How The Pythagorean Theorem Helps Solve a Right Triangle

The Pythagorean equation is most often attributed to Pythagoras of Somos, but we now know that many ancient civilizations like those in Egypt, India and China had discovered the mathematical relationship independently.

That said, the man whom this math trick is named for is nearly as fascinating. Pythagoras, an ancient Greek thinker who was born on the island of Samos and lived from 570 to 490 B.C.E, was kind of a trippy character — equal parts philosopher, mathematician and mystical cult leader.

In his lifetime, Pythagoras wasn’t known as much for solving for the length of the hypotenuse as he was for his belief in reincarnation and adherence to an ascetic lifestyle that emphasized a strict vegetarian diet, adherence to religious rituals and plenty of self-discipline that he taught to his followers.

Pythagoras biographer Christoph Riedweg describes him as a tall, handsome and charismatic figure, whose aura was enhanced by his eccentric attire — a white robe, trousers and a golden wreath on his head. Odd rumors swirled around him — that he could perform miracles, that he had a golden artificial leg concealed beneath his clothes and that he possessed the power to be in two places at one time.

Pythagoras founded a school near what is now the port city of Crotone in southern Italy, which was named the Semicircle of Pythagoras. Followers, who were sworn to a code of secrecy, learned to contemplate numbers in a fashion similar to the Jewish mysticism of Kaballah. In Pythagoras’ philosophy, each number had a divine meaning, and their combination revealed a greater truth.

With a hyperbolic reputation like that, it’s little wonder that Pythagoras was credited with devising one of the most famous theorems of all time, even though he wasn’t actually the first to come up with the concept. Chinese and Babylonian mathematicians beat him to it by a millennium.

“What we have is evidence they knew the Pythagorean relationship through specific examples,” writes G. Donald Allen, a math professor and director of the Center for Technology-Mediated Instruction in Mathematics at Texas A&M University, in an email. “An entire Babylonian tablet was found that shows various triples of numbers that meet the condition: a² + b² = c².”

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