One of the simplest and most important proofs is the Pythagorean Theorem . It provides a valuable engineering insight on how to create a right angle using any material to form the angle and a measuring device. It is named after the legendary Greek mathematician Pythagoras of Samos who according to legend was the first to provide a proof of this theorem. A right triangle is any triangle where one of its interior angles is 90 degrees. Clearly, there can only be one such angle. If there were two, then the two opposite lines forming the right angles would be parallel and not be able to form a triangle (this idea is known as the parallel postulate and while it is intuitive, its proof requires some very non-trivial assumptions). When we look at a right triangle, we can see that the line opposite the right angle is the longest side which is called the hypotenuse. According to Wikipedia , this name is derived from the Greek for "subtending the right angle". ...