These cultures had a very different view than Babylonians and the Egyptians towards mathematics. They saw it in very practical terms such as "aligning shafts through a pyramid so that the ka of the dead pharaoh could be launched in the direction of Sirius." Some Greek mathematicians believed that numbers were the very core of their beliefs rather than just tools that supported mystical beliefs. There was a cult around 550 BCE centered on Pythagoras, that believed that mathematics-especially numbers-were the basis of their creation. We hear of this cult from famous philosophers, Plato and Aristotle.
"They developed mystical ideas about the harmony of the universe, based in
part on the discovery that harmonious notes on a stringed instrument are related
to simple mathematical patterns."
To produce a note of one octave higher than the original, the string must be half the length of what it was when the original note was produced. They investigated many number patterns, especially polygonal numbers. Polygonal patterns were made from arranging different objects into polygonal shapes. For example, the numbers 1, 3, 6, and 10 are known as triangular numbers because when arrange, they form triangles.; whereas 1, 4, 9, and 16, are known as square numbers because they form squares.
Pythagoreanism classified the number 2 to be male, and the number 3 to be female. They had some pretty "nutty numerology". Greek geometry eventually became less mystical however, and they saw it as less of a tool and more of a branch of philosophy.
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