Pythagoras's Theorem/Proof 4
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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
- For a video presentation of the contents of this page, visit the Khan Academy.