The Pythagorean theorem

Abstract

The Pythagorean theorem constitutes one of the first great ideas of mathematics. Its importance is evident in the fact that it has been taught in schools throughout human history; it has had many applications in science and engineering; it has cropped up in numerous other mathematical ideas; it has led to discoveries, such as Fermat’s last theorem; and the list could go on and on. In a phrase, the theorem is one of those ideas that have mattered to mathematics and to human history. This chapter looks at the theorem and at why it is so profoundly important. It also deals with some key concepts that the theorem has introduced, including irrational numbers.