The Pythagorean theorem is not Pythagoras’s!

What if I told you that the Pythagorean theorem wasn’t actually discovered by Pythagoras? You’d be surprised, right? But historical evidence suggests exactly that!

Is there anyone in this country who hasn’t heard of the Pythagorean theorem? Students memorize it extensively during lower and secondary school. Some even learn to understand and prove it.
 

The theorem states that in a right-angled triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides.
 

Don’t be intimidated by this formal definition. For those who haven’t thought about it in a while, here’s a simpler explanation: A right-angled triangle has one angle of 90 degrees. The side opposite this angle is called the hypotenuse. Let’s name the three sides a, b, and c, where c is the hypotenuse (opposite the 90-degree angle). According to the theorem, (a^2 + b^2 = c^2).
 

Historical evidence shows that the theorem attributed to Pythagoras was known long before him—or perhaps he merely rediscovered it. A clay tablet from ancient Babylon demonstrates the use of this theorem to calculate the length of a diagonal within a quadrilateral. This tablet is known as IM 67118. It dates back to around 1770 BCE, while Pythagoras was born in 570 BCE.

That’s not all. Another tablet, dated between 1800 and 1600 BCE, depicts a triangle within a square. The Babylonians used a base-60 number system, and translations show that they clearly knew the theorem. Back then, it certainly wasn’t called “Pythagoras’ theorem.” Moreover, they were familiar with many other advanced mathematical concepts long before Pythagoras’ time.

 

This topic needs a bit more explanation, which is clearly presented in a research paper by American mathematician Bruce Ratner titled “Pythagoras: Everyone Knows His Famous Theorem, But Not Who Discovered It 1000 Years Before Him”, published in the Springer journal. The title in Bengali would translate as: “Pythagoras: Everyone Knows His Famous Theorem, But Nobody Knows Who Discovered It a Thousand Years Before Him.”
 

Ratner writes, “The evidence is undeniable. The Babylonians knew the relationship between the diagonal of a square and its sides: (d = \sqrt{2}).” In his words, “This is probably the first known irrational number. Viewed differently, it also means they were familiar with the theorem that later became known as Pythagoras’ theorem. At the very least, they knew its special application the length of a square’s diagonal, (d^2 = a^2 + a^2 = 2a^2) (where (a) is the side of the square). And this was nearly a thousand years before the famous Pythagoras.”
 

There is another application of the Pythagorean theorem called the Pythagorean Triple. In Bengali, this can be called Pythagoras’ Triplet. These are sets of three positive integers whose squares satisfy the equation (a^2 + b^2 = c^2). Essentially, for a right-angled triangle with sides (a), (b), and (c) (hypotenuse), the numbers themselves form a Pythagorean triple. For example, ((3, 4, 5)).
 

A papyrus from 18th century BCE Middle Egypt contains a problem whose solution is the Pythagorean triple ((6, 8, 10)), though no triangle is explicitly mentioned in the text.

Not only Egypt, but ancient India’s Shulba Sutras also mention Pythagorean triples and the theorem. In these texts, the theorem and triples are applied specifically to isosceles right-angled triangles. That is, it is a particular application rather than the general usage of the theorem or triple. The Shulba Sutras date back to roughly 8th to 5th century BCE.


 

It is said that Pythagoras learned this theorem during his time in Egypt. So the question arises: why did it become famous under his name? How did he earn this credit? The answer is that none of Pythagoras’ own writings have survived in history. At that time, he had established a school whose students were called “Pythagoreans.” The school was located in what is now southern Italy. The knowledge he taught there gradually spread over time, and most of it eventually became associated with his name in historical records.
 

Why are none of his writings found? Because Pythagorean knowledge was taught orally, and written documentation was not common in that manner. As a result, many discoveries by the school’s students later became attributed to him.

Even if Pythagoras did not originally discover the theorem, his school popularized it. In this way, over a thousand years of history, the theorem gained fame under Pythagoras’ name.
 

Sources: IFLScience.com, Live Science, Springer, Wikipedia