Who Invented the Pythagorean Theorem?

Who invented the Pythagorean Theorem? That is hard to say, since its fundamental principles have been known since ancient times. Still, there is a great history behind this theorem that both mathematicians and historians should know.

Hundreds of years before Pythagoras, Egyptians discovered a way to make a right angle. In their construction of buildings, they had a rope with evenly spaced knots. They knew that if they made a triangle with it, and the sides were three, four, and five lengths, the angle between the two shorter sides would be a right angle, or a 90 degree angle. This is called a special triangle because it shows the relationship of right triangles in a simple and useful way.  Since you could use this rope to make a right angle, characteristics or all right triangles were not discovered until years later.

The Chinese were also aware of this special relationship between the sides of a right triangle. Tschou-Gun, who lived in 1100 BC, understood these relationships.  Archeological evidence shows that the Babylonians and Caldeans were also aware of this special right triangle.  

The Right Angle

Ancient peoples knew about the relationship, but did not have a theorem about it.  Back then, they explained mathematical principles with words. It took someone to study right angles to see if there was a principle that was true of all right triangles. 

After much study, the mathematical relationship in right triangles was discovered: In a right triangle, if you square the length of the two shorter sides and add them together, that will equal the length of the longest side squared. So, 3 squared is 9, 4 squared is 16, and 5 squared is 25. 9 plus 16 equals 25. This was only the first step. The next question is whether or not this applies to all right triangles. With further study, Pythagoras proved that this relationship was true for any right triangle. Today, there are hundreds of proofs of this theorem.  

Who Invented the Pythagorean Theorem?

Sometimes the person credited with a discovery, or theorem, simply publishes his findings or explains what he has learned. Pythagoras formed a group called the Brotherhood of Pythagoreans. They tried to find mathematical explanations for everything in nature. 

Pythagoras thought everything could be explained through numbers and their relationships. Since he was a famous scholar and leader of this group, he demonstrated this theorem and it became popular. Hence, it bears his name. 

Pythagoras

So, who invented the Pythagorean Theorem?  It is named after Pythagoras, who was born around 570 B.C. in Greece. When he was around 18, he studied astronomy, mathematics, and philosophy, among other things. As a young man, he traveled to Egypt to further his studies and learned geometry Egyptian priests.

He started the group the Brotherhood of Pythagoreans, which was almost a cult, as they seemed to worshipped numbers and their relationships. They explored mathematics and wrote geometric proofs, but wanted to keep their findings secret. Therefore, we don’t know if he is actually the person responsible for the theorem.

The Pythagoreans made an interesting and disturbing discovery. Because of their secrecy, no one else knew about it. They discovered irrational numbers. This came from trying to find out if the theorem applied to all right triangles. In looking at an isosceles triangle, if the 2 equal sides measure 1, the hypotenuse will measure the square root of 2. This number cannot be expressed using a ruler; hence it is an irrational number. 

This baffled the Pythagoreans, so they considered these numbers to be “unutterable.” All the Pythagoreans were warned not to mention the existence of these numbers. It was not until much later that people found a way to deal with these numbers. Two hundred years later, Eudoxus, a Greek mathematician, formulated a means of dealing with “unutterable” numbers. The answer to the question, “Who invented the Pythagorean Theorem?” would have to be Pythagoras. Perhaps he had help from the Pythagoreans, but he certainly demonstrated and taught that theorem to the world.