Pythagoras - Research Article from Macmillan Science Library: Mathematics

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How Pythagoreans Conceptualized Numbers

Pythagoreans believed that all relationships could be reduced to numbers in order to account for geometrical properties. This generalization originated from the observation that whenever the ratios of lengths of strings were whole numbers, harmonious tones were produced when these strings were vibrated.

The society studied properties of numbers that are familiar to modern mathematicians, such as even and odd numbers, prime and square numbers. From this viewpoint, the Pythagoreans developed the concept of number, which became their dominant principle of all proportion, order, and harmony in the universe.

The society also believed in such numerical properties as masculine or feminine, perfect or incomplete, and beautiful or ugly. These opposites, they believed, were found everywhere in nature, and the combination of them brought about the harmony of the world.

The primary belief of Pythagoreans in the sole existence of whole numbers was later challenged by...

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This section contains 1,182 words
(approx. 4 pages at 300 words per page)
Buy the Pythagoras Encyclopedia Article
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Macmillan Science Library: Mathematics
Pythagoras from Macmillan Science Library: Mathematics. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.
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