# A Practical Demonstration of the Pythagorean Theorem

The Pythagorean Theorem is probably the most popular theorem in school mathematics. Surely, you have heard or read about it at least once from elementary school to high school. The Pythagorean Theorem states that given a right triangle with shorter sides $a$, $b$, and hypotenuse $c$, the following equation holds

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

This theorem is illustrated above, but in a slightly different manner.  Notice that the demonstration shows equality in volume and not in area. The volume of the colored liquid inside the two smaller square prisms is equal to the volume of the water in the larger square prism. However, looking at the front view of the prisms (the square), the demonstration seems to verify the Pythagorean theorem.

Do you think the demonstration is valid? How do you think the square prisms were constructed?

The beauty of the Pythagorean Theorem lies in its hundreds of proofs (see example).  Even James Garfield, the 20th President of the United States was able to prove it.