Hello, here are some drawings made with epicycloids, http://www.plouffe.fr/nknmod M/ as you may know, epicycloids are gears in some way. the formula is simple n*2^n mod M where M is equal to various values, the drawings are mysterious and still unsolved as far as I am concern, I have lots of others at http://www.plouffe.fr/graphes/ but not arranged in a web page yet. for M = 131 and k=2 the graph is a complete graph, but for M = 1285 the period is 16*1285 = 20560 and really not like the case M= 131 and this is the whole point : why is it like that and why does it varies so much for no apparent reason. Another direction on the thing, you may try with M = n*257, nice too. ! Best regards, Simon plouffe 2014-06-19 12:58 GMT+02:00 Bill Gosper <billgosper@gmail.com>:
No. The gears shown in the picture, gosper.org/Moregears.png while as they are both can always be pulled apart orthogonally and don't work physically due to very slight intersection, can probably be modified so that they work physically and in some phases can't be pulled apart orthogonally. Combining this with the multilayer gear idea (so that you're always in such a phase), it would be possible to make a pair of gears which can't ever be separated orthogonally. They could probably still be separated without using the third dimension, though. Assuming that those modifications work. I might give it a try.
Julian
On Wed, Jun 18, 2014 at 4:54 PM, rwg <rwg@sdf.org> wrote:
-------- Original Message -------- Subject: Re: [math-fun] Spirography Date: 2014-06-18 13:38 From: Allan Wechsler <acwacw@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Reply-To: math-fun <math-fun@mailman.xmission.com>
Gosper, is Julian all pessimistic because the classic spirograph has the rotor rolling around the inside of the stator? Does the problem persist if the rotor rolls around the outside?
On Wed, Jun 18, 2014 at 4:23 PM, Steve Witham <sw@tiac.net> wrote:
Date: Mon, 16 Jun 2014 11:54:40 -0400 [in issue 29]
From: James Propp <jamespropp@gmail.com>
Has anyone designed a mechanism that permits the spirographer to focus on circumferential force?
The knockoff product I have, has holes in both parts, suitable for pushing pins through, so in theory you only have to push on the pen tip. Rather than a wax tray the first thing I'd think of would be corrugated cardboard & the second, cork.
I'm imagining something like a latchable/unlatchable zipper.
That's a fascinating idea in itself. It could be used in funicular
railways, for instance.
Although the zipper tooth design is asymmetrical, I have a coat that unzips from both ends.
--Steve _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun