AP Wheel Geometry

[Oystein]

Of course I understand.

And that proves why we are talking of two different things.

As I have said, I am not talking of the inner anchor point in any way, at this time.

I am talking of the physical width of the white field. the length of the arc, if you like. The length of the arc is approx. 360/15 This is ALL I have said. these 360 degrees is actually 360 divisions of the rim. 24 of those fit onto the arc of the white field.

Again these 360 degrees (The rim), has nothing to do what so ever with the gap/angle number of the white fields.

If you try to make the white field have an 24 degrees opening, they will not reach the pentagram, and that is just what you showed you tried, so many times..

[Silvertiger]

I understand you, but they are related; not two different things. You can't talk about one without the other. When you change where the lines converge, that is when the wheel is no longer divided into 15 arc-segments, which is the reason the pentagon doesn't fit. If the lines did converge at the center, we would not be having this discussion. The length of the arc segments is determined by the respective radius of the lines from where their common center of convergence is, which in this case is not the center of the wheel itself. :)

[Oystein]

No you are wrong.

Isn't the screw holes spaced 1/15th apart on the rim or not?

Let's say you must build the AP Wheel, by hand and have no arms yet.

You have just managed to build a hub, spokes and the rim.

Where do you drill the holes in the rim then ??

What if you spaced them 1/15th of the rim apart.

Now sit and wait for the arms to arrive from the hardware store..

Isn't this the first step of constructing the figure?
(This is all I am discussing and claiming)

[Silvertiger]

If you look closely at this post of yours: http://www.besslerwheel.com/forum/download.php?id=18450

You have drawn lines to the center of the wheel, rather than to a point of convergence of the circumference of the axle. Look close and you'll see that the lines you have drawn deviate from the lines on the drawing and thus form a different angle than what is actually on the wheel.

[Oystein]

Yes, and if you read all the text, you will see that it was to point out our difference. It was made for you to understand me. And you didn't.

I say that we start with a rim, a pie a circle, whatever, and divide it into 15 parts.

THEN we draw lines inwards towards a point AWAY from the axle.

I have said. This is NOT where I am at yeat, in the thread!

I just want to locate the 15 outer attachment points by simple and proven means.

I really don't care if you don't understand by now, but my PROBLEM is that you have used erroneous calculations to prove that my decoding was wrong, in my thread. I don't like that! I don't like it. because you don't understand what I wrote in the thread, and how that apply to your computer software.

[Silvertiger]

I already did that in the video, just for you. Pretty easy. Takes less than 30 seconds to draw. And it was the first thing I drew. Go back and watch it. Come back when you are ready to discuss the geometry of the AP Wheel instead of trying to prove a point that everybody already understands. The positions along the rim of the "15 outer attachment points" change as soon as you change where those lines converge.

[Oystein]

And you haven't yet answered, how many 27 degrees "pies" fit onto the full circle/wheel?

[Silvertiger]

It doesn't work like that. You're asking the wrong question, as the wheel is not divided into slices like a pie. And the true angle is 25.7143 degrees.

[Silvertiger]

I can array 15 slices around the center of the wheel, but because the slices converge on points along the circumference of the axle, there are gaps. And the arc length of those slices at their widest point is less than the arc length of 1/15 of the rim itself.

[Oystein]

What bothers me is that you write false claims on my thread, and at the same time you never answers any of my questions, because you know the answer will make you look bad. Nor do you read my answers to your false claims thoroughly.

AP Wheel quiz:

1.Pizza-slices with and opening angle of 26-27 degrees is spaced around a wheel. Yes/no?
2. The pizza-slices is connected at a hub away from center. Yes/no
3. There are room for 15 of those around the circle, if they are still attached at that hub, in the same manner away from center.. Yes/no?
4. 27 degrees x 15 is 405 degrees. Yes/no?
5. A circle has 360 degrees. Yes/no
6. We are talking of two different things, where you don't understand that I talk of the first pie, wheel or circle you must draw to find where the outer part, the point A of the inward pointing lines is placed on the rim/circumference. Yes/no?

[Silvertiger]

1. No. They are 25.7 degrees.
2. Yes
3. Yes
4. Wrong question, but yes.
5. Yes
6. Yes

You're still not asking the right questions. :)

[Oystein]

here I have used your drawing to show what you argue about.

Actually the only thing you now argue, is that you noticed I and JC was talking of 24 degrees. Then you measured the opening to be more than 24.

Yes, that is of course correct, because the attachment-point (B) is closer to A-A. If it was close enough, it could be 90, even 180 degrees, as in Euclids original drawing (That you of course has studied thoroughly? Or else you wouldn't comment right?)

You discovered that 26-27 degrees (Please don't bother commenting it is 27,5) was different from 24 degrees.
Other thought of this as basic and natural, you went to your computer sim..

The angle of A-A-C is 24 degrees.
The angle of A-A-B is 26-27 degrees. 27,5..Happy??

You know this right?

In my thread I said A-A-C is 24 degrees. Others agreed. I can measure it by measuring tools, so it must be so! THIS IS ALL! NOTHING TO ARGUE
This was because 15 parts of white will fit into the whole circle, as your drawing show. 360/15 is 24 degrees. Therefor A-A-C IS 24 Degrees.

You say this is NOT true, because if the opening A-A-B is 24 degrees, it will not fit the implied by Euclid formula, pentagram and triangle spacing.

YOU ARE DAMN RIGHT! Of Course it don't fit!

This is so basic to the point of embarrassing, and that is why it is VERY hard to understand what you can't agree to?

Your pictures of the AP wheel in my thread is very wrong, and you try to fit white parts (A-A-B) with an opening of 24 degrees, and it don't fir.

NO IT WILL NOT FIT, because you try to disprove something that nobody wonder about. The problem excists in you mind only..

Nobody has wanted to fir white parts with a gap of 24 degrees onto the wheel..NOBODY! Only you though..

[Silvertiger]

The long answer is yes, that 27 will fit. Red lines are yours; white lines are what I drew. Neither one has the angles I measured in AP. These are simply to prove that you can fit 15 27deg slices into the wheel. The further away from center you choose to have the lines converge, the greater the angle will become.

[Silvertiger]

Go back to my very first post on this thread to the very first picture and look at the measurements: the small angle of the white area in AP Wheel is 25.7 degrees. Disagree all you want. It's right there to see. The picture is from YOUR website. Can you argue with that?

[Silvertiger]

Regarding your drawing overlay of mine labeling points A, A', and B - those are not thick lines. They are GAPS. "A" is actually two points on the rim separated by a small arc length. Here, have a closer look: