The history of this theorem can be divided into three parts: the discovery of Pythagorean number, the discovery of the relationship between the sides of right triangle and the proof of its theorem.
The Pythagorean number was found earlier, such as (3,4,5) in Egyptian cursive script, and the largest Pythagorean array involved in Babylonian clay tablets was (13500, 12709, 1854 1). Later, China's mathematics classics and Indian and Arabic mathematics books were also recorded.
In China, (3, 4, 5), a set of Pythagorean numbers, was also recorded in the book "Weekly Parallel Computing". When Ye Li, a mathematician in Jin Dynasty, measured the sea mirror, he established a systematic celestial technique through the relationship between 15 pythagorean shapes and the diameter of the pythagorean circle schema, and deduced the formulas of each side of 692 pythagorean shapes, taking several groups of pythagorean numbers as examples.
The quantity and quality of Pythagoras numbers obtained by Babylonians are unlikely to be obtained purely by measurement. Pythagoras himself has no works handed down from generation to generation. However, a thousand years after his death, Proch in the 5th century attributed the earliest discovery and proof to Pythagoras School when he annotated Euclid's masterpiece The Elements of Geometry.
Plutarch and Cicero also attributed this discovery to Pythagoras, but there is no evidence that Pythagoras proved Pythagoras theorem, and Pythagoras, who is famous for his vegetarian diet, is even more incredible in killing cattle.
In China, mathematics books about the Qin Dynasty did not record Pythagorean theorem, but only recorded some Pythagorean numbers.
In Nine Chapters Arithmetic Notes, Liu Hui used Pythagorean Theorem to find pi for many times, and used "digging and filling method" to make a "blue-black diagram" to complete the geometric proof of Pythagorean Theorem.
There is still much debate about whether Pythagorean theorem has been discovered more than once.
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There are many ways to prove this theorem, and the method to prove it may be the most among many theorems in mathematics. Elisha Scott Loomis's Pythagorean proposition always mentions 367 ways of proof.
Some people will try to prove Pythagorean theorem by trigonometric identities (such as Taylor series of sine and cosine functions), but all basic trigonometric identities are based on Pythagorean theorem, so they cannot be used as proof of Pythagorean theorem (see circular argument).