Pythagorean Theorem

http://en.wikipedia.org/wiki/Pythagorean_Theorem

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in

Euclidean geometry among the three sides of a right triangle. The theorem is named after

the Greek mathematician Pythagoras, who by tradition is credited with its discovery,

although knowledge of the theorem almost certainly predates him. The theorem is known

in China as the "Gougu theorem" for the (3, 4, 5) triangle. Chou Pei Suan Ching 500–

200 BC.

The Pythagorean theorem: The sum of the areas of the two squares on the legs (a and

b) equals the area of the square on the hypotenuse (c).

If we let c be the length of the hypotenuse and a and b be the lengths of the other two

sides, the theorem can be expressed as the equation

or, solved for c:

A Pythagorean triple consists of three positive integers a, b, and c, such that

a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known

example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for

any positive integer k. A primitive Pythagorean triple is one in which a, b and c

are coprime.

(3, 4, 5) (20, 21, 29) (11, 60, 61) (13, 84, 85)

(5, 12, 13) (12, 35, 37) (16, 63, 65) (36, 77, 85)

(8, 15, 17) (9, 40, 41) (33, 56, 65) (39, 80, 89)

(7, 24, 25) (28, 45, 53) (48, 55, 73) (65, 72, 97)