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Did you know that the Pythagoreans did a lot more than make famous the a-squared plus b-squared equals c-squared equation for the hypotenuse of a right triangle? They were a school of thought in ancient Greece interested in exploring the very essence of numbers and how numbers could be used to understand the world.
They were likely the first to divide numbers into odd and even. Odd numbers were associated with the limited while even numbers were associated with the unlimited. Putting the two together resulted in harmony and balance.
They did not consider "1" a number. Instead, they regarded "1" as the essence and origin of all numbers. Even numbers were considered female while odd numbers were considered male. Five represented marriage since it was the union of the first female number (2) and the first male number (3). Four represented justice since it was the first perfect square (2 x 2).
The Pythagoreans thought that odd numbers were the best because you could add them to get perfect squares (check out the middle grades color tiles kit for more on this!): 1 + 3 = 2 squared, 1 + 3 + 5 = 3 squared. When even numbers were added, you got rectangles--obviously not as wonderful as squares! 2 + 4 = 3 x 2, 2 + 4 + 6 = 4 x 3.
copyright 2003, Center for Hands-On Learning