The Pythagorean theorem is one of the most ancient theorems of mathematics. The Pythagorean theorem states that in a right triangle (a triangle with a 90 degree angle), the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse; the legs of a right triangle are the two sides adjoining the 90 degree angle, and the hypotenuse is the opposite side. In terms of symbols, if the lengths of the legs are labeled a and b, and the hypotenuse is labeled c, the Pythagorean theorem states the famous relationship that a^2+b^2=c^2, the form in which the theorem is most commonly remembered. The Pythagorean theorem is one of the most powerful of the fundamental theorems of geometry. It is the basis for the definition of the distance between two points in the rectangular coordinate system...