Did ancient China prove the Pythagorean theorem? 70

Zhao Shuang of the <> Three Kingdoms era on the "Zhou Ji Sutra".

The Pythagorean theorem.

Zhao Shuang created a "Pythagorean square diagram", which was obtained by combining shapes and numbers, and gave a detailed proof of the Pythagorean theorem.

Liu Hui. The Pythagorean theorem was also proved in Liu Hui's note. Qingzhu entry and exit diagram is a geometric proof method used by mathematician Liu Hui in the late Eastern Han Dynasty to prove the Pythagorean theorem by using the relationship between numbers and shapes according to the "cutting and mending technique", which has distinctive characteristics and is easy to understand.

Liu Hui described this diagram, "Hook self-multiplication is the Zhu square, and the strand is multiplied by the green square, so that the entry and exit complement each other, each according to its class, because the rest does not move, and the power of the string square is synthesized." The opening square is divided, that is, the chord also. It is roughly meaning that an arbitrary right triangle.

The red square with the hook width is the Zhu square, and the cyan square with the strand length is the green square. The two squares of Zhu Fang and Qing Fang are arranged at the bottom edge, and then they are filled with surplus to make up for the void, and the line is not moved in the line, and the outside of the line is "each according to its class", and the square of the synthesized string is the chord square, and the chord square is the chord length.

It has been proved that the ancient Chinese Zhao Shuang string diagram proved the Pythagorean theorem.

Some were first proved by ancient people.

Proven. I learned it before, but I forgot about emmmmm

According to the account in the "Zhou Ji Sutra", in the dialogue between Zhou Gong and Shang Gao on numbers for more than 1,000 years BC, Shang Gao explained in detail the elements of the Pythagorean theorem with three specific numbers of three, four, five as examples. Second, "both outside the square, half a moment, ring and a total disk, to become three, four, five." The total length of the two moments is twenty and five, which is called the product moment.

First of all, it is affirmed that a right triangle with a base width of three and a height of four must have a chord length of five. The most important thing is to prove that the square of the chord length must be the sum of the squares of the two right-angled sides, and establish the principle that the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse. The method of determination was ignored by later generations because it was not known to the world.

In addition, the "Zhou Ji Sutra" clearly records the formula of the Pythagorean theorem narrated by Chen Zi, a descendant of the Duke of Zhou: "If you seek the evil solstice, take the sun as the hook, the day height as the stock, multiply the Pythagorean by each other, and open the square to remove it, and get the evil solstice."

Zhao Shuang of the Three Kingdoms period expressed the Pythagorean theorem in the "Notes on the Calculation of the Zhou Dynasty" as "the Pythagorean multiplies each other, and it is a string." Divide the square by the string. ”。

The application of the Pythagorean theorem is discussed in detail in chapter 9 of the Nine Chapters of Arithmetic, and the Wei mathematician Liu Hui repeatedly used the Pythagorean theorem to find pi.

The Jin Dynasty mathematician Li Ye's "Measuring the Circle of the Sea Mirror" established a systematic Tianyuan technique through the relationship between the fifteen Pythagorean shapes and diameters of the Pythagorean circle schema, and deduced 692 formulas for each side of the Pythagorean shape, in which multiple groups of Pythagorean numbers were used as examples.

11th century BC, Zhou Dynasty.

The mathematician Shang Gao put forward the "hook."

III. Shares. Fourth, string five". "Zhou Ji Sutra".

records a conversation between Shang Gao and Zhou Gong. Shang Gao said: "....Therefore, the folding moment, the hook wide three, the stock repair four, the meridian five.

This means that when the two right-angled sides of a right-angled triangle are 3 (hook) and 4 (strand) respectively, the radial corner (chord) is 5. Later, people simply said that this fact was "Pythagorean four strings five", and according to this allusion, it was called the Pythagorean theorem.

is the quotient height theorem.

In the 3rd century AD, Zhao Shuang of the Three Kingdoms period made a detailed annotation of the Pythagorean theorem in the "Zhou Ji Sutra", which was recorded in the "Nine Chapters of Arithmetic" "Pythagorean multiplication, and divide by the square, that is, the string", Zhao Shuang created a "Pythagorean square diagram", using the combination of shapes and numbers to obtain the method, and gave a detailed proof of the Pythagorean theorem. Later Liu Hui also proved the Pythagorean theorem in Liu Hui's note.

