1) brachistochrone (quickest hill to roll down) 2) axiom of choice 3) discrete differential geometry (computers measuring curvature) 4) RSA cryptography 5) impossible compass-and-straightedge problems (trisection, squaring the circle, doubling the cube) using Galois theory (in this case, counting dimensions of field extensions) 6) knot theory 7) Fibonacci numbers 8) Catalan numbers 9) combinatorial game theory 10) mathematics of poker
11) non-Euclidean geometry 12) Bertrand's paradox in probability 13) Russell's paradox in set theory 14) Hilbert's third problem (scissors equivalence) 15) Niven's proof that pi is irrational 16) Mercator projection and cartography 17) spherical geometry (similar to #11 but narrower) 18) graph theory and Euler's formula 19) number theory (and AKS primality test maybe?) 20) Penrose tilings 21) probabilistic method of proofs 22) computability theory
23) Benford’s Law 24) The Shoelace Theorem 25) Butterfly Curves 26) Conchoid of Nicomedes 27) What is pi 28) approximating pi 29) Lagrange points 30) The Basel Problem 31) Quaternions 32) Retrograde Orbits 33) Kepler's laws 34) Alhazen’s Problem 35) Multinomial Theorem 36) Applications of Differential equations 37) Pentagonal numbers 38) Pythagorean Triples 39) Faulhaber’s Formula 40) Queuing Theory 41) Sizes of Infinity
sorry @CalvinKhor but do you mind explaining to me this stuff in a few hours. I have to sleep now. It's almost midnight in Singapore, and I still have exams.
