... square when a smaller square was cut out of one corner. According to the Pythagoreans a number that equaled the sum of its divisors including 1 but not the number itself was a perfect number such as 6, 28 and 496. Those, which exceeded the sum of the divisors, were known as excessive and those that were less were called defective. Numbers to the Pythagoreans meant only whole numbers. They did not deal ... They helped others understand the concept of a number, which became for them the ultimate principle of all proportion, harmony and order of the universe. Through their studies they estab...

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