Thursday, September 9, 2010

Pentagons and Isosceles Trapezoids

This dot pattern diagram from the series, Self-similar Boundaries, is based on pentagons and isosceles trapezoids. The trapezoids are the scaling polygons. They share non-parallel sides with a pentagon and parallel sides with scaled pentagons. The trapezoids generate one pentagon that scales down and one that scales up. The initial pentagon generates one trapezoid, with two scaled pentagons. Each subsequent iteration could double the number of pentagons, except that many are duplicates. In this example I follow three scaling iterations which might have produced 1 + 2 + 4 + 8 = 15 different pentagons, but since some are equal the pentagons produced are 10.

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