This theorem is one of the most famous and useful theorems in
geometry. Pythagoras (580-496 B.C.), a Greek mathematician, was the first to
prove this theorem, so it has become known as the Pythagorean Theorem. However,
it appears that the Babylonians may have been aware of the theorem because they
were using its converse (If the square of the length of the hypotenuse equals
the sum of the squares of the lengths of the legs, then the triangle is a right
triangle) more than 1300 years before Pythagoras.
It is a theorem that states a relationship that exists in any
right triangle. If the lengths of the legs in the right triangle are a and b and
the length of the hypotenuse is c, we can write the theorem as the following
A model of the theorem is shown below. Squares have been
constructed on the sides of the right triangle and the area of each square has
been dissected into squares. Count the gridded cells in the two squares
constructed on the legs of the triangle. They should add up to the number of
gridded cells in the square constructed on the hypotenuse.
Many people have come up with their own version of the proof of
the Pythagorean Theorem. Even President Garfield wrote a special version of the
proof in 1876. Click to see Garfield's
proof of the Pythagorean Theorem.