Pythagorean theorem is a pearl in geometry, so it is full of charm. For thousands of years, people have been eager to prove it, including famous mathematicians, amateur mathematicians, ordinary people, distinguished dignitaries and even national presidents. Perhaps it is precisely because of the importance, simplicity and attractiveness of Pythagorean theorem that it has been repeatedly hyped and demonstrated for hundreds of times. 1940 published a proof album of Pythagorean theorem, which collected 367 different proof methods. In fact, that's not all. Some data show that there are more than 500 ways to prove Pythagorean theorem, and only the mathematician Hua in the late Qing Dynasty provided more than 20 wonderful ways to prove it. This is unmatched by any theorem.

Among these hundreds of methods of proof, some are very wonderful, some are very concise, and some are very famous because of the special identity of witnesses.

In foreign countries, especially in the west, Pythagorean theorem is usually called Pythagorean theorem. This is because they think that the right triangle has the property of "hook 2+ chord 2= chord 2", and Pythagoras, an ancient Greek mathematician, was the first to give a strict proof.

In fact, in earlier human activities, people have realized some special cases of this theorem. In addition to the Pythagorean theorem discovered in China more than 0/000 years ago, it is said that the ancient Egyptians also used the law of "hooking three strands, four chords and five" to determine the right angle. However, this legend has aroused the suspicion of many mathematical historians. For example, Professor M. Klein, an American mathematical historian, once pointed out: "We don't know whether the Egyptians realized the Pythagorean theorem. We know that they have people who pull the rope (surveyors), but the theory that they tied a knot on the rope, divided the whole length into three sections, 3, 4 and 5, and then used it to form a right triangle has never been confirmed in any literature. " However, archaeologists discovered several pieces of ancient Babylonian clay tablets, which were completed around 2000 BC. According to expert research, one of them is engraved with the following question: "A stick with a length of 30 units stands upright on the wall. How far is its lower end from the corner when its upper end slides down by 6 units? " This is a special case of a triangle with a side length of 3:4:5; Experts also found that there is a strange number table engraved on another board, in which * * * is engraved with four columns and fifteen rows of numbers, which is a Pythagorean number table: the rightmost column is the serial number from 1 to 15, while the left three columns are the values of stocks and hook chords respectively, and a * * * records/kloc-0.

Proof method:

Take four identical right triangles first. Put an (a+b) square, and the area of the beige square in the middle is c2. Figure (1) If you change the position of the triangle, you will see two beige squares with an area of (a2, b2). The areas of the four triangles in Figure (2) are unchanged, so the conclusion is: a2+b2 = c2.

History of Pythagorean Theorem;

Shang Gao was a native of 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 Warring States period.

Zhou Shu Yun Jing, a mathematical work in the Western Han Dynasty, recorded a dialogue between Shang Gao and Duke Zhou. Shang Gao said, "... so the moment is folded, and the shares are changed four times."

The phrase "Gao Gao" means that when the two right-angled sides of a right-angled triangle are 3 (short side) and 4 (long side) respectively, the diameter.

The angle (i.e. chord) is 5. In the future, people will simply call this fact "three strands, four strings and five". This is the famous Pythagorean theorem.

Regarding the discovery of Pythagorean theorem, Zhou said: "So, Yu ruled the world because of the birth of this number." "This number" means "hook"

"Three strands, four strings and five" means that the relationship between three strands, four strings and five was discovered when Dayu was in charge of water control.

Zhao Shuang:

Wu people from the end of the Eastern Han Dynasty to the Three Kingdoms period.

He took notes for Zhou Pian and wrote the Pythagorean Square.

Zhao Shuang's proof is ingenious and innovative. He proved the consistency between algebraic expressions by cutting, cutting, spelling and supplementing geometric figures.

Equivalence is not only rigorous but also intuitive, which is inseparable from the unity of form and number and the close combination of algebra and geometry in ancient China.

The unique style sets a good example. Later mathematicians mostly inherited this style and developed it. Liu Hui, for example, proved it later.

Pythagorean theorem is also a method to prove numbers in form, but the division, combination, displacement 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, especially among them.

The thinking method of "unity of form and number" is of great significance to scientific innovation. In fact, the thinking method of "unity of form and number" is correct.

It is an extremely important condition for the development of mathematics. As Wu Wenjun, a contemporary mathematician in China, said, "In China's traditional mathematics, the relationship between quantity and quantity.

Descartes invented analytic geometry in17th century, which is the traditional thought of China.

After hundreds of years of pause, ideas and methods reappear and continue. "

At the beginning of China's earliest mathematical work "Parallel Calculation of Classics in Weeks", there was a dialogue in which the Duke of 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 go with a ruler. "

A measurement, so how can we get the 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 a right triangle is a moment.

When one right-angled side "hook" equals 3 and the other right-angled side "strand" equals 4, then its hypotenuse "chord" must be 5. This truth was summed up when Dayu was in charge of water conservancy.