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### History of Odd and Even Numbers

```Date: 02/12/2004 at 09:15:31
From: Osha, Charmaine, and Caleb
Subject: Odd and Even Numbers

We were talking about odd and even numbers in class and we know that
odds end in 1,3,5,7,9 and evens end in 0,2,4,6,8 but we don't know why
they are called odds and evens.  We're in third grade and we just
wondered.

```

```
Date: 02/12/2004 at 10:01:25
From: Doctor Peterson
Subject: Re: Odd and Even Numbers

Hi, Osha, Charmaine, and Caleb.

To see where math words came from, I look here:

Earliest uses of mathematical words
http://jeff560.tripod.com/mathword.html

That says this:

ODD NUMBER and EVEN NUMBER.  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."

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

Odd and even are found in English in various Middle Age
documents including Art of Nombrynge (around 1430) "Compt the
nombre of the figures, and wete yf it be ode or even" (OED2).

In English, gonomon is found in 1660 in Stanley, Hist. Philos.
(1701): "Odd Numbers they called Gnomons, because being added to
Squares, they keep the same Figures; so Gnomons do in Geometry"
(OED2).

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 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.

Etymology of Odd and Even
http://mathforum.org/library/drmath/view/61374.html

That tells us that the original meaning of "odd" was "sticking out",
which fits the picture I gave; and "even" means "level" (nothing
sticking out!).

So in both Greek and English, the words we use are pictures of the
shapes a number makes.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Math History/Biography
High School History/Biography
Middle School History/Biography

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