*Elements*

Many mathematicians from antiquity to modern times had marveled at this rule and proved it in different ways. Here we will see how Bhaskara, one of the most important mathematicians of old India proved it geometrically.

The theorem says **a ^{2} + b^{2} = c^{2}** : where

*a*and

*b*are sides of a right triangle and

*c*is its hypotenuse

Bhaskara gives the following diagram to prove the theorem:

*Bhaskara’s description of Pythagoras Theorem*

From the picture, you can see that

Area Large squire is = Area of all 4 triangles + area of smaller squire

c * c = 4 * ( 1/2 ) a * b + (b-a) * (b-a) = 2ab – ( a^{2} + b^{2} + 2ab)**c ^{2} = a^{2} + b^{2}**

which is the Pythagorean theorem

Area Large squire is = Area of all 4 triangles + area of smaller squire

c * c = 4 * ( 1/2 ) a * b + (b-a) * (b-a) = 2ab + a2 + b2 – 2ab = a2 + b2

c2 = a2 + b2

which is the Pythagorean theorem