History of Odd and Even NumbersDate: 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/ |
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