The Pythagorean Theorem by Bhāskara's Visual Demonstration (1114ca. 1185)
Minute Math presented by Math U.


Bhaskara's proof is a dissection proof. It is similar to the proof provided by Pythagoras. Bhaskara was born in India. He was one of the most important Hindu mathematicians of the twelve century AD. He used the following in proving the Pythagorean Theorem.

The red triangles are all congruent and the red squares are congruent. First we need to find the area of the big square two different ways. First let's find the area using the area formula for a square.
Thus, A=c^2.
Now, lets find the area by finding the area of each of the components and then sum the areas.
Area of the red triangles = 4(1/2)ab
Area of the red square = (ba)^2
Area of the big square = 4(1/2)ab + (ba)^2
= 2ab + b^2 2ab + a^2
= b^2 + a^2

Since, the square has the same area no matter how you find it
A = c^2 = a^2 + b^2,
concluding the proof.

Reference
jwilson.coe.uga.edu/emt668/emt668.student.folders/headangela/essay1/pythagorean.html