Humorous story about the Pythagorean Theorem

Pythagorean was discovered on a weekend evening in 1876. On the outskirts of Washington, the capital of the United States, a middle-aged man was walking and admiring the beautiful scenery at dusk. He was the Republican Party of Ohio at that time. Congressman Garfield. As he was walking, he suddenly found two children on a small stone bench nearby who were concentrating on something, sometimes arguing loudly, sometimes discussing in a low voice. Curiosity drove Garfield to follow the sound and walked toward the two children, trying to find out what the two children were doing. I saw a little boy leaning over and drawing a right triangle on the ground with a branch. So Garfield asked them what they were doing. The little boy said without raising his head: "Excuse me, sir, if the two right-angled sides of a right triangle are 3 and 4 respectively, then what is the length of the hypotenuse?" Garfield replied: "It is 5." The little boy asked again: "If the two right-angled sides are 5 and 7 respectively, then what is the length of the hypotenuse of this right triangle?" Garfield replied without thinking: "The square of the hypotenuse must be equal to 5 Square plus 7 squared." The little boy said again: "Sir, can you tell the truth?" Garfield was speechless for a moment, unable to explain, and felt very uncomfortable. So Garfield stopped walking and immediately went home to discuss the problems the little boy had left for him. After repeated thinking and calculation, he finally figured out the reason and gave a concise proof method. On April 1, 1876, Garfield published his proof of the Pythagorean Theorem in the New England Educational Journal. In 1881, Garfield became the 20th President of the United States. Later, in order to commemorate his intuitive, simple, easy-to-understand, and clear proof of the Pythagorean theorem, people called this proof method the "presidential" proof method. The Pythagorean Theorem is also one of the most widely used theorems in mathematics. For example, starting from the Pythagorean theorem, the square root and the cube root were gradually developed; the Pythagorean theorem was used to calculate pi. It is said that the four right angles at the base of the pyramid are determined by applying this relationship. To this day, it is still used on construction sites to lay out lines and perform "returning", that is, placing lines at "right angles". Because of this, it is not surprising that people highly recommend this theorem. In 1955, Greece issued a stamp with a pattern of three checkerboards. This stamp commemorates the Pythagoreans, a school and religious group in Greece 2,500 years ago, its founding and cultural contributions. The image on the stamp is an illustration of the Pythagorean Theorem. The method of proof shown on Greek stamps was first recorded in Euclid's Elements. Nicaragua issued a set of ten commemorative stamps in 1971, with the theme of "the ten most important mathematical formulas" in the world, one of which was the Pythagorean theorem. The 2002 World Congress of Mathematicians was held in Beijing, China. This was the first major gathering of mathematicians in the 21st century. The logo of this conference selected the "string diagram" that verified the Pythagorean Theorem as the central pattern. It can be said that It fully reflects the achievements of ancient mathematics in my country and fully promotes the mathematical culture of ancient my country. In addition, after hard work, my country finally won the right to host the 2002 Mathematicians Conference. This is also the international mathematics community's full affirmation of the development of my country's mathematics. Today, almost everyone in the world does not know the tangram and the tangram. It is called "Tangram" abroad, which means Chinese figure (it was not a figure invented in the Tang Dynasty). The history of the jigsaw puzzle may be traced back to the ancient book "Zhou Bi Suan Jing" in my country's Pre-Qin Dynasty, which contains the square cutting technique and proved the Pythagorean theorem. At that time, a large square was cut into four identical triangles and a small square, which was a chord diagram, not a jigsaw puzzle. The current jigsaw puzzle has gone through a historical evolution process. Some people have even made the suggestion of building a large-scale device on the earth to show the existence of intelligent life to the "extraterrestrial visitors" who may visit. The most appropriate device is a symbol of the Pythagorean theorem. The huge graphics can be set in the Sahara Desert, Soviet Siberia or other vast wastelands. Because all knowledgeable creatures must know this extraordinary theorem, using it as a sign is most easily recognized by outsiders! ? What’s interesting is that: except for the three-dimensional quadratic equation x2 + y2 =z2 (where x, y, and z are all unknowns), which has positive integer solutions, the other n-dimensional three-dimensional equations xn + yn =zn (n is a known positive Integers, and n>2) cannot have positive integer solutions.

This theorem is called Fermat's Last Theorem (Fermat was a 17th-century French mathematician).

