Rolling Regular Polygons around a Circle

[benice]

(1)Polygonal Epicycloid

 

(2)Polygonal Epitrochoid

 

 

 

 

 

 

 

 

 

 

[michel123456]

Nice, Benice.

Does it have some practical application?

 

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I saw in your examples that the curve ends where it started. You managed to equalize the perimeter of the circle with the perimeter of the polygon...

Edited December 11, 2011 by michel123456

[Daedalus]

That's a really neat type of spirograph you have constructed : )

[Appolinaria]

Ooh, I like these.

 

Pretty.

[Daedalus]

Ooh, I like these.

 

Pretty.

 

Yeah I like them too. Benice, I was wondering did you develop the software for your spirographs or just create animations? Because there might be a market for children and some adults to generate spirographs on their computer. Afterall, a lot of my friends had spirographs when I was a kid and it might actually be something that would be fun / safe for them to create on a computer (safe in that it doesn't incorperate violence and other things that parents worry about when buying games / software for kids).

[benice]

Hello everyone!

 

Thank you for your appreciation.

 

 

 

 

 

 

 

Nice, Benice.

Does it have some practical application?

 

----------------------

I saw in your examples that the curve ends where it started. You managed to equalize the perimeter of the circle with the perimeter of the polygon...

Hi michel123456,

 

I made them just for fun.

The epicycloid curves have some applications in gear design. (http://en.wikipedia....ki/Cycloid_gear)

 

If k (defined in this page) is a rational number, then the curve is closed and periodic.

If k is an irrational number, then the curve never closes.

 

 

 

 

That's a really neat type of spirograph you have constructed : )

Hi Daedalus,

 

we may superpose different curves with different colors on the same picture to make more beautiful patterns.

 

I was wondering did you develop the software for your spirographs or just create animations?

I use an open software called GeoGebra(v4.0) to make animations.

Edited December 13, 2011 by benice