We were Always Wrong About the Origin of the Pythagoras Theorem

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Origin of Pythagoras theorem

There is no need for an introduction to the Pythagoras theorem. Everyone in their academics must have read Pythagoras theorem i.e

sqar(length) + sqar(height) = sqar(hypothesize).

But do you know Pythagoras wasn’t the first who invented this equation? Then who and when this equation was first used. What is the Pythagoras contribution to this?  In today’s video, we are going to explore the origin of the Pythagoras equation. So without losing time let’s start today’s video.

Egyptian Version

The Egyptians had a very interesting strategy to improve the stability of the pyramids’ walls that originates in 2,500 BC in Egypt.  They used a rope, with 12 knots tied evenly spaced, which resulted in the famous 3-4-5 triangle, forming a 90°angle. 

Knotted cords were used by rope stretchers, who measured out the boundaries of fields in Ancient Egypt. The knotted cords were 100 royal cubits in length with a knot every hayt. A hayt is 10 royal cubits (1.9102196752627) . The rope stretchers stretched the rope in order to take the sag out it and keep the measures uniform.

Twelve know rope egypt

Let’s take one example:- Suppose Egyptians were creating the pyramid and they had a mechanism to pull the stone through rope already in place. So to get the length of rope to pull the stone till the top of the pyramid they might have used this way.

Let’s assume they wanted to build a 150 m high and 400 m wide pyramid. Then the length of the rope will be 250  the output of the Pythagoras equation as well. 

(200/4)*5 = 250 which will be the output of Pythagoras equation as well.

12 knot example

There is no doubt that Egyptians were well aware of this Pythagoras triplets but didn’t use by this name and there is no written evidence as well. There’s a big probability that they had knowledge of it.

More Reading

Mesopotamian Version

We already know that each and every information in ancient Mesopotamia was written on the clay tablets in cuneiform script. A Mesopotamian version of the Pythagoras theorem is available on one of the clay tablets which is believed to have been written about 1800 BC.

That tiny clay tablet has a table of four columns and 15 rows of numbers in the cuneiform script of the period. This table lists two of the three numbers in what is now called Pythagorean triples, i.e.,

integers ab, and c satisfying a2 + b2 = c2.

Pythagoras clay tablet mesopotamia

From a modern perspective, a method for constructing such triples is a significant early achievement, known long before the Greek and Indian mathematicians discovered solutions to this problem.

[These 5 Clay Tablet Presents Sumerian Mathematical Strength]

The main content of the tablet is a table of numbers, with four columns and fifteen rows, in Babylonian sexagesimal notation or base 60. A fourth column is just a row number, in order from 1 to 15. The second and third columns are completely visible in the surviving tablet.

Pythagoras clay tablet mesopotamia in decimal format

Let’s take one example from above table. Equation

Pythagoras clay tablet mesopotamia example

That tablet shows that ancient Mesopotamian people had a knowledge of the Pythagorean theorem in a more general framework. But again there’s no written statement of the theorem.

Indian Version

Indian Version of the as Pythagoras theorem is known as Baudhayana theorem which is available in the Baudhāyana Sulba Sūtra which perhaps compiled in the 8th to 6th centuries BCE probably three centuries before the Pythagoras. There’s the first explicitly written Pythagoras theorem that says: if you have a right triangle, the square of the length of the hypotenuse is the sum of the square of the length of the two legs.

Pythagoras Indian Version

A rope stretched along the length of the diagonal produces an area which the vertical and horizontal sides make together

Original statement

Since the diagonal of a rectangle is the hypotenuse of the right triangle formed by two adjacent sides, the statement is seen to be equivalent to the Pythagorean theorem. That is written for the first time as a theorem for a general triangle in the Shuba Sutra of Baudhayan. At least, it is the first recorded instance.”

[Ancient Indian Mathematician Baudhayana’s Theorems and Practical Usage]

Greek Version

Pythagoras theorem is in the name of Pythagoras of Samos 570 – c.495 BC) who was an ancient Greek mathematician and philosopher and his statement of Pythagoras theorem state that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of these triangles have been named as Perpendicular, Base, and Hypotenuse.

For checking his proof consider the following figure. 

Example

The area of the first square is given by (a+b)^2 or 4(1/2ab)+ a^2 + b^2.

The area of the second square is given by (a+b)^2 or 4(1/2ab) + c^2.

Since the squares have equal areas we can set them equal to another and subtract equals. The case (a+b)^2=(a+b)^2 is not interesting. Let’s do the other case. 

4(1/2ab) + a^2 + b^2 = 4(1/2ab)+ c^2

Subtracting equals from both sides we have a^2 + b^2 = c^2 concluding Pythagoras’ proof.

Conclusion

If wee see Pythagoras theorem chronologically, we will find that Egyptian was the oldest one using this but didn’t had any connection with mathematics, second record we find on Mesopotamian clay tablet where we see mathematic relationship between numbers. N Indian version we can see that Baudhayana proves this theorem with the help of area and finally Pythagoras who proved this theorem geometrically.

Who invented first it depends on what standard we are using. If you want to be really rigorous and (ask) who first totally understood even the proof of that then it would naturally be the Pythagoras.

I hope you read something new today. Share your views in the comments section below.

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DHEERAJ JAIN

Hello, My name is Dheeraj Jain. I am a software engineer by profession and hobbyist historian. I am trying yo write content that has not been explored in the past. More info about me @ https://tathastuu.com/about-me

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