Sperner's Lemma.
What is it about? A Mathematical Droodle

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Definition

A Sperner labeling of a triangle's triangulation is a labeling that satisfies the following conditions:

  1. The vertices of the original triangle are labeled with three different letters A, B, and C.
  2. Vertices of the triangulation that lie on the side AB are labeled either A or B. A similar condition holds for the vertices on sides BC and AC.
  3. There is no restriction on labeling of the vertices of the triangulation inside the original triangle.

Sperner's Lemma

Every Sperner's labeling contains at least one complete triangle.

Explanation

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Copyright © 1996-2018 Alexander Bogomolny
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