Perfect numbers
They also operated with perfect numbers. A perfect number is a number whose factors sum up to the number itself. (6: 1+2+3) Between one and 10,000 there are only four of these; 6, 28, 496 and 8128. The Pythagoreans compared this to humans: very few are perfect, good and beautiful. But imperfection in numbers is common, just like evil and ugliness in people.
The Golden Ratio
a/b= 1.618
If you divide the longest side of a square with the short side of the square and get 1.618 the square has a Golden Ratio. Here is an example:
If you divide 3.2 cm with 2.0 cm you get 1.618. Therefore the square is considered as a pretty one.
Most people find things with a golden ratio beautiful. If you divide your height with the height from your feet to your bellybutton and get 1.618, you’re "perfect". The golden ratio also exists in snails houses and in other different subjects in nature.
Division of numbers
The division of numbers started with even (“male”, who can be divided by two) or odd (“female”, not divisible by two) numbers. Then the numbers were separated into even-odd numbers (divisible by two only once), even-even numbers (can be divided by two until one is reached) odd-even numbers (can be divided by two several times without ever reaching one) and odd-odd numbers (products of two odd numbers). Like this they found out that some numbers can not be reduced by any number but the number itself or one. These are the prime numbers.
Even 4 6 8 10 12
Odd 3 5 7 9 11
Even-odd 6 10 14 18 22
Even-even 4 8 16 32 64
Odd-even 12 20 28 36 42
Odd-odd 9 15 21 27 33
Prime numbers 3 5 7 11 13
Pythagoras Theorem
The Pythagoras theorem states that the sum of the squares of the lengths of the two adjacent legs of a right angle triangle is equal to the square of the length of the hypotenuse.
a² + b² = c²
The sum of square C is equal to the sum of square A and B. ( 25 = 9 + 16 )
The Egyptian surveyors, the Chinese and Babylonians knew this rule already about 2000 BC, but they couldn’t prove it. The first people we know proved it are the Pythagoreans, it might have been Pythagoras himself. Thereby they raised the rule to the status of a theorem.
The theorem is important to the evolution of the Greek concept of number and the proof demonstrates how the Greeks used such proofs.
Pythagoras theorem can also be used for triangles that aren’t right. Then it goes:
c² = a² + b² - 2ab