The first time this theorem was proposed and proved in the West was in ancient Greece in the 6th century BC.

of the Pythagoreans, he deductively proved that the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right sides. So in the West, the Pythagorean theorem is called the "Pythagorean theorem."

Regarding the name of the Pythagorean theorem, in our country, it used to be called the Pythagorean theorem, which was the name translated with the introduction of Western mathematics. In the 50s of the 20th century, there was a discussion on the naming of this theorem in the academic circles, and finally the "Pythagorean theorem" was used, which was widely recognized by the educational and academic circles.

In 1993, the National Committee for the Examination and Approval of Natural Science Terminology published mathematical terms, and determined that the Chinese name of this theorem is the Pythagorean theorem, and its corresponding English name is Pythagoras Theorem, and the note says: "It is also known as the 'Pythagorean theorem'." It used to be called 'Shanggao theorem'

So far, the "Pythagorean theorem" has become the standard name established in our country.

The history of this theorem can be divided into three parts: the discovery of the Pythagorean number, the discovery of the relationship between the length of the sides in a right triangle, and the proof of the theorem.

The Pythagorean number was discovered earlier, for example, in Egyptian papyrus (3,4,5) this set of Pythagorean numbers, and in Babylon.

The largest Pythagorean array involved in a clay tablet is (13500, 12709, 18541). Later Chinese arithmetic scriptures, Indian and Arabic mathematics books are also recorded.

In China, the Sutra of the Calculations of the Zhou Dynasty

The group of Pythagorean numbers (3,4,5) is also described; Jin Dynasty.

Mathematician Li Ye in "Measuring the Circle of the Sea Mirror".

Through the relationship between the fifteen Pythagorean shapes and their diameters in the Pythagorean circle diagram, a systematic Tianyuan technique was established, and 692 formulas for each side of the Pythagorean shape were derived, in which multiple sets of Pythagorean numbers were used as examples.

It is unlikely that the quantity and quality of the Pythagorean number obtained by the Babylonians could have been obtained purely by means of measurement. Pythagoras himself did not write any writings, but a thousand years after his death, Proclus in the 5th century gave Euclid his famous Geometry Primitives

The annotations attribute the earliest discoveries and proofs to the Pythagoreans.

Plutarch and Cicero also give credit to Pythagoras for their discovery, but there is no collapsing evidence that Pythagoras proved the Pythagorean theorem.

Pythagoras, famous for its vegetarian diet, slaughtered cattle even more incredible.

In China, the arithmetic books of the Qin Dynasty do not record the Pythagorean theorem, but only some Pythagorean numbers.

In the Nine Chapters of Arithmetic Notes, Liu Hui repeatedly uses the Pythagorean theorem to find pi.

And use the "cutting and mending" to do the "Qingzhu entry and exit diagram" to complete the geometric proof of the Pythagorean theorem.

Until now, there has been much debate about whether the Pythagorean theorem has been discovered more than once.

In the 11th century B.C., the mathematician Shang Gao (a native of the early years of the Western Zhou Dynasty) proposed "Gou."

III. Shares. Fourth, string five". The manuscript of the Zhou Sutra, written before the first century B.C., records a conversation between Shang Gao and the Duke of Zhou. Shang Gao said: "....

Therefore, the folding moment, the hook wide three, the stock repair four, the meridian five. This means that when the two right-angled sides of a right-angled triangle are 3 (hook) and 4 (strand) respectively, the radial corner (chord) is 5.

Later, people simply said that this fact was "Pythagorean four strings five", and according to this allusion, the Pythagorean theorem was called the quotient high theorem.

In the third century AD, Zhao Shuang of the Three Kingdoms period made a detailed annotation of the Pythagorean theorem in the "Zhou Ji Sutra", which was recorded in the "Nine Chapters of Arithmetic" "Pythagorean multiplication, and divide by the square, that is, the string", Zhao Shuang created a "Pythagorean square diagram", and used the method of combining Zen numbers and shapes to give a detailed proof of the Pythagorean theorem. Later, Liu Hui also proved the Pythagorean theorem in Liu Hui's note.

