A visual proof of the Pythagorean theorem

Wolfgang Slany
http://slany.org/wolfgang/
http://www.dbai.tuwien.ac.at/proj/pf2html/

April 25, 2002

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 $b^2$.

82

Proof:

show proof

Bibliography

1
Chou pei suan ching: The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven, a Chinese astronomical and mathematical treatise. Exact date of origin unknown http://www.google.com/search?q=chou+pei+suan+ching.

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A visual proof of the Pythagorean theorem

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