Proving the theory of Pythagoras

Pythagoras theory is one theory that has been known to mankind since ancient civilizations. The name of this theory is named for the Greek mathematician named Pythagoras. Pythagoras was born on the island of Samos, Greece, circa 570 BC. In accordance with the advice of his teacher Thales, Pythagoras young visiting Egypt around 547 BC and stayed there.The ancient Egyptians knew that a triangle with sides 3, 4 and 5 will form a right angle. They used ropes by a knot at some point and use it to form a right angle at their buildings including the pyramid. It is believed that they only know about the triangle with sides 3, 4 and 5 that form a right triangle, while the generally accepted theory of right-angled triangles they do not know.
     In China, Tschou-Gun who lived around 1100 BC also know this theory. Likewise in Babylon, this theory has been known in the past more than 1000 years before Pythagoras. A piece of clay from Babylon was never found and the manuscript contains roughly reads as follows: "4 is length and 5 the diagonal. What is the implication? "Pythagoras was the one who had to make generalizations and make this theorem became popular. Briefly Pythagorean theorem reads:
 

In a right-angled triangle, the square of the hypotenuse is equal to the number of squares of the other sides.

 

1.    Proof of the School of Pythagoras

The nature of the right triangle has actually been known for centuries before the time of Pythagoras, as in Mesopotamia, also China. But the first written records that provide evidence comes from Pythagoras. Proof of the Pythagorean school presented in the figure below.
Note that:

 

The total area of the black in the image (1) is a² + b²

The total area of the black in the image (2) is c²

Therefore a² + b² = c²

 

2.    Other evidence using diagrams Pythagoras

The following evidence is simpler but use a little algebraic manipulation. Fourth right triangle is congruent arranged to form the image below.

By calculating the area of a square wake happens to be obtained in two ways:

(a + b)                     =          c² + 4. ½ ab

a² + 2ab + b²          =          c² + 2 ab

a² + b²                     =          c²