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.

For more details, see this page:

  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/