Joined: Jan 24, 2010
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February 28th, 2013 at 12:06:09 PM permalink
It seems that "trochoid" and "roulette" indeed are the terms for this type of curve. Thank you for finding that out for me!

Everything I have found has agreed with the notion that only one or two circles are involved in the creation of a trochoid. The original picture had no explanation to it; No formulas, no distances. I did some measuring, estimating, and guessing, and was able to figure out all of the associated radii and rotation speeds for each circle.

I haven't done any "zoomed in" versions of the curve, but want to look into it. I don't expect it to be a fractal per se (with repeating patterns), but I am interested in seeing what is happening near the compass points especially.

I am also working on a bit of a higher resolution, smoother animated gif of the curve, which might not come to fruition due to lack of tools in creating it.
Joined: Apr 19, 2010
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February 28th, 2013 at 12:40:38 PM permalink
I find it amusing that it is a type of (mathematical) roulette, based on the board you asked the question :)
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
Joined: Nov 15, 2011
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March 1st, 2013 at 10:48:37 AM permalink

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