Proof of the Pythagorean Theorem Attributed to Pythagoras

There is a proof of the Pythagorean theorem that is said to have been given by Pythagoras himself.

However, since Pythagoras's original writings have not survived, we cannot be 100% certain that this was indeed his proof. According to ancient records (e.g., Proclus's commentary on Euclid's Elements), Pythagoras proved the theorem, and the achievement was passed down to later generations.

The proof traditionally attributed to Pythagoras uses a method of rearranging shapes. The four triangles in the first figure and the four triangles in the second figure have the same area, so the sum of the areas of the light yellow square and the light pink square equals the area of the light blue square.

Figure 1	Figure 2

Figure 3

Since the area of a square is the square of the length of its side, the right triangle in the third figure satisfies the Pythagorean theorem:

$a^2 + b^2 = c^2$