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#1 2011-11-22 00:41:30

benice
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Rolling Regular Polygons around a Circle

Rolling Regular Polygons around a Circle:

(1) Polygonal Epicycloid

(2) Polygonal Epitrochoid (new!)


http://i1216.photobucket.com/albums/dd371/benice_chen/polygonal_epitrochoid_parameters.gif

Last edited by benice (2011-11-28 21:14:22)


My Gallery of Math Art: benice equation
 

#2 2011-11-22 00:46:54

bobbym
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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.
 

#3 2011-11-22 00:52:10

bob bundy
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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
 

#4 2011-11-28 00:51:00

benice
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Re: Rolling Regular Polygons around a Circle

Hello everyone!

Thank you for your appreciation. smile

Polygonal Epitrochoid


My Gallery of Math Art: benice equation
 

#5 2011-11-28 01:16:09

bobbym
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Re: Rolling Regular Polygons around a Circle

Hi benice;

Those are really cool! Here is my favorite:

http://1.bp.blogspot.com/-CiO5FpowH4w/TtICm086CPI/AAAAAAAAAX4/htjPEdq-K2Q/s1600/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.
 

#6 2011-12-02 10:59:49

John E. Franklin
Star Member

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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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