The Pythagorean Theorem

 

Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in southern Italy. Pythagoras was a teacher, a philosopher, a mystic and, to his followers, almost a god. His thinking about mathematics and life was riddled with numerology.

 

The Pythagorean Theorem exhibits a fundamental truth about the way some pieces of the world fit together. Many mathematicians think that the Pythagorean Theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a2 + b2 = c2

 

The figure above at the right is a visual display of the theorem's conclusion. The figure at the left contains a proof of the theorem, because the area of the big, outer, green square is equal to the sum of the areas of the four red triangles and the little, inner white square:

 

c2 = 4(ab/2) + (a - b)2 = 2ab + (a2 - 2ab + b2) = a2 + b2