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This week's Math Colloquium is "Subdividing Squares into Equal Area Triangles" by Dr. Ben Schmidt, Michigan State University.
Given a square and any even number 2n, it is always possible to subdivide the square into 2n triangles of equal area. For instance, first subdivide the square in the obvious fashion into n rectangles of equal area and then further subdivide each of these rectangles into two triangles by adding a diagonal. Is it similarly possible to subdivide a square into an odd number of equal area triangles? While Euclid could have asked this seemingly innocuous question, it remained unresolved until 1970! In this talk, I will do my best to describe the solution.