No. The ancient Babylonians knew and applied the Pythagorean theorem as far back as about the third millennium BC, and they also knew many Pythagorean arrays. In the library of Columbia University in the United States, there is an ancient Babylonian clay tablet numbered "Princeton 322", which records many Pythagorean numbers.

The ancient Egyptians also applied the Pythagorean theorem when building magnificent pyramids and measuring land after the flooding of the Nile.

In the 11th century B.C., Shang Gao, a mathematician of the Zhou Dynasty in China, put forward the "hook."

III. Shares. Fourth, string five". The Pythagorean theorem is a fundamental geometric theorem that states that the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse. In ancient China, the right-angled triangle was called the Pythagorean shape, and the smaller of the right-angled sides was the hook, the other long right-angled side was the strand, and the hypotenuse was the string, so this theorem was called the "Pythagorean theorem", and some people called it the "Shanggao theorem".

In the West, the Pythagoreans of ancient Greece in the 6th century BC were the first to propose and prove this theorem, who used the deductive method to prove that the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right angles. Therefore, Westerners are accustomed to calling this theorem "Pythagorean theorem".

The proof of the Pythagorean theorem was 500 years earlier in China than in the West.

China: In the 11th century B.C., Shang Gao, an old mathematician in the Zhou Dynasty, proposed the "hook."

III. Shares. Fourth, string five". The "Zhou Ji Sutra" records a conversation between Shang Gao and Zhou Gong. Shang Gao said: "....Therefore, the folding moment, the hook wide three, the stock repair four, the meridian five. ”

This means that when the two right-angled sides of a right-angled triangle are 3 (hook) and 4 (strand) respectively, the radial corner (chord) is 5. Later, people simply said that this fact was "Pythagorean four strings five", and according to this allusion, the Pythagorean theorem was called the quotient high theorem.

Foreign: In the sixth century B.C., the Greek mathematician Pythagoras proved the Pythagorean theorem, which is why Westerners are accustomed to calling this theorem the Pythagorean theorem.

Therefore, the proof of the Pythagorean theorem was five centuries earlier than in the West, that is, 500 years.

The Pythagorean theorem, also known as the Pythagorean theorem, is a glorious pearl in geometry, known as the "cornerstone of geometry", and has a wide range of applications in higher mathematics and other disciplines. Because of this, several ancient civilizations in the world have been discovered and studied extensively and deeply, so there are many names.

Our country is one of the oldest countries to discover and study the Pythagorean theorem. Ancient mathematicians in China called the right-angled triangle the Pythagorean, the shorter right-angled side is called the hook, the other right-angled side is called the strand, and the hypotenuse is called the mill and the string sensitive hole, so the Pythagorean theorem is also called the Pythagorean theorem. In more than 1000 B.C., it is recorded that Shang Gao (about 1120 B.C.) replied to Zhou Gong and said, "Therefore, I thought that the sentence was wide and blind and missed three, the stock repair was four, and the diameter corner was five."

Both square, the outer half of its moment, ring and a total plate, into three, four five. The total length of the two moments is twenty and five, which is called the product moment. Therefore, the Pythagorean theorem is also known as the "quotient high theorem" in China

In the 7th to 6th centuries B.C., a Chinese scholar Chen Zi once gave the trilateral relationship of any right triangle, that is, "take the sun as the hook, the sun height as the strand, and the hook and the strand are multiplied and divided by the square to get the evil solstice."

In France and Belgium, the Pythagorean theorem is also known as the "donkey bridge theorem".Other countries call the Pythagorean theorem the "square theorem".

One or two hundred years after Chen Zi, the famous Greek mathematician Pythagoras discovered this theorem, so many countries in the world call the Pythagorean theorem "Pythagorean" theorem. In order to celebrate the discovery of this theorem, the Pythagoreans killed a hundred cows as a reward for worshiping the gods, so this theorem is also called the "Hundred Oxen Theorem".