Math Gems Chart
Math Gems is an assortment of some of the most amazing and significant mathematical marvels in all branches of mathematics. It is intended to provide sparks of inspiration for students of all ages (primary school, middle school, high school, college) as well as adults. It encourages students to investigate on their own to find out more.
There are 36 math gems, including: fun arithmetic with the numbers 9 and 7, magic square, pi, areas and volumes, elegant infinite series and infinite products, factorials, gamma function, prime numbers, zeta function, binomial coefficients, Pascal's triangle, quadratic equation, trigonometry, golden ratio, Fibonacci numbers, exponentials and logarithms, calculus, bell curve, vector multiplication, polyhedra, hypercube, Moebius strip, Klein bottle, and fractals. Of course, it has the most beautiful formula of all: Euler's formula relating pi, e, and the imaginary square root of minus one. It contains three remarkably compact complete proofs: visual proof of the Pythagorean theorem, proof of the irrationality of the square root of two, and Cantor's diagonal proof that there are different levels of infinity. It ends by mentioning Goedel's astounding proof that arithmetic is incomplete.
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