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Rolling Regular Polygons around a Circle
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#2
11 December 2011 - 08:29 PM
michel123456 
Molecule
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...
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...
This post has been edited by michel123456: 11 December 2011 - 08:32 PM
Michel
- Posts: 2,899 | Joined: 28-November 09
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#3
12 December 2011 - 04:09 AM
Daedalus
Atom
That's a really neat type of spirograph you have constructed : )
No trees were harmed in the creation of this post.
But billions of electrons, photons, and electromagnetic waves were terribly inconvenienced during its transmission!
But billions of electrons, photons, and electromagnetic waves were terribly inconvenienced during its transmission!
- Posts: 243 | Joined: 03-July 11
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#4
12 December 2011 - 04:17 AM
Appolinaria
Molecule
Ooh, I like these.
Pretty.
Pretty.
- Posts: 695 | Joined: 03-October 11
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#5
12 December 2011 - 11:27 PM
Daedalus
Atom
Appolinaria, on 12 December 2011 - 04:17 AM, said:
Ooh, I like these.
Pretty.
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).
No trees were harmed in the creation of this post.
But billions of electrons, photons, and electromagnetic waves were terribly inconvenienced during its transmission!
But billions of electrons, photons, and electromagnetic waves were terribly inconvenienced during its transmission!
- Posts: 243 | Joined: 03-July 11
- Reply
#6
13 December 2011 - 09:32 PM
benice
Lepton
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.
Hi Daedalus,
we may superpose different curves with different colors on the same picture to make more beautiful patterns.
I use an open software called GeoGebra(v4.0) to make animations.
Thank you for your appreciation.
michel123456, on 11 December 2011 - 08:29 PM, said:
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.
Daedalus, on 12 December 2011 - 04:09 AM, said:
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.
Daedalus, on 12 December 2011 - 11:27 PM, said:
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.
This post has been edited by benice: 13 December 2011 - 09:39 PM
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