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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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#1 2013-11-29 02:58:50

benice
Full Member

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Infinite Families of Circles

(A) Concentric Circles

http://i1216.photobucket.com/albums/dd371/benice_chen/an_infinite_family_of_concentric_circles_zps45fbec37.png
Regions enclosed by an infinite family of concentric circles.


http://i1216.photobucket.com/albums/dd371/benice_chen/five_infinite_families_of_concentric_circles_zpsaddc8f34.png
Regions enclosed by five infinite families of concentric circles. (Animation Pictures)




(B) Tangent Circles

http://i1216.photobucket.com/albums/dd371/benice_chen/an_infinite_family_of_tangent_circles_zpsf9e2e0e2.png
Regions enclosed by an infinite family of tangent circles.


http://i1216.photobucket.com/albums/dd371/benice_chen/five_infinite_families_of_tangent_circles_zps460c520b.png
Regions enclosed by five infinite families of tangent circles. (Animation Pictures)


My Gallery of Math Art: benice equation
 

#2 2013-11-29 03:15:45

bobbym
Administrator

Online

Re: Infinite Families of Circles

Hi benice;

Amazing detail and beauty, very good!


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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