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Unformatted text preview: So you can suppose that no pair is colinear; you next pick any further point, call it B , and label the other points, C , D , E ,... clockwise and in order around A starting from B . Now look at the eight distinct and disjoint triangles with vertices ABC , ACD , ADE ,... The union of the eight triangles lies in the interior of the square, so the sum of the areas must be less than 1. One of the triangles must therefore have area less than 1/8. to this page....
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- Spring '10
- Combinatorics, English-language films, Burkart Venzke, disjoint triangles