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### An Odd bit of Math

December10

ODD and EVEN NUMBERS. The Pythagoreans knew of the distinction between odd and even numbers. The Pythagoreans used the term gnomon for the odd number.

A fragment of Philolaus (c. 425 B. C.) says that “numbers are of two special kinds, odd and even, with a third, even-odd, arising from a mixture of the two.” [I know that sounds odd]

Euclid, Book 7, definition 6 says:An even number is that which is divisible into two parts.”

So the ancient Greeks had a word for “odd” that was the word they used for this kind of shape: An “odd” number is one that makes that shape (with a bit sticking out) when you try to arrange it in two rows:

o o o o
o o o

There is an “odd” object left over that doesn’t line up. An even
number makes an “even” rectangle:

o o o o
o o o o

You can see in the quotation above that the words “odd” and “even” were used of numbers in English by the 1400’s; the words were used in other ways earlier. [from Mathword here]

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