>>11063882Just a few ideas:
- Cardinalities. Cantor's diagonalization argument.
- Proof of Ramsey(3,3)=6. IMO one of the most wonderful proofs in simple maths, really fun to explain and understand, and easily appreciated by normies.
- Euclid's proof of infinitude of primes.
- sqrt(2) is irrational
- Game of chomp: Take a nxm square grid. Two players take turns, in each of which they choose which square to eat along with all the squares to the right and up of it (example in pic related). Proof that first player has a winning strategy: if not, the second player has it, so at the first turn as the first player you eat the upper right square (so just one). Whatever the next player does gets him into the winning situation, but you could have done it also in your first move, and then you would have won, a contradiction.
- e^ix = cosx + i sinx. Maybe use it to prove angle addition formulas or something. The correspondence between algebra and geometry is interesting here.
- use of polynomials to encode secrets. You could use polynomials to show that it's possible to encode a secret in such a way that given secret codes to n people, any m group of people cannot decode it by themselves, but if the group has more than m people, it can. This is done by sampling the polynomial at distinct points, but not enough points to determine the polynomial, give different samples to different people and tell them the degree of the polynomial. The secret code could be the coefficients, for example, or f(0), or whatever.
- Fundamental group. Don't have to be rigorous, but it can be intuitively understood by normies, and is quite fun.
- Proof that 100x100 square board with 2 opposite corners removed ( so consisting of 100x100 - 2 squares), cannot be completely covered with 2x1 domino tiles. Maybe some variants of this too, can be quite entertaining.
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