### An Odd bit of Math

**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]