The Pythagoreans

We are all probably familiar with Pythagoras of Samos from high school geometry class and while reading this weekend, I became aware of a society that he belonged to called the Pythagoreans. Little is known about th is group, except that it was started by Pythagoras and they were students of mathematics and strongly believed that "Everything is a Number". The Pythagoreans spent much of their time trying to uncover numbers that were hidden in everything from music to planetary orbits, and the natural world. Pythagoras's theorem on right angles forms a cornerstone of the structure of the three dimensional world we live in. I just had a geometry flashback!

The Pythagoreans were interested in this notion of a perfect number. A perfect number is one in which all the factors of a number add up to that number. For example the factors of the number '6' are '1', '2', and '3'. If you add up all the factors 1+2+3, the result is the original number which is 6. The next perfect number is 28. 1+2+4+7+14=28.

'Perfect Numbers' demonstrate even more interesting characteristics in that they are always the sum of consecutive numbers. For example :

1+2+3=6
1+2+3+4+5+6+7= 28

The Pythagoreans attempted to connect these 'perfect numbers' to phenomena in the natural world. For example, the moon orbits the earth every 28 days and 28 is a 'perfect number'. There was another interesting pattern called 'slightly defectiv'e numbers and they dealt primarily powers of the number 2. For example :

2^2=2x2 = 4 Factors = 1, 2 Sum of Factors =3
2^3=2x2x2 =8 Factors= 1,2,4 Sum of Factors=7

The sum of the factors with powers of the number 2 seem t o be 'slightly defective' or 1 less than the exponentiation.