Two Elegant Proofs of the Pythagorean Theorem

Here’s Looking at Euclid by Helen Friel

Although one of the most well-known names in the mathematics world, we know very little about Pythagoras. Even though we named one of the most popular math theorems after him, we don’t even know if he was a brilliant mathematician or the leader of a terrorism-based cult, completely against innovation. Because we lack knowledge any deeper than legend from before 6 B.C., these traits will likely remain unknown.

Regardless, when we trace the past of the Pythagorean Theorem or a²+b²=c², i.e., the addition of the squares of the base and side of a right triangle equals the square of the hypotenuse, all clues lead to the time of Pythagoras and his cult. Modern discoveries, however, show that the Pythagorean Theorem was not unique to ancient Greece and was also used by the largest civilizations of the time, namely ancient China. To gain detailed information about the topic, you can read Frank Swetz, and T. Kao’s Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China.

But who first used the Pythagorean Theorem, and when? It is completely normal for you to first think of Pythagoras, but we don’t have any proof of that. We first see the Pythagorean Theorem and its proof in the 46th proposition of the father of Geometry, Euclid’s, Elements. In his book about Euclid, Proclus: A Commentary on the First Book of Euclid’s Elements…