On Pythagoras's Theorem
Pythagoras's Theorem states that if one draws squares on the sides of a right triangle, the largest square has area the sum of the two smaller square areas. This means it must be possible to split the large square into two rectangles, each having area matching the area of a smaller square.
In this video I show you how to do this swiftly and easily. It's a charming little tidbit. (And then ... Who says you have to stick with squares???)
Generating Pythagorean Triples
Here's how you can use an ordinary multiplication table to list infinitely many different examples of Pythagorean Triples! Everyone knows 3^2 + 4^2 = 5^. I'll show you how to create examples like 767^2 + 1656^2 = 1825^2.
Pythagoras in 3-D: Two Ways
In this video we take Pythagoras's theorem and generalise it to a three-dimensional version in two ways. The first is the classic way as everybody does (which I am obligated to show, I guess) and the second is a snazzy not-well-known approach due to de Gua from the 1700s. Really cool!
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