Most students have encountered the famous “a2 + b2 = c2” equation at some point during their academic journeys. This is the equation which maps out the correlation between the largest side of a right triangle, called the hypotenuse, and the two smaller sides, in which the sum of the two smaller sides squared (a2 + b2) is equal to the length of the hypotenuse squared (c2). This relationship is commonly referred to as the Pythagorean Theorem and attributed to the Greek mathematician and philosopher Pythagoras. Contrary to popular belief, Pythagoras was not the first to discover this relationship between the sides of a triangle.
Several tablets dating back to over 1,000 years before Pythogoras showcased the use of the theorem with which he is credited. The oldest tablet found is from 1800 BC and called the Plimpton 322. While this tablet does not directly present the use of the theorem, it lists 15 sets of Pythagorean triples, a set of numbers that satisfy the Pythagorean equation. This implies that the theorem had long been discovered and even put into practice. IM 67118 is another Babylonian tablet from the year 1770 BC which uses text and a diagram to determine how to find the area of a rectangle and the length of its diagonal. The final step to solving this problem, as carved on the tablet, utilizes the Pythagorean Theorem. The most advanced mathematical use of this formula is on the tablet labeled YBC 7289 which is estimated to be from between 1800 BC to 1600 BC. The carvings indicate that the use of the Pythagoras’ Theorem was in order to prove that the ratio between the sides of an isosceles right triangle is 1:1:√2. The math shown for defining this relationship was done on the Mesopotamian base of 60. Even though ancient Mesopotamians used a different number system compared to our standard base of 10 system, the writing on this tablet is still recognizable as the Pythagorean Theorem.
The tablets certainly change the perception that Pythagoras is the one behind the famous and useful equation. It also begs the question: Why is Pythagoras credited with such an important mathematical concept if there were many others who made use of it first? There are many possible explanations as to why this is the base, but what all stories have in common is that oral story-telling and the passing down of knowledge through word of mouth played a significant role. One theory is that Pythagoras, who was a very well-established philosopher, founded a school where every student truly believed in the brilliance of their educator. The pupils of Pythagoras were called the Pythagoreans and passage of knowledge via spoken word was extremely common within this group. This, combined with the respect the Pythagoreans had for their instructor, led them to credit him with the famous “a2 + b2 = c2” equation. Whether this is true or not is very difficult to confirm, as no original writing made by Pythagoras exists today, and his mentions in the accounts of others do not provide enough information on this. For this reason, if you ever find yourself struggling to solve the equation “a2 + b2 = c2,” do not solely blame Pythagoras.