Reference: //wenwen.sogou/z/q657954815 The Pythagorean theorem is also called the Pythagoras theorem. Pythagoras was a famous philosopher, mathematician, and astronomer in ancient Greece. He was born in Samos around 580 BC and died in Tarinton around 500 BC. In his early years, he traveled to Egypt, Babylon and other places. In order to get rid of the tyranny, he moved to Crotone in the southern part of the Italian peninsula and organized a secret group that integrated politics, religion, and mathematics. Later, he failed in the political struggle and was killed. The Pythagoreans attached great importance to mathematics and tried to use numbers to explain everything. The purpose of their studying mathematics is not for practical purposes, but to explore the mysteries of nature. Pythagoras himself is famous for discovering the Pythagorean theorem. In fact, this theorem had been known to the Babylonians and Chinese for a long time, but the earliest proof should be attributed to Pythagoras. Pythagoras was also the originator of music theory. He clarified the relationship between the sound of a single string and its length. In astronomy, he pioneered the theory of a round earth. Pythagoras' thoughts and doctrines had a huge influence on Greek culture. The beginning of "Zhou Bi Suan Jing", one of China's earliest mathematical works, records a conversation in which Zhou Gong asked Shang Gao for mathematical knowledge: Zhou Gong asked: "I heard that you are very proficient in mathematics. I would like to ask: Tian There is no ladder to go up, and the earth cannot be measured section by section, so how can we get data about the sky and the earth?" Shang Gao replied: "The generation of numbers comes from the understanding of shapes such as squares and circles. : When the 'hook' of a right-angled side of a right triangle is equal to 3 and the 'strand' of the other right-angled side is equal to 4, then its hypotenuse 'chord' must be 5. This principle is that Dayu was controlling water. It was summed up at that time.” From the dialogue quoted above, we can clearly see that the people of ancient my country discovered and applied the important mathematical principle of the Pythagorean Theorem thousands of years ago. . Readers who have a little knowledge of plane geometry will know that the so-called Pythagorean theorem means that in a right triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse. As shown in the figure, we use Figure 1 of the right triangle to represent the right triangle with hooks (a) and strands (b) respectively to obtain two right-angled sides, and use chord (c) to represent the hypotenuse, then we can get: Hook 2 + Strand 2 = Chord 2, that is: a2+b2=c2 The Pythagorean theorem is called the Pythagoras theorem in the West. It is said that it was first discovered by Pythagoras, an ancient Greek mathematician and philosopher, in 550 BC. In fact, in ancient my country, people discovered and applied this mathematical theorem much earlier than Pythagoras. If Dayu's flood control cannot be accurately verified due to its long history, then the dialogue between Zhou Gong and Shang Gao can be determined to be in the Western Zhou Dynasty around 1100 BC, more than 500 years earlier than Pythagoras. The hook with 3 strands, 4 strings and 5 mentioned in it is a special application case of the Pythagorean theorem (32+42=52). So now the mathematical community calls it the Pythagorean Theorem, which should be very appropriate. In the later "Nine Chapters on Arithmetic", the Pythagorean Theorem received a more standardized general expression. The "Pythagorean Chapter" in the book says: "Multiply the hooks and strands by themselves, then add their products, and then take the square root, you can get the string." Put this passage into a formula, it is: string = (Gou 2 + Gu 2) (1/2) That is: c = (a2 + b2) (1/2) Ancient Chinese mathematicians not only discovered and applied the Pythagorean theorem very early, but also tried it very early Prove the theoretical proof of the Pythagorean theorem. The first person to prove the Pythagorean Theorem was Zhao Shuang, a mathematician from the State of Wu during the Three Kingdoms period. Zhao Shuang created a "Pythagorean Circle and Square Diagram", using the method of combining shapes and numbers to give a detailed proof of the Pythagorean theorem. In this "Pythagorean Square Diagram", the square abde obtained with the chord as the side length is composed of 4 equal right triangles plus the small square in the middle. The area of ??each right triangle is ab/2; if the side length of the small square in the middle is b-a, then the area is (b-a)2.

So 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) Figure 2 Pythagorean square diagram and the story of Garfield’s proof of the Pythagorean theorem. On a weekend evening in 1876, on the outskirts of Washington, the capital of the United States, a middle-aged man was walking and admiring the beautiful scenery at dusk. He was Ohio State* in the United States at that time. **And Party MP Garfield. As he was walking, he suddenly found two children on a small stone bench nearby who were concentrating on something, sometimes arguing loudly, sometimes discussing in a low voice. Driven by curiosity, Garfield followed the sound and walked towards the two children, trying to find out what the two children were doing. I saw a little boy leaning over and drawing a right triangle on the ground with a branch. So Garfield asked what they were doing? The little boy said without raising his head: "Excuse me, sir, if the two right-angled sides of a right triangle are 3 and 4 respectively, then what is the length of the hypotenuse?" Garfield replied: "It is 5." The little boy Then he asked: "If the lengths of the two right-angled sides are 5 and 7 respectively, then what is the length of the hypotenuse of this right triangle?" Garfield replied without thinking: "The square of the hypotenuse must be equal to 5 squared plus 7 square." The little boy said again: "Sir, can you tell the truth?" Garfield was speechless and couldn't explain, and he felt very uncomfortable. So Garfield stopped walking and went home immediately, where he concentrated on discussing the problems the little boy had asked him. After repeated thinking and calculation, he finally figured out the reason and gave a concise proof method. On April 1, 1876, Garfield published his proof of the Pythagorean Theorem in the New England Educational Journal. 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 the Pythagorean theorem, people called this proof the "presidential" proof of the Pythagorean theorem. This became a legend in the history of mathematics. After learning about similar triangles, we know that in a right triangle, the height on the hypotenuse divides the right triangle into two right triangles that are similar to the original triangle. As shown in the figure, in Rt△ABC, ∠ACB=90°. As CD⊥BC, the vertical foot is D. Then △BCD∽△BAC, △CAD∽△BAC. From △BCD∽△BAC, we can get BC2=BD ? BA, ① From △CAD∽△BAC, we can get AC2=AD ? AB. ② We find that by adding the two equations ① and ②, we can get BC2+AC2=AB (AD+BD), and AD+BD=AB, so BC2+AC2=AB2, which is a2+b2=c2. This is also a way to prove the Pythagorean Theorem, and it is also very simple. It utilizes the knowledge of similar triangles. In the numerous proofs of the Pythagorean Theorem, people also make some mistakes. For example, someone has given the following method to prove the Pythagorean theorem: Assume that in △ABC, ∠C=90°, and according to the cosine theorem c2=a2+b2-2abcosC, because ∠C=90°, so cosC=0. So a2+b2=c2. This proof seems correct and simple, but in fact it makes the mistake of circular proof. The reason is that the proof of the cosine theorem comes from the Pythagorean theorem. And in ancient China, there was a hook with 3 strands, 4 strings and 5