The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Specifically, if c is the length of the hypotenuse and a and b are the lengths of the other two sides, the theorem can be expressed as a2 + b2 = c2. The theorem is named after the Greek mathematician Pythagoras, who is traditionally credited with its discovery. It has applications in many areas of mathematics and is one of the most famous theorems in geometry.

1. 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)