been made from the combined measurements of the radius of the circle plus 1 eighth of the of the circumference of the circle.

Method 4: Beginning with the circle:

The circle and the square do NOT share the same center in this example:

Use the diameter of the circle as the second longest edge length of a Kepler right triangle while 1 quarter of the circle’s circumference is used as the shortest edge length of the Kepler right triangle.

Use the diameter of the circle plus 1 quarter of the circle’s circumference as the shortest edge length of the Kepler right triangle for the diameter of a semi-circle. From the pole of the vertical diameter of the circle that has the shortest edge length of the Kepler right triangle emanating from it a straight line must touch the circumference of the semi-circle that has been made from the combined measures of the diameter of the full circle and the shortest edge length of the Kepler right triangle.

The line that emanates from the pole of the vertical diameter of the full circle that also has the shortest edge length of a Kepler right triangle emanating from it is the edge of the square that has the same surface area as the full circle.


THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal polynomial:

x4 + 16x2 – 256 = 0.

Please click on the following links for visual proof:

Quadrature 36: https://www.geogebra.org/geometry/nxkv7vfk

Quadrature 144: https://www.geogebra.org/geometry/na4uya7z

Quadrature 64: https://www.geogebra.org/geometry/svs6thhw


11 methods for finding the surface area of a circle�:

Method 1 .The surface area of a circle can be known if the radius of a circle is squared and then multiplied by Golden Pi = 4/√φ = 3.144605511029693144.
.

Method 2. The surface area of a circle can also be known if half the circumference of the circle is multiplied by the measure for the diameter of the circle and then the result of multiplying half the measure for the circumference of the circle must be divided into 2 resulting in the measure for the surface area of the circle. An isosceles triangle that is made from 2 Kepler right triangles has the same surface area as a circle that has a diameter that is equal in measure to the height of the isosceles triangle that is made from 2 Kepler right triangles. If half the circumference of a circle is divided by the diameter of the circle the result is the half of the ratio Pi.

Method 3. The surface area of a circle can also be found if the radius of the circle is multiplied by half the circumference of the circle. If half the circumference of a circle is divided by the radius of a circle the result is the ratio Pi.

Method 4. The surface area of a circle can also be discovered if 1 quarter of the circle’s circumference is multiplied by the measure for the diameter of the circle.

Method 5. If the surface area of square that has a width equal in measure to 1 quarter of a circle’s circumference is multiplied by the square root of the Golden ratio = 1.272019649514069 the result is the surface area of the circle.

Method 6. If the diameter of a circle is divided by the ratio 1.127838485561682 the result is the edge of a square that has the same surface area as the circle. Please remember that the ratio 1.127838485561682 is the square root of the ratio 1.272019649514069 and the ratio 1.272019649514069 is the square root of the Golden ratio of Cosine (36) multiplied by 2 = 1.618033988749895.

Method 7. If the surface area of a square that has a width that is equal in measure to the diameter of a circle is divided by the square root of the Golden ratio = 1.272019649514069 the result is the surface area of the circle.

Method 8. If the surface area of a square that has a diagonal that is equal in measure to the diameter of a circle is multiplied by half of Golden Pi = 4/√φ = 3.144605511029693144 = 1.572302755514847 the result is the surface area of the circle.

Method 9. If the surface area of a square that has a diagonal that is equal in measure to the diameter of a circle is divided by half the square root of the Golden ratio = 0.636009824757035 the result is the surface area of the circle.

Method 10: Multiply the diameter of the circle by the ratio 1.347419325335723 to get the edge of an equilateral triangle that has the same surface area as the circle. Multiply the edge of the equilateral triangle by half the width of the equilateral triangle times the square root of 3 divided by 2 to get the surface area of the equilateral triangle and confirm that both the equilateral triangle and the circle have the same surface area.

The ratio 1.347419325335723 can be derived through the following formulas:

2/(√ (√3) X √√ φ = 1.347419325335723.

2/(√ (√3) multiplied by √√ φ = 1.347419325335723.

2/(√ (√3) multiplied by 1.127838485561682= 1.347419325335723.

