Proofs from THE BOOK

pp 131-138

One square and an odd number of triangles

  • Martin AignerAffiliated withFU Berlin
  • , Günter M. ZieglerAffiliated withFU Berlin

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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.