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Young World
WORLD OF SCIENCE
Perfect numbers
DR. T. V. PADMA
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A perfect number is that is equal to the sum of its divisors.
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Photo: V. Sreenivasa Murthy
Numbers: What’s the magic?
The Arabs were fascinated by magic squares — number grids in which each row, each diagonal and each column adds up to the same sum. They loved creating and solving magic squares and other complicated mathematical puzzles.
Another interesting numerical fancy of theirs was perfect numbers. A perfect number is a number that is equal to the sum of its divisors, other than the number itself. A divisor of a number is one that divides it leaving zero as the remainder. For example, the divisors of the number 6 are 6, 1, 2, and 3. That’s because 6 x 1 = 6 and 2 x 3 = 6. Now, if we add the divisors of six other than itself, we get 1 + 2 + 3, which equals six!
Just the thing
Twenty-eight, another perfect number, has as its divisors, 28, 1, 14, 2, 7, and 4; 28 = 1 + 14 + 2 + 7 + 4. The ancients knew two other perfect numbers: 496 and 8,128.
The Arabs discovered three more by the 13th century. Perfect numbers haven’t got any practical application that we can think of as yet. Despite the lack of application, the Arabs enjoyed working with perfect numbers, thus evincing an early interest in the field of “pure” mathematics (mathematics that doesn’t necessarily have a practical application — maths for maths’ sake).
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