Pythagorean law, also known as Pythagorean chord theorem and Pythagorean theorem, is a basic geometric theorem, which means that the sum of squares of two right-angled sides (called hook length and head) of a right-angled triangle is equal to the square of hypotenuse length (called chord length). It is one of the most proven theorems in mathematical theorems, and it is also one of the ties of combining numbers with shapes. In ancient China, right-angled triangles were called pythagorean, the smaller right-angled side was a hook, the other longer right-angled side was a chord, and the hypotenuse was a chord, so it was called pythagorean theorem.
In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse. If the lengths of two right-angled sides of a right-angled triangle are A and B, respectively, and the length of the hypotenuse is C, then it can be expressed in mathematical language as: A? + b？ =c？ . Pythagorean theorem is a special case of cosine theorem.
1 1 century BC, proposed by Shang Gao, a mathematician of the Zhou Dynasty? Hook three, strand four, string five? . A dialogue between Shang Gao and Duke Zhou was recorded in The Book of Balance Calculation in Zhou Dynasty. Shang Gao said: therefore, the moment is folded, the hook is wide, the stock is repaired, and the angle is five. ? Meaning: When two right-angled sides of a right-angled triangle are 3 (hook) and 4 (chord) respectively, the radius angle (chord) is 5. In the future people will simply describe this fact as? Hook three strands, four strings and five? According to this allusion, Pythagorean theorem is called quotient height theorem.
In the 3rd century, Zhao Shuang in the Three Kingdoms period made detailed comments on the Pythagorean theorem in Nine Chapters of Arithmetic in Zhou Pian Shu Jing? Pythagoras shares are multiplied separately and divided by squares, that is, chords? Zhao Shuang created a picture? Pythagoras diagram? The Pythagorean theorem is proved in detail by combining shape and number. Later, Liu Hui also proved the Pythagorean theorem in Liu Hui's notes. Hua Hua, a mathematician in China in the late Qing Dynasty, put forward more than twenty proofs of Pythagorean theorem.
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The ancient Babylonians knew and applied Pythagorean theorem as early as around 3000 BC, and they also knew many Pythagorean sequences. How many pieces are collected in the library of Columbia University? Printon 322? Ancient Babylonian clay tablets recorded many Pythagorean figures. The ancient Egyptians also used Pythagorean theorem when building magnificent pyramids and measuring the land after the Nile flooded.
In the 6th century BC, the Greek mathematician Pythagoras proved the Pythagorean theorem, so westerners used to call it Pythagorean theorem.
In the 4th century BC, the Greek mathematician Euclid gave a proof in the Elements of Geometry (Volume I, Proposition 47).
On April 1876 and 1 day, Garfield published his proof of Pythagorean theorem in the New England Journal of Education. The Pythagorean proposition was published in 1940, and 367 different proofs were collected.