1. Pythagoras
Pythagoras was a Greek scholar and philosopher ca 548 BC to 495 BC.
Known as “the father of numbers, his teachings covered a variety of areas such as mathematics, music, astronomy, and topography.
Born in Samos, he is best known for the Pythagorean Theorem which bears his name.

2. c b a The Theorem states:
Given a right triangle with leg lengths a, b, and hypotenuse length c
Hypotenuse c 2
The area of the square whose side length is the hypotenuse (c)… c b 2 b
Leg a
Is equal to the sum of the areas of the squares whose side lengths are the legs (a) and (b). a 2
Leg
In other words:

3. One such proof is to create a square with side lengths a+b.
Although he did not discover the Theorem, he was the first to prove it.
One such proof is to create a square with side lengths a+b.
Area of large square = (a+b) 2 a b
= a + 2ab + b 2 a b c c
Area of each triangle = ab 2
a+b
Area of all four triangles = 4ab 2 c c b a
Area of small square = c 2 b a
Area of everything = 4ab + c 2
Therefore, Area of everything = Area of large square 2
4ab + c = a + 2ab + b 2 1
2ab + c = a + 2ab + b 2
c = a + b 2