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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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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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