The fixed point theorem Brouwer is one of the most beautiful theorems of mathematics. Has a reputation that 99% of mathematicians know him, but only 1% are able to prove it.
This is because the known proofs use heavy tools weighing algebraic topology.
However, one of the best mathematicians of our time, John Milnor, a public elementary mathematics review a proof of the theorem (download article here ), which only uses calculation of several variables. His proof is short and elegant, well all he has done Milnor is elegant.
This theorem is the basis of Nash theorem, which is the basis of game theory, which in turn is becoming the foundation of modern economics.
The exhibition is to present the proof of Milnor, it is possible to present the theorem of Nash.
By the way, wrote a beautiful article Milnor (download here ) in honor of Nash and the Nobel laureate in economics, where he presents the Nash theorem in a way so clear that envy the capabilities of this mathematical expository in the same article says the game of Hex, invented by Nash.
The Hex is a game mathematically interesting, it's still super fun, and point theorem follows also fixed some game properties.
I was a teacher in Hex, my girlfriend also was good playing, but I think he got tired of that win, I officially retired when I lost for the first time, it's so hard to lose, but get over it.
you can opt for the demonstration based on the HEX, it might even make a board and organize a mini tournament of HEX in the class, the winner has a special prize.
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