nested polygon - Wolfram|Alpha

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Input interpretation

nested polygon

Definition

Beautiful patterns can be created by drawing sets of nested polygons such that the incircle of the nth polygon is the circumcircle of the (n + 1)st and successive polygons are rotated one half-turn at each iteration. The results are shown above for nested triangles through heptagons in alternating black and white and in a cyclic rainbow coloring.
The animation above shows successive iterations of a nested octagon.
The black region of a nested square has area
A = sum_(n = 0)^∞ (-1)^n/2^n = 2/3
if the initial square has unit edge length.

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Related terms

circular chessboard | continuous line illusion | derived polygon | midpoint polygon | polygonal spiral | polygon circumscribing | polygon inscribing | tangential polygon | whirl

Subject classifications

MathWorld

polygons

MSC 2010

51E12 | 51M04

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