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Cutting a Polyomino into Triangles of Equal Areas

by Sherman K. Stein

This article originally appeared in:
American Mathematical Monthly
March, 1999

Subject classification(s): Geometry and Topology | Plane Geometry | Triangles | Numbers and Computation | Measurement | Area
Applicable Course(s): 4.9 Geometry

A standard square in the xy-plane is a unit square whose corners have integer coordinates.  This note shows that when a polyomino consisting of an odd number of standard squares is cut into triangles of equal areas, the number of triangles is even.

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