請給我畢氏定理的歴史(請用english回答)(十五分鐘内回答)

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In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery,[1] although knowledge of the theorem almost certainly predates him. The theorem is known in China as the "Gougu theorem" (勾股定理) for the (3, 4, 5) triangle.
History
The history of the theorem can be divided into three parts: knowledge of Pythagorean triples, knowledge of the relationship between the sides of a right triangle, and proofs of the theorem.
Megalithic monuments from 4000 BC in Egypt, and in the British Isles from circa 2500 BC, incorporate right triangles with integer sides.[1] Bartel Leendert van der Waerden conjectures that these Pythagorean triples were discovered algebraically.[2]
Written between 2000–1786 BC, the Middle Kingdom Egyptian papyrus Berlin 6619 includes a problem whose solution is a Pythagorean triple.
During the reign of Hammurabi, the Mesopotamian tablet Plimpton 322, written between 1790 and 1750 BC, contains many entries closely related to Pythagorean triples.
The Baudhayana Sulba Sutra, the dates of which are given variously as between the 8th century BCE and the 2nd century BCE, in India, contains a list of Pythagorean triples discovered algebraically, a statement of the Pythagorean theorem, and a geometrical proof of the Pythagorean theorem for an isosceles right triangle.
The Apastamba Sulba Sutra (circa 600 BC) contains a numerical proof of the general Pythagorean theorem, using an area computation. Van der Waerden believes that "it was certainly based on earlier traditions". According to Albert Bŭrk, this is the original proof of the theorem, and Pythagoras copied it on his visit to India. Many scholars find van der Waerden and Bŭrk's claims unsubstantiated[citation needed].
Pythagoras, whose dates are commonly given as 569–475 BC, used algebraic methods to construct Pythagorean triples, according to Proklos's commentary on Euclid. Proklos, however, wrote between 410 and 485 AD. According to Sir Thomas L. Heath, there is no attribution of the theorem to Pythagoras for five centuries after Pythagoras lived. However, when authors such as Plutarch and Cicero attributed the theorem to Pythagoras, they did so in a way which suggests that the attribution was widely known and undoubted.
Around 400 BC, according to Proklos, Plato gave a method for finding Pythagorean triples that combined algebra and geometry. Circa 300 BC, in Euclid's Elements, the oldest extant axiomatic proof of the theorem is presented.
Written sometime between 500 BC and 200 AD, the Chinese text Chou Pei Suan Ching (周髀算经), (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) gives a visual proof of the Pythagorean theorem — in China it is called the "Gougu Theorem" (勾股定理) — for the (3, 4, 5) triangle. During the Han Dynasty, from 200 BC to 200 AD, Pythagorean triples appear in The Nine Chapters on the Mathematical Art, together with a mention of right triangles.[3]
There is much debate on whether the Pythagorean theorem was discovered once or many times. B.L. van der Waerden asserts a single discovery, by someone in Neolithic Britain, knowledge of which then spread to Mesopotamia circa 2000 BC, and from there to India, China, and Greece by 600 BC. Most scholars disagree however, and favor independent discovery.
More recently, Shri Bharati Krishna Tirthaji in his book Vedic Mathematics claimed ancient Indian Hindu Vedic proofs for the Pythagoras Theorem.

Pythagoras' Theorem claims that the sum of (the areas of) two small squares equals (the area of) the big one.

The theorem is of fundamental importance in the Euclidean Geometry where it serves as a basis for the definition of distance between two points.

The statement of the Theorem was discovered on a Babylonian tablet circa 1900-1600 B.C. Whether Pythagoras (c.560-c.480 B.C.) or someone else from his School was the first to discover its proof can't be claimed with any degree of credibility. Euclid's (c 300 B.C.) Elements furnish the first and, later, the standard reference in Geometry. In fact Euclid supplied two very different proofs: the Proposition I.47 (First Book, Proposition 47) and VI.31. The Theorem is reversible which means that a triangle whose sides satisfy a2 + b2 = c2 is necessarily right angled. Euclid was the first (I.48) to mention and prove this fact.

W. Dunham [Mathematical Universe] cites a book The Pythagorean Proposition by an early 20th century professor Elisha Scott Loomis. The book is a collection of 367 proofs of the Pythagorean Theorem and has been republished by NCTM in 1968. In the Foreward, the author rightly asserts that the number of algebraic proofs is limitless as is also the number of geometric proofs, but that the proposition admits no trigonometric proof. Curiously, nowhere in the book does Loomis mention Euclid's VI.31 even when offering it and the variants as algebraic proofs 1 and 93 or as geometric proof 230.

Pythagoras (569-500 B.C.E.) was born on the island of Samos in Greece, and did much traveling through Egypt, learning, among other things, mathematics. Not much more is known of his early years. Pythagoras gained his famous status by founding a group, the Brotherhood of Pythagoreans, which was devoted to the study of mathematics. The group was almost cult-like in that it had symbols, rituals and prayers. In addition, Pythagoras believed that "Number rules the universe,"and the Pythagoreans gave numerical values to many objects and ideas. These numerical values, in turn, were endowed with mystical and spiritual qualities.

Legend has it that upon completion of his famous theorem, Pythagoras sacrificed 100 oxen. Although he is credited with the discovery of the famous theorem, it is not possible to tell if Pythagoras is the actual author. The Pythagoreans wrote many geometric proofs, but it is difficult to ascertain who proved what, as the group wanted to keep their findings secret. Unfortunately, this vow of secrecy prevented an important mathematical idea from being made public. The Pythagoreans had discovered irrational numbers! If we take an isosceles right triangle with legs of measure 1, the hypotenuse will measure sqrt 2. But this number cannot be expressed as a length that can be measured with a ruler divided into fractional parts, and that deeply disturbed the Pythagoreans, who believed that "All is number." They called these numbers "alogon," which means "unutterable." So shocked were the Pythagoreans by these numbers, they put to death a member who dared to mention their existence to the public. It would be 200 years later that the Greek mathematician Eudoxus developed a way to deal with these unutterable numbers.