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#1 2011-11-21 01:41:30

benice
Member
Registered: 2010-06-10
Posts: 110

Rolling Regular Polygons around a Circle

Rolling Regular Polygons around a Circle:

(1) Polygonal Epicycloid

(2) Polygonal Epitrochoid (new!)


polygonal_epitrochoid_parameters.gif

Last edited by benice (2011-11-27 22:14:22)


My Gallery of Math Art: benice equation

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#2 2011-11-21 01:46:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,472

Re: Rolling Regular Polygons around a Circle

Hi benice;

Good use of geogebra!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2011-11-21 01:52:10

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,097

Re: Rolling Regular Polygons around a Circle

hi benice,

That's real mathematical beauty.  Excellent!  smile

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2011-11-27 01:51:00

benice
Member
Registered: 2010-06-10
Posts: 110

Re: Rolling Regular Polygons around a Circle

Hello everyone!

Thank you for your appreciation. smile

Polygonal Epitrochoid


My Gallery of Math Art: benice equation

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#5 2011-11-27 02:16:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,472

Re: Rolling Regular Polygons around a Circle

Hi benice;

Those are really cool! Here is my favorite:

polygonal_epitrochoid_n5_k3_theta0_5t2_dbplusa.gif


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#6 2011-12-01 11:59:49

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,552

Re: Rolling Regular Polygons around a Circle

When a corner is pivoting, all is easy, however, when the edge of the polygon is rolling of the circle, things get harder, in my "at a glance" opinion.  Consider rolling along a flat edge  instead of a circle, then the edge rolling doesn't happen.


igloo myrtilles fourmis

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