By applying the Pythagorean theorem to irrational numbers , a beautiful array of patterns emerges , as was initially discovered by Euclid . Other mathematicians have even managed to take the Theorem into three dimensions . Incredibly , the Pythagorean theorem as it was originally expressed , in whole numbers only , was limited . But using it as a platform for other geometries sparked an entire cosmology in mathematics and philosophy , demonstrating that the Theorem is fairly universal in its ability to be the springboard to other...











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