Wednesday, January 24, 2007

A Visual Proof of the Pythagorean Theorem

Here's a neat visual proof of the Pythagorean theorem:

Theorem ([1]): The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides. Stated algebraically, for a right triangle with sides of lengths $a$, $b$, and $c$, where $c$ is the length of the hypotenuse,

\begin{displaymath}a^2 +b^2 = c^2\;.\end{displaymath}

For example, the area of the square labeled $c^2$ in the following figure is equal to the sum of the areas of the squares labeled $a^2$ and $b^2$.

Here's a visual proof showing exactly how the theorem works:

See more examples of visual explanation.

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