Quotient height theorem Quotient height was born in China in 1 1 century BC. At that time, China's dynasty was the Western Zhou Dynasty, which was a slave society. In ancient China, it was about the mathematical works of the Western Han Dynasty during the Warring States Period &; Nbsp Zhou Xie nbsp The Book of Changes records a conversation between Shang Gao and Zhou Gong. Shang Gao said: "... so fold the moment, tick three, fix four, and cross the corner five." Quotient height means that when two right-angled sides of a right-angled triangle are 3 (short side) and 4 (long side) respectively, the radius angle (chord) is 5. In the future, people will simply describe this fact as "hooking three strands, four strings and five". This is the famous Pythagorean theorem. Nbsp; Regarding the discovery of Pythagorean Theorem, "Zhou Parallel Computing Book" said: "So, the reason why Yu ruled the world was born of this number." This number "refers to" hook three strands, four chords and five ",which means that this relationship was discovered by Pythagoras theorem when Dayu was in charge of water control. It is said that Pythagoras theorem was first discovered by ancient Greek mathematicians more than 500 BC. Therefore, this theorem is also called "Pythagoras Theorem". France and Belgium call it "donkey bridge theorem", Egypt calls it "Egyptian triangle" and so on. However, they were all discovered much later than our country. Proof of Zhao Shuang and Pythagorean Theorem Zhao Shuang is unique and innovative. He proved the identity relationship between algebraic expressions by cutting, cutting, spelling and supplementing geometric figures, which was rigorous and intuitive, and set a model for China's unique ancient style of proving numbers by shape, unifying numbers by shape, and closely combining algebra and geometry. Later mathematicians mostly inherited this style and developed it from generation to generation. For example, Liu Hui later proved Pythagorean theorem by means of formal proof of numbers, but the division, combination and complement of specific numbers are slightly different. The discovery and proof of Pythagorean theorem by ancient mathematicians in China has a unique contribution and position in the history of mathematics in the world. In particular, the thinking method of "unity of form and number" embodied in it is of great significance to scientific innovation. In fact, the thinking method of "unity of form and number" is an extremely important condition for the development of mathematics. As Wu Wenjun, a contemporary mathematician in China, said: "In traditional mathematics in China, the relationship between quantity and spatial form often develops side by side ... Descartes invented analytic geometry in17th century, which is the reappearance and continuation of China's traditional thought and method after hundreds of years' pause. Why did the president think of proving Pythagorean theorem? Is he a mathematician or a math lover? The answer is no. Here's the story. 1876 One weekend evening, on the outskirts of Washington, D.C., a middle-aged man was walking and enjoying the beautiful scenery in the evening. He was a party member in Ohio and Garfield. As he was walking, he suddenly found two children on a small stone bench nearby, talking intently and sometimes arguing loudly. Sometimes, I whisper. Curious, Garfield went to the two children to find out what they were doing. I saw a little boy bend down and draw a right triangle on the ground with branches. So Garfield asked them what they were doing. The little boy said without looking up, "Excuse me, sir, if the two right angles of a right triangle are 3 and 4 respectively, what is the length of the hypotenuse?" Garfield replied, "It's 5." The little boy asked again, "If the two right angles are 5 and 7 respectively, what is the length of the hypotenuse of this right triangle?" Garfield replied without thinking, "The square of the hypotenuse must be equal to the square of 5 plus the square of 7." The little boy added, "Sir, can you tell the truth?" Garfield was speechless for a moment, unable to explain, and his psychology was very bad. So Garfield stopped walking and went home immediately to concentrate on discussing the problems left by the little boy. After repeated thinking and calculation, he finally figured out the truth and gave a concise proof method. Applications are designed to solve this problem. A right triangle knows the length of two long sides and finds the third side.