Pythagoras's Theorem/Proof 4

Theorem

Let $\triangle ABC$ be a right triangle with $c$ as the hypotenuse.

Then:

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


Proof

Dissect the square on the left (which has area $c^2$) as shown.

Rearrange the pieces to make the two squares on the right, with areas $a^2$ and $b^2$.

$\blacksquare$


Source of Name

This entry was named for Pythagoras of Samos.


Historical Note

This proof was discovered by Bhaskara II Acharya.

As he is then reported as saying:

Behold!


Sources

  • 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.1$: The Pythagorean Theorem
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