Hex (board game)
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Hex is a two-player abstract strategy board game in which players attempt to connect opposite sides of a rhombus-shaped board made of hexagonal cells. Hex was invented by mathematician and poet Piet H
The end of a game of Hex on a standard 11×11 board. Here, White wins the game.
A Parker Brothers edition of the game
Brouwer fixed-point theorem
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Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. Brouwer. It states that for any continuous function f mapping a nonempty compact convex set to itself, there is
Hex (board game)
…board. Despite the simplicity of its rules, the game has deep strategy and sharp tactics. It also has profound mathematical underpinnings related to the Brouwer fixed-point theorem, matroids and graph connectivity. Hex is a finite, two-player perfect information game, and an abstract strategy game that belongs to the general…
For flows in an unbounded area, or in an area with a "hole", the theorem is not applicable.
John Nash used the theorem in game theory to prove the existence of an equilibrium strategy profile.