Problem of the Week 1050

Twin Polygons

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.

21 February 2006