# Math Museum

### From TheTangentSpace

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== Surprising ideas from statistics == | == Surprising ideas from statistics == | ||

- | The birthday paradox can be demonstrated to any group of the right size (say 25-40 people is usually enough to give a shared birthday and seem surprising). The Monte Carlo problem might surprise people. We could also play games of chance with unexpected outcomes, and explain what happened. Maybe use a pseudo-random number generator to mix up some numbers and show how pseudo-randomness can fail. We could teach people how to do coin tosses in their head with extremely high accuracy (that is, very close to 50/50 choices). | + | The birthday paradox can be demonstrated to any group of the right size (say 25-40 people is usually enough to give a shared birthday and seem surprising). The Monte Carlo problem might surprise people. We could also play games of chance with unexpected outcomes, and explain what happened. Maybe use a pseudo-random number generator to mix up some numbers and show how pseudo-randomness can fail. We could teach people how to do coin tosses in their head with extremely high accuracy (that is, very close to 50/50 choices). And something on Poisson processes(life-death processes), poisson distributions (soccer goals, light bulb lifetimes and frequency of floods). Simpson's Paradox. |

== Games from game theory == | == Games from game theory == | ||

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== Tessellations == | == Tessellations == | ||

- | We could show an exhibit of various tessellations, both of the usual plane, of hyperbolic space, or of standard 3 dimensions (or others?). We could showcase the works of M.C. Escher here. We could also allow audience members to build their own tessellations by modifying existing patterns. Some interesting history of Penrose tilings. We could relate these to crystal structures and maybe demonstrate how crystal sugar or quartz patterns might arise from basic tiling building blocks. Also "Islamic" tilings | + | We could show an exhibit of various tessellations, both of the usual plane, of hyperbolic space, or of standard 3 dimensions (or others?). We could showcase the works of M.C. Escher here. We could also allow audience members to build their own tessellations by modifying existing patterns. Some interesting history of Penrose tilings. We could relate these to crystal structures and maybe demonstrate how crystal sugar or quartz patterns might arise from basic tiling building blocks. Also "Islamic" tilings, the story of Majorie Rice and her non-periodic tiles (something for the girls). |

== The game of life and cellular automata == | == The game of life and cellular automata == | ||

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We could mention a few easy-to-understand problems (like the 3x+1 problem, or the Goldbach conjecture) and a few harder problems, like the Riemann hypothesis. We could also mention things that are impossible to do in math, such as the implications of Godel's incompleteness theorem or solving the quintic. It might be nice to leave the audience with an idea of some problems they can actually think about, but they are known to be still unsolved (of course, give them fair warning!). And to not kill their brains include some warm-up problems so they at least feel better when they can't solve the hard ones. | We could mention a few easy-to-understand problems (like the 3x+1 problem, or the Goldbach conjecture) and a few harder problems, like the Riemann hypothesis. We could also mention things that are impossible to do in math, such as the implications of Godel's incompleteness theorem or solving the quintic. It might be nice to leave the audience with an idea of some problems they can actually think about, but they are known to be still unsolved (of course, give them fair warning!). And to not kill their brains include some warm-up problems so they at least feel better when they can't solve the hard ones. | ||

+ | Plus the connection between Hilbert's 10th problem, renumerable sets (work of Davis, Putnam and Robinson) and Diophantine equations and primes (Matajasevic, Jones, Wada et al)See wikipedia "Hilbert's 10th problem". The Busy Beaver Problem. The Word Problem. The connection between some tessellations and decision problems. | ||

== Other possible exhibits == | == Other possible exhibits == | ||

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* History of "Circle Squarers" | * History of "Circle Squarers" | ||

* Special numbers: pi, e, phi, etc | * Special numbers: pi, e, phi, etc | ||

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+ | [[Category: Math]] |