One square and an odd number of triangles

Abstract

Suppose we want to dissect a square into n triangles of equal area. When n is even, this is easily accomplished. For example, you could divide the horizontal sides into \( \frac{n}{2} \) segments of equal length and draw a diagonal in each of the \( \frac{n}{2} \) rectangles. But now assume n is odd. Already for n = 3 this causes problems, and after some experimentation you will probably come to think that it might not be possible.