[lbo-talk] science notes

[John Thornton]

Charles A. Grimes wrote:
> ``...seeing two 53 tooth gears in a machine from such a date...'' JT
>
> -----
>
> I found this at work, so I have to wait to get home. But here is my
> interest. 
>
> Since it's complex rotary machine, it means that you have to be able
> to partition the circumference of circle into (n) number of equal
> parts (teeth, cogs, etc). 
>
> If (n) is even, fine. But if (n) is not
> even, it has to prime. Constructing a prime equi-partitioning of
> a circle, is still on the books as a famous math problem. According to
> most of the histories I've read, antiquity only had the platonic
> regular polygons. Gauss made himself famous instantly by a
> demonstration proof of the 17 sided partitioning of circle.
>
> I am trying to think about ways to construct or draw 53 point star
> that cut the circumference in 53 equal parts. There has to be a trick
> of the trade here, someway to scribe off only peaks or only valleys,
> that drops the number or increases the number to 52 or 54...
>
> Computing...still computing....
>
> Any suggestions?
>
> CG

Compound indexing.
With my dividing head, which has a 40 to 1 worm drive I need a 66 and a 
37 hole dividing plate.
That is a plate with 24 holes evenly spaced around the circumference and 
a plate with 66 holes even spaced around the circumference.
I then rotate the worm 7 holes on the 66 plate and 24 holes on the 37 plate.
This moves the gear which is attached to the 40 to 1 worm rotate 
99.99897% of the outer circumference of the gear after 53 turns.
This makes the last tooth space off by .0000103%.  Insignificant really.

John Thornton