2/(square root (square root 3) multiplied by square root square root Phi = 1.347419325335723.

2 (φ/3)^(1/4)/ √ φ = 1.347419325335723.

2 (1.618033988749895/3)^(1/4)/ 1.272019649514069 = 1.34741932533572.

2/(3 X Golden Ratio)^(1/4) = 1.347419325335723.

2/(3 times Golden Ratio)^(1/4) = 1.347419325335723.

2/(3 x Cos (36) x 2)^(1/4) = 1.347419325335723.

2/(3 x Sin (54) x 2)^(1/4) = 1.347419325335723.

2/(3 multiplied by φ)^(1/4) = 1.347419325335723.

2 divided by the Golden ratio multiplied by 3 ^(1/4) = 1.347419325335723.

3 times the Golden ratio = 4.854101966249685.

1/2 + √ (5)/2 = The Golden ratio = 1.618033988749895.

Method 11: Divide the diameter of the circle by the ratio = 1.479351567442321 to get the edge of a Pentagon that has the same surface area as the circle. Multiply the edge of the Pentagon by half the edge of the Pentagon times TAN (54) divided by 2 times 5 to calculate the surface area of the Pentagon and also confirm that both the Pentagon and the circle have the same surface area.

The ratio 1.479351567442321 can be derived through the following formulas:


√ (34 times 17 times TAN (54)/2 times 5) times √√φ/34 = 1.479351567442321.

√ (34 times 17 times TAN (54)/2 times 5) times 1.127838485561682/34 = 1.479351567442321.

(75/32 + (35 square root (5))/32)^(1/4)= 1.479351567442321.

1/2 (5/2 (15 + 7 square root (5)))^(1/4) = 1.479351567442321.

1/2 square root (5) (1/2 (1 + 2/square root (5)) (1 + square root (5)))^(1/4) = 1.479351567442321.


34 multiplied by 17 multiplied by TAN (54) divided by 2 multiplied by 5 = 1988.87187508084575.

34 X 17 X TAN (54)/2 X 5 = 1988.87187508084575.

Square root of 1988.87187508084575 multiplied by √√φ = the square root of the square root of Phi = 1.127838485561682 divided by 34 = 1.479351567442321.

√1988.87187508084575 multiplied by √√φ/34 = 1.479351567442321.

√1988.87187508084575 X √√φ/34 = 1.479351567442321.

THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal Polynomial:

x4 + 16x2 – 256 = 0.

https://www.tiger-algebra.com/drill/x~4-16x~2-256=0/

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144:

Please copy and paste the following link into your web browser if you cannot click onto the following link:

https://www.wolframalpha.com/input/?i=4 ... lden+ratio

PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144.

Minimal polynomial:

x4 + 16x2 – 256 = 0

https://www.wolframalpha.com/input/?i=x ... +256+%3D+0

3D plot of a graph proving that the real value of Pi is NOT transcendental:

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINK

https://drive.google.com/file/d/1nT0xGI ... sp=sharing

• Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html

• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html
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re: Circle the Square

Post by Liddz »

Folding circles a.k.a Carl D Thompson’s Geometric proofs for Golden Pi = 4 divided by the square root of the Golden ratio = 3.144605511029:

PI IS THE RATIO OF A CIRCLE'S CIRCUMFERENCE DIVIDED BY A CIRCLE'S DIAMETER.

TO DISCOVER PI YOU MUST DIVIDE THE CIRCUMFERENCE OF A CIRCLE BY THE DIAMETER OF A CIRCLE.

PI COMES FROM CIRCLES SO TO PROVE PI YOU MUST USE AN IMAGE OF A CIRCLE LIKE ALL THE OTHER MATHEMATICIANS THAT I HAVE LEARNED FROM.

THE FOLLOWING VIDEOS ARE FROM CARL THOMPSON A GEOMETRICIAN THAT ALSO HAS THE SAME VALUE OF PI AS ME 4 DIVIDED BY THE SQUARE ROOT OF THE GOLDEN RATIO = 3.144605511029:

Pi Versus Pi (A comparison):

https://www.youtube.com/watch?v=LrColR3yCOE

The Search For a Proof of Pi - Volume 1:

https://www.youtube.com/watch?v=f55GaZsR6JA

The Search For a Proof of Pi - Volume 2:

https://www.youtube.com/watch?v=M7dm7Ww8Vmg&t=1s

Pi = 3.144:

https://www.youtube.com/watch?v=asJ1xDh4UfU

The search for a mathematical proof of Pi:

http://www.proofpi.com/
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re: Circle the Square

Post by Liddz »

Squaring the circle description for a diagram of a circle that has the diameter of the circle divided into the golden ratio = 1.6180339887499.

Diameter of circle R has been divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887499 resulting in 2 Kepler right triangle being inscribed inside of circle R.

The larger part of the diameter of circle R has been divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887499 and is equal to 2.3584541332723 equal units of measure and is also the second longest edge length of the larger Kepler right triangle that has been inscribed inside of circle R.

The shorter part for the circle’s diameter that has been divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887499 is equal to 1.45760481527 equal units of measure and is also the same measure as M S the shorter measure for the edge of Golden rectangle E that has been divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887499.

2.3584541332723 equal units of measure is also equal to K M the longer measure for the longer edge of Golden rectangle E that has been divided into the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887499.

The hypotenuse of the smaller Kepler right triangle that has been inscribed inside of circle R is also equal to K M and DM and is also equal to 2.3584541332723 equal units of measure.

The second longest edge length of the smaller Kepler right triangle that has been inscribed inside of circle R is the same measure as the shortest edge length for the larger Kepler right triangle that has been inscribed inside of circle R.

The shorter edge length of Golden rectangle T is also equal to both the shortest edge length of the larger Kepler right triangle that has been inscribed of circle R and also the second longest edge of the smaller Kepler right triangle that has been inscribed inside of circle R.

The shortest edge length of the larger Kepler right triangle that has been inscribed inside of circle R is equal to 1.8541019662497 equal units of measure.

The second longest edge length of the smaller Kepler right triangle that has been inscribed inside of circle R is also equal to 1.8541019662497 equal units of measure.

The shorter edge for the Golden rectangle T is also equal to 1.8541019662497 equal units of measure.

The longer measure for Golden rectangle T is 3 and 3 is equal to 1 quarter of the circumference for circle R.

The edge of square A is 3 and is also equal to 1 quarter for the circumference of circle R.The width of square A is also the hypotenuse for the larger Kepler right triangle that has been inscribed inside of circle R . The hypotenuse for the larger Kepler right triangle that has been inscribed inside of circle R also is equal to 3.

Please apply the Pythagorean theorem to all the edges of the larger Kepler right triangle to confirm that the diameter of circle R is equal to 3.8160589485423 equal units of measure beginning with the hypotenuse of the larger Kepler right triangle that is 3 equal units of measure while the shortest edge length of the Kepler right triangle that has been inscribed inside of circle R is equal to 1.8541019662497 equal units of measure.

Remember that if the hypotenuse of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle then the result is the Golden ratio of Cosine (36) multiplied by 2 = 1.6180339887499.

Remember that if the second longest edge length of a Kepler right triangle is divided by the shortest edge length of a Kepler right triangle the result is the square root of the Golden ratio = 1.2720196495141.

The hypotenuse of the larger Kepler right triangle that has been inscribed inside of circle R is 3 equal units of measure.

The shortest edge length for the hypotenuse of the larger Kepler right triangle that has been inscribed inside of circle R is equal to 1.8541019662497 equal units of measure.


3 squared is 9

1.8541019662497 equal units of measure squared = 3.437694101251 equal units of measure.

9 subtract 3.437694101251 equal units of measure is equal to 5.562305898749 equal units of measure.

The square root of 5.562305898749 equal units of measure is equal to 2.3584541332723 equal units of measure .
2.3584541332723 equal units of measure divided by 1.8541019662497 equal units of measure = the square root of the Golden ratio = 1.2720196495141.

