One of the cornerstones in Mathematics was proven by Pythagoras around 520 BC. Today we know this as the Pythagorean theorem, which states the sum of the squares of two sides of a triangle equal the square of its hypotenuse (a2 + b2 = c2). Pythagoras not only discovered this theorem, but he also started a philosophical and religious school where his followers worked and lived. They were known as the Pythagoreans and they lived by a specific set of rules, which dictated when they spoke, what they wore, and what they ate. Their lives were dedicated to universal discoveries and proving theorems. Pythagoras was the Master of these men and women, who were known as mathematikoi.
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| A graphic from Some of Infinity. |
In our book, Some of Infinity, the author, David Craft, briefly talks about the Pythagoreans and goes on to prove the Pythagorean theorem. He touches on numerous sections of Mathematics such as Numbers, Infinity, Probability, Fractals, Calculus, and more. The idea for the book came about from trying to convince his friends that math is fun and cool. He does a very good job of portraying that math actually is fun and interesting, while keeping the reader engaged with cool puzzles and riddles.
Watch the proof here!
Suggestion: when you go to triangles of side-length a and b, it's no longer obvious that the quadrilateral with side-length c is a square. Maybe it's a non-square rhombus? You should at least address this. (You could argue from symmetry that it must be a square, since there's no prefered choice for the short diagonal. Or you could derive it from the fact that the two non-orthogonal triangle angles must add to 90 degrees, and so the quadrilateral's interior angles must each be 90 degrees, too.)
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