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Problem of the Week 1050

Twin Polygons

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True or False: For every nonregular polygon, there is a noncongruent one having the same area and perimeter and the same number of vertices.

Source: Inspired by "A Non-Visual Counterexample in Elementary Geometry" by Marita Barabash, College Math Journal, Nov 2005.

© Copyright 2006 Stan Wagon. Reproduced with permission.

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21 February 2006