2.3584541332723 equal units of measure multiplied by the Golden ratio of cosine (36) multiplied by 2 = 1.6180339887499 is equal to 3.8160589485423.
Circumference of circle R is 12

Diameter of circle R is 3.8160589485423.

Diameter of circle is 3.8160589485423 divided by the square root of the Golden ratio = 1.2720196495141 = 3 the edge of the square. 3 multiplied by 4 = 12. The perimeter of the square = 12.


12 divided by 3.8160589485423 = Pi = 4/√φ = 3.1446055110296. 4/√φ = Pi = 3.1446055110296 multiplied by the diameter of the circle = 3.8160589485423 = 12.

The circumference of the circle has the same numerical value as the perimeter of the square.

4/√φ = 3.1446055110296 is the true value of Pi.

The true value of Pi = 3.144605511029 is NOT Transcendental:

Pi = 4/√φ = 4 divided by 1.2720196495141 = 3.144605511029.
π = 4/√φ = 3.144605511029693144.

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINKS,

Example of Proof:
https://drive.google.com/file/d/1aqbUEp ... sp=sharing


Geometric scan:

https://drive.google.com/file/d/1Sgj8E2 ... sp=sharing


THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal Polynomial:

x4 + 16x2 – 256 = 0.

https://www.tiger-algebra.com/drill/x~4-16x~2-256=0/

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144:

Please copy and paste the following link into your web browser if you cannot click onto the following link:

https://www.wolframalpha.com/input/?i=4 ... lden+ratio

PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144.

Minimal polynomial:

x4 + 16x2 – 256 = 0

https://www.wolframalpha.com/input/?i=x ... +256+%3D+0

3D plot of a graph proving that the real value of Pi is NOT transcendental:

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINK

https://drive.google.com/file/d/1nT0xGI ... sp=sharing

• Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html

• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html
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re: Circle the Square

Post by WaltzCee »

Sir, get a grip.

I'm certain you're noticing how nobody is responding to you. This is friggin discussion
board. If you want a discussion, you're going to have to be a little bit more concise. Stop
giving people reading assignments with all your links.

Concisely State your point. Get to the point. I personally know that there is a geometry that
resides between euclidean and non-euclidean. That was the basis of my batshit-crazy
wheel.

Kindly stop spamming this forum.
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All rights reserved. Do not even quote me w/o my expressed written consent.
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re: Circle the Square

Post by Liddz »

Too many people have been spreading lies about squaring the circle and Pi for more than 2000 years and I am here to set the record straight and the fact is that the circle can be squared and does require Pi to be involved.

The square root of the Golden ratio is the key to squaring any circle.


The problem is that the traditional Pi value of 3.141592653589793 that is programmed into most calculators is wrong and is not connected to circles but instead the traditional Pi value of 3.141592653589793 represents a polygon with more than a trillion edges divided by the diagonal of the polygon.

Traditional Pi value of 3.141592653589793 is false.

It is impossible for a polygon to become a circle and that means that Pi must be larger than 3.141592653589793 .

I am shocked to discover that for more than 2000 years most mathematicians have not tried to measure the amount of times the diameter of a circle fits into the curvature of a circle.

If the diameter of a circle is 1 then the circumference of the circle is Pi.

Pi means the ratio of a circle's circumference divided by a circle's diameter

If you create a circle with a 1 meter diameter and you measure the amount of times that the diameter of the circle fits around the curvature of the circle you will be shocked to discover that the correct value for Pi = 3.1446 and NOT 3.1415.

After you have measured a circle with tape and you discover with your own eye balls that Pi = 3.1446 and NOT 3.1415 you should then get a scientific calculator and divide 4 by 3.1446 and you will get an approximation for the square root of the golden ratio = 1.272.

Then square 1.27201 to get 1.618 and then it become clear that the real value of Pi = 4 DIVIDED BY THE SQUARE ROOT OF THE GOLDEN RATIO = 4/√φ = 3.144605511029693144.

THE TRUE VALUE OF PI = 4/√φ = 3.144605511029693144 HAS REMAINDED HIDDEN INSIDE OF THE KEPLER RIGHT TRIANGLE FOR MORE THAN 2000 YEARS WAITING FOR MATHEMATICANS TO DISCOVER IT.

