Kanika Khara
Feb 18, 2019

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The Pythagorean theorem got its name from the ancient Greek mathematician Pythagoras, who was considered to be the first to provide the proof of this theorem. But it is believed that people noticed the special relationship between the sides of a right triangle, long before Pythagoras.

The Pythagorean theorem plays a significant role in many fields related to mathematics. For example, it forms the basis of trigonometry, and in its arithmetic form, it combines both geometry and algebra.

The theorem is a relation in Euclidean geometry among the three sides of a right triangle. It states that '*the sum of the squares of the lengths of the two other sides of any right triangle will equal the square of the length of the hypotenuse*'.

Mathematically, the theorem is usually written as: **a**^{2} + b^{2} = c^{2} - where 'a' and 'b' represent the lengths of the two other sides of the triangle, and 'c' represents the length of the hypotenuse.

The history of the Pythagorean theorem can be divided as: knowledge of Pythagorean triples, the relationship among the sides of a right triangle and their adjacent angles, and the proofs of the theorem.

Around 4000 years ago, the Babylonians and the Chinese were aware of the fact that a triangle with the sides of 3, 4, and 5 unit lengths must be a right triangle.

They used this concept to construct right angles, and designed a right-angled triangle by dividing a long string into twelve equal parts, such that one side of the triangle is three, the second side is four, and the third side is five sections long.

Around 2500 BC, the Megalithic monuments in Egypt and Northern Europe comprised right triangles with integer sides. Bartel Leendert van der Waerden hypothesized that the Pythagorean triples were identified algebraically.

During the reign of Hammurabi the Great (1790 - 1750 BC), the Mesopotamian tablet Plimpton 32 consisted of many entries that were closely related to Pythagorean triples.

In India (8^{th} - 2^{nd} century BC), the Baudhayana Sulba Sutra comprised a list of Pythagorean triples, a statement of the theorem, and the geometrical proof of the theorem for an isosceles right-angled triangle.

Pythagoras (569-475 BC) used algebraic methods to construct the Pythagorean triples. According to Sir Thomas L. Heath, there was no ascription of the theorem for nearly five centuries after the time of Pythagoras.

However, authors like Plutarch and Cicero attributed the theorem to this Greek mathematician in such a way, that the attribution was widely known and accepted. In 400 BC, Plato established a method for finding Pythagorean triples, which blended both algebra and geometry.

Around 300 BC, in the Euclid's Elements, the oldest existing axiomatic proof of the theorem is presented. The Chinese text *Chou Pei Suan Ching* written between 500 BC and 200 AD had the visual proof of the Pythagorean theorem or 'Gougu theorem' (as known in China) for the right-angled triangle.

During the Han Dynasty (202 BC - 220 AD), the Pythagorean triples appear in the Nine Chapters on the Mathematical Art, along with the mentioning of such triangles. The first recorded use of the theorem in China was known 'Gougu theorem', and in India as the 'Bhaskara theorem'.

However, it is not yet confirmed whether Pythagoras was the first person to have found the relationship between the sides of the right triangles, as no texts written by him were found. Nevertheless, the theorem has still got his name credited to it.