At the beginning of China's earliest mathematical work "Parallel Calculation of Classics in Weeks", there was a dialogue in which Duke Zhou asked Shang Gao for mathematical knowledge. Duke Zhou asked, "I heard that you are very proficient in mathematics. Excuse me: there is no ladder to go up in the sky, and you can't use a ruler to measure one by one on the ground. So how can we get data about heaven and earth? " Shang Gao replied: "The number comes from the understanding of the other party and the circle." There is a principle: when the moment of a right triangle gets a right-angled side' hook' equal to 3 and the other right-angled side' chord' equal to 4, then its hypotenuse' chord' must be 5. This truth was summed up when Dayu was in charge of water conservancy. "From the above conversation, we can clearly see that people in ancient China discovered and applied the pythagorean theorem, an important principle of mathematics, thousands of years ago. Readers who know a little about plane geometry know that the so-called Pythagorean theorem means that in a right triangle, the sum of the squares of two right-angled sides is equal to the square of the hypotenuse. Pythagorean Theorem is called Pythagorean Theorem in the west, in which hook (a) and chord (b) respectively represent right triangles to get two right-angled sides, and chord (c) represents hypotenuse. In fact, this mathematical theorem was discovered and applied in ancient China much earlier than Pythagoras. If it can't be verified that Dayu's flood control is a long time ago, then the dialogue between Duke Zhou and Shang can be determined in the Western Zhou Dynasty around 1 100 BC, more than 500 years earlier than Pythagoras. Hooking 3 strands, 4 strings and 5 strings is a special application of Pythagorean theorem (32+42=52). So it should be very appropriate to call it Pythagorean Theorem in the field of mathematics now. In the later book "Nine Chapters of Arithmetic", Pythagorean Theorem got a more standardized general expression. The book Pythagorean Sheet says that you can multiply the hook and the stock separately, then add up their products, and then do the square root, and you can get the string. "Write this passage as an equation, that is, chord = (Gou 2+ Gu 2)( 1/2), that is, c=(a2+b2)( 1/2). Mathematicians in ancient China not only discovered and applied Pythagorean theorem very early, but also tried to prove it theoretically. Zhao Shuang, a mathematician of the State of Wu in the Three Kingdoms period, was the first to prove the Pythagorean theorem. Zhao Shuang created "Pythagorean Square Diagram" and gave a detailed proof of Pythagorean theorem by combining shape and number. In this Pythagorean Square Diagram, the square ABDE with the chord as the side length is composed of four equal right triangles and a small square in the middle. The area of each right triangle is AB/2; If the side length of a small square is b-a, the area is (b-a)2. Therefore, the following formula can be obtained: 4×(ab/2)+(b-a)2=c2. After simplification, we can get: a2+b2=c2, that is, c=(a2+b2)( 1/2).