The Pythagorean Theorem
If the animation does not appear, click
here.
This animation gives a visual proof of the Pythagorean theorem.
(See notes below.)
The squares on the sides of the triangle deform into parallelograms, but the
parallelograms have the same bases as the original squares and the same
heights (because each is constrained by a pair of parallel lines,
so their areas remain identical to those of the squares. When the
moving parallelograms meet at the lower left, they deform upward together,
each constrained now by a different pair of parallel lines, into
the square on the hypotenuse. Once again, the deformations preserve areas,
so the area of the square on the hypotenuse is the sum of the areas of the
squares on the two sides. (11/16/07)