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 member of the Ohio * * * and Garfield Party. As he was walking, he suddenly found two children on a small stone stool 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 is speechless, unable to explain, and has a bad psychology. So Garfield stopped walking and immediately went home to discuss the problems left by the little boy. After repeated thinking and calculation, he finally figured it out and gave a concise proof method. On April 1876, Garfield published his proof of Pythagorean theorem in the New England Journal of Education. 188 1 year, Garfield became the twentieth president of the United States. Later, in order to commemorate his intuitive, simple, understandable and clear proof of Pythagorean theorem, people called this proof "presidential proof". Pythagorean theorem is also one of the most widely used theorems in mathematics. For example, starting from Pythagorean theorem, square roots and square roots are gradually developed; Finding pi by pythagorean theorem. It is said that the four right angles at the bottom of the pyramid are determined by this relationship. It is still used to pay off and "return to the square", that is, right-angle pay-off. Because of this, it is not surprising that people admire this theorem. Greece issued a stamp on 1955. The design consists of three chessboards. This stamp commemorates the Pythagorean School, a school and religious group in Greece 2,500 years ago, its establishment and its cultural contribution. The design on the stamp is an explanation of Pythagorean theorem. The proof method displayed on Greek stamps was first recorded in Euclid's Elements of Geometry. Nicaragua issued a set of ten commemorative stamps at 197 1 with the theme of "the ten most important mathematical formulas in the world", one of which is Pythagorean theorem. In 2002, the World Congress of Mathematicians was held in Beijing, China, which was the first gathering of mathematicians in the 2/kloc-0 century. The symbol of this congress chose the "string diagram" to verify Pythagorean theorem as the central pattern, which can be said to fully display the achievements of ancient mathematics in China and fully promote the ancient mathematics culture in China. In addition, through hard work, China finally won the right to host the 2002 Mathematicians' Congress, which is also the development of mathematics in China by the international mathematics community. Today, almost no one in the world doesn't know puzzles and puzzles. In foreign countries, it is called "Tangram", which means China map (not a map invented in the Tang Dynasty). Perhaps the history of Tangram can be traced back to Zhou Pian Shu Jing, an ancient book in pre-Qin China, in which square cutting was used to prove the Pythagorean theorem. At that time, the big square was cut into four identical triangles and a small square, that is, a string diagram, not a puzzle. Now the jigsaw puzzle has gone through a historical evolution. It was even suggested that a large-scale device should be built on the earth to show the visiting whispers that there is intelligent life on the earth. The most suitable device is a huge figure symbolizing Pythagorean theorem, which can be located in the Sahara desert, Siberia in the Soviet Union or other vast wasteland. Because all knowledgeable creatures must know this extraordinary theorem, outsiders are most likely to recognize it as a sign! ? Interestingly, except for the ternary quadratic equation x2+y2 =z2 (where X, Y and Z are unknowns), other ternary quadratic equations Xn+Yn = Zn (where N is a known positive integer and N > 2) cannot have positive integer solutions. This theorem is called Fermat's last theorem (Fermat was a French mathematician in17th century). References:

//wenwen.sogou/z/q657954815 Pythagorean theorem is also called Pythagorean theorem. Pythagoras was a famous philosopher, mathematician and astronomer in ancient Greece. Born in Samos about 580 BC, he died in Tarrington about 500 BC. In his early years, he traveled to Egypt and Babylon. In order to get rid of tyranny, he moved to Crotone in the south of the Italian peninsula and organized a secret society that integrated politics, religion and mathematics. Later, he lost in the political struggle and was killed. The Pythagorean school attaches great importance to mathematics and tries to explain everything with numbers. The purpose of their study of mathematics is not to be practical, but to explore the mysteries of nature. Pythagoras himself is famous for discovering Pythagoras theorem. In fact, Babylonians and China knew this theorem for a long time, but the earliest proof should be attributed to Pythagoras. Pythagoras was also the founder of music theory. He expounded the relationship between the musical sound of Dan Xian and the string length. In astronomy, he initiated the theory of the earth circle. Pythagoras' thoughts and theories have a great influence on Greek culture. 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. As shown in the figure, the right triangle of 1 in our figure is represented by a hook (a) and a chord (b) to get two right-angled sides, and the hypotenuse is represented by a chord (c), so that we can get the Pythagorean theorem of hook 2+ chord 2= chord 2, that is, a2+b2=c2, which is called Pythagoras theorem in the west. It is said that the ancient Greek mathematician and philosopher Pythagoras 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. Then we can get the following formula: 4×(ab/2)+(b-a)2=c2. After simplification, we can get: a2+b2=c2, that is, c=(a2+b2)( 1/2). Fig. 2 Pythagorean diagram and Garfield's story of proving Pythagorean theorem 1876. Walking, he suddenly found two children talking about something with rapt attention on a small stone bench nearby, arguing loudly and discussing in a low voice. Driven by curiosity, Garfield followed the sound and came 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, "Five." 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 and unable to explain, and he was very unhappy. So Garfield stopped walking and immediately went home to discuss the questions the little boy gave him. After repeated thinking and calculation, he finally figured it out and gave a concise proof method. On April 1876, Garfield published his proof of Pythagorean theorem in the New England Journal of Education. Five years later, Garfield became the twentieth president of the United States. Later, in order to commemorate his intuitive, simple, easy-to-understand and clear proof of Pythagorean theorem, people called this proof "presidential proof" of Pythagorean theorem and it was passed down as a story in the history of mathematics. After studying similar triangles, we know that in a right triangle, the height on the hypotenuse divides the right triangle into two right triangles similar to the original triangle. As shown in the figure, in Rt△ABC, ∠ ACB = 90. Let CD⊥BC and vertical foot be D. Then △BCD∽△BAC, △CAD∽△BAC. From △BCD∽△BAC, we can get BC2=BD? BA, ① AC2=AD can be obtained from △CAD∽△BAC? AB .② We found that by adding ① and ②, we can get BC2+AC2=AB(AD+BD) and AD+BD=AB, so we have BC2+AC2=AB2, which means a2+b2=c2. This is also a method to prove Pythagorean theorem, and it is also very concise. It makes use of similar triangles's knowledge. In the numerous proofs of Pythagorean theorem, people also make some mistakes. For example, some people have given the following methods to prove Pythagorean theorem: let △ABC, ∠ C = 90, and cosC=0 follow the cosine theorem c2=a2+b2-2abcosC, because ∠ C = 90. So a2+b2=c2. This seemingly correct and simple proof method actually makes a mistake in the theory of circular proof. The reason is that the proof of cosine theorem comes from Pythagorean theorem. In ancient China, there were 3 strands, 4 strings and 5 hooks.