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. I want to ask: there is no ladder in the sky to go up, and there is no ruler on the ground to measure. So how can you 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 is that in a right triangle, the sum of the squares of two right-angled sides is equal to the square of the hypotenuse. As the picture shows, we can see that

Figure 1 right triangle

Using hook (a) and rope (b) to represent right-angled triangle respectively to get two right-angled sides, and using chord (c) to represent hypotenuse, you can get:

Square of hook+square of strand = square of chord

Namely:

a^2+b^2=c^2

Pythagoras theorem is called Pythagoras theorem in the west, and it is said that Pythagoras, a mathematician and philosopher of Pythagoras, first discovered it in 550 BC. 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. Hook 3 strands, 4 chords and 5 is a special application of Pythagorean theorem (3 2+4 2 = 5 2). 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 Gou Gu Zhang said: "Multiply the hook and the stock separately, then add up their products and make a square root, and you can get the string." Put this passage into an equation, that is:

Square of chord = square of hook+square of strand.

Namely:

c^2=a^2+b^2

Mathematicians in ancient China not only discovered and applied Pythagorean Theorem very early, but also tried to prove Pythagorean Theorem in theory very early. 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 you can get the following formula:

4×(ab/2)+(b-a)^2=c^2

After simplification, you can get:

a^2+b^2=c^2

Namely:

c=√(a^2+b^2)

Figure 2 Pythagoras Square Diagram

Zhao Shuang's proof 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, 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. 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 China's traditional mathematics, the relationship between quantity and spatial form often develops side by side ... Descartes invented analytic geometry in the17th century, which is the reappearance and continuation of China's traditional thoughts and methods after hundreds of years of pause."

I hope it can be adopted. I wish you a happy new year.