The Pythagorean Theorem
Here is a simple geometric proof of the Pythagorean theorem. The theorem says that if a and b are the lengths of the sides of a right triangle, and c is the length of the hypoteneuse, then we know that
This is one of the most elementary and important facts in mathematics. It is really at the foundation of the whole subject.
Just draw a large square of side (a + b) with a smaller, rotated, square of side c inside. Then express the area of the larger square in two ways: First, as (a + b)2 and, second, as the smaller c2 square plus the four triangles each (ab)/2. A liitle algebra and we have it.
Three lines of algebra and a diagram -- all you really need to prove one of our most important mathematical facts!