ANOTHER LIE THAT HAS BEEN TOLD TO US ABOUT PI IS THAT PI IS TRANSCENDENTAL.

THE REAL VALUE OF Pi IS NOT TRANSCENDENTAL BECAUSE THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144 IS THE ONLY VALUE OF PI THAT CAN FIT THE FOLLOWING POLYNOMIAL EQUATION:

4th dimensional equation/polynomial for Golden Pi = 3.144605511029693

Minimal Polynomial:

x4 + 16x2 – 256 = 0.

https://www.tiger-algebra.com/drill/x~4-16x~2-256=0/

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144:

Please copy and paste the following link into your web browser if you cannot click onto the following link:

https://www.wolframalpha.com/input/?i=4 ... lden+ratio

PLEASE CLICK ON THE RED DOTS IN THE FOLLOWING LINK TO CONFIRM THAT THE REAL VALUE OF PI = 4/√φ = 3.1446 IS NOT TRANSCENDENTAL.

THE REAL VALUE OF PI = 4/√φ = 3.144605511029693144.

Minimal polynomial:

x4 + 16x2 – 256 = 0

https://www.wolframalpha.com/input/?i=x ... +256+%3D+0

3D plot of a graph proving that the real value of Pi is NOT transcendental:

(Please click on to the following links or copy and them into your web browser):

PLEASE DOWNLOAD THE GOOGLE DRIVE LINK

https://drive.google.com/file/d/1nT0xGI ... sp=sharing

• Panagiotis Stefanides fourth order equation:

http://www.stefanides.gr/Html/piquad.html

• Panagiotis Stefanides: Quadrature of circle, theoretical definition:

http://www.stefanides.gr/Html/QuadCirc.html


The True Value of Pi revealed = 4/√φ = 3.144605511029693144:

https://www.youtube.com/watch?v=AHAOn7UfXt8

Pi by phi quadrature: https://www.youtube.com/watch?v=CRkIKSkVzPA

Pi by Phi saved archive: http://archive.is/b02DL

Pi by Phi quadrature: http://quadrature-code.blogspot.co.uk/

Quadrature blogspot conclusions http://quadrature-code.blogspot.co.uk/p ... sions.html

Quadrature blogspot Holistic: http://quadrature-code.blogspot.co.uk/p ... -view.html

√√φ = 1.127838485561682 is the key to creating a circle and a square with the same surface area.

The following Wolfram alpha site gives us information about the ratio √√φ = 1.127838485561682 =

http://www.wolframalpha.com/input/?i=&# ... 8730;φ

MEASURING PI SQUARING PHI: www.measuringpisquaringphi.com


The Non Transcendental, Exact Value of π and the Squaring of the Circle 1: https://www.youtube.com/watch?v=ccxVW2M ... 1876258142

The Non Transcendental, Exact Value of π and the Squaring of the Circle 3: https://www.youtube.com/watch?v=-QCtnZjZIsw

• Kepler right triangle information:

https://houseoftruth.education/en/teach ... at-pyramid

https://www.goldennumber.net/triangles/

https://en.wikipedia.org/wiki/File:Kepl ... uction.svg

The real value of Pi = 4/√φ on Facebook:

https://m.facebook.com/TheRealNumberPi/

Website for the real value of pi = 4/√φ: www.measuringpisquaringphi.com

Download for free and keep and read The book of Phi volume 8: The true value of Pi = 3.144, by Mathematician and author Jain 108:

https://lists.gnu.org/archive/html/help ... jmqrL6.pdf

Download for free and keep and read The book of Phi volume 9: The true value of Pi = 3.144, by Mathematician and author Jain 108:

https://drive.google.com/file/d/1cIEvbb ... sp=sharing
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re: Circle the Square

Post by WaltzCee »

No one has the time for your spam.
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¯\_(ツ)_/¯ the future is here ¯\_(ツ)_/¯
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Walter Clarkson
© 2023 Walter W. Clarkson, LLC
All rights reserved. Do not even quote me w/o my expressed written consent.
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