What is the Pythagorean theorem called? What is the Pythagorean theorem?

The Pythagorean theorem, also known as the Pythagorean theorem, states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its two right-angled sides.

In fact, the Babylonians of Hammurabi's time had already discovered this theorem, and Pythagoras was only the first to prove it.

The Pythagorean proof of this theorem no longer exists, and it is generally believed that he used the partition proof method. Let a, b, and c represent the two right-angled sides and the collapsed sides of the right-angled triangle, respectively, and consider the two squares with sides of length a+b. The first square is divided into 6 pieces, i.e., two squares with right-angled sides as the sides and 4 triangles congruent with a given triangle, the difference of which is equal minus the same amount.

Thus it follows that a square with an hypotenuse as an edge is equal to the sum of the squares with a right angle as an edge.

The Pythagorean theorem originated very early in India, and there is a diagram in the book "Altar Architecture": making a square is the sum of two other squares, and giving a proof that the intents believe that this is the Indian Pythagorean theorem.

India is also very good in the application of the Pythagorean theorem, and there are many questions about the application of the phoenix theorem in the Bhashgara's Lirovati.

Actually, the homeland of the Pythagorean theorem should be in our country. At least the "Zhou Ji Sutra", which was written in the Western Han Dynasty, began to record a dialogue between the Duke of Zhou (about 1100 BC) in the early years of the Zhou Dynasty in China and the scholar Shang Gao at that time about the nature of right triangles. The concern is this:

Once upon a time, the Duke of Zhou asked Shang Gao how Fuxi in ancient times determined the degree of the celestial sphere? You must know that the sky cannot be climbed with a ladder, and it cannot be measured with a ruler, so what does the number come from? Shang Gao wrote about this, he said, the art of numbers began with the study of circles and squares, circles are produced by squares, and squares are produced by rectangles folded at right angles.

Before studying the rectangle, it is necessary to know the ninety-nine formula, and imagine that a rectangle is cut diagonally so that the length of the short right-angled side (hook) is three, the length of the long right-angled side (strand) is four, and the length of the side (chord) is five. This is the often referred to Pythagorean theorem.

Because Pythagorean is 600 years later than Shang Gao, some people advocate that the Pythagorean theorem should be called the "Shang Gao theorem", and the "Zhou Ji Sutra" records that Chen Zi after the Zhou Gong had used the Pythagorean theorem and the similar proportional relationship to calculate the distance between the earth and the sun and the diameter of the sun, so some people advocate calling the Pythagorean theorem "Chen Zi's theorem", and finally decided to use the "Pythagorean theorem" to name it, which not only accurately reflects the glorious achievements of ancient mathematics in China, but also vividly illustrates the specific content of this theorem.

It should also be mentioned that so far there are as many as 400 ways to prove the Pythagorean theorem.

What is the Pythagorean theorem?

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Analysis: Pythagorean theorem: In any right triangle, the sum of the squares of the two right-angled sides must be equal to the squares of the hypotenuses. This theorem is also known as the "Shang Gao Theorem" in China and the "Pythagorean Theorem" in foreign countries.

The Pythagorean theorem (also known as Shang Gao's theorem, Pythagorean theorem) is a basic geometric theorem that was discovered by Shang Gao as early as the Shang Dynasty in China. It is said that after Pythagoras discovered this decision, he immediately beheaded a hundred oxen to celebrate, so it is also called the "Hundred Oxen Theorem".

The Pythagorean theorem states:

The sum of the squares of the two right-angled sides (i.e., "hooks", "strands") of a right triangle is equal to the square of the sides of the hypotenuse (i.e., "chord").

That is, let the two right-angled sides of a right-angled triangle be a and b, and the hypotenuse side is c, then.

a2 + b2 = c2

The Pythagorean theorem has now found about 400 ways to prove it, making it one of the most provable theorems among mathematical theorems.

Pythagorean array. A positive integer array satisfying the Pythagorean theorem equation a2 + b2 = c2 (a,b,c). For example, (3,4,5) is a set of Pythagorean arrays.

Since there are 3 unknowns in the equation, there are countless groups of Pythagorean arrays.

Popularize. If the hypotenuse of a right-angled triangle is regarded as a vector on a two-dimensional plane, and the two hypotenuse sides are regarded as projections on the coordinate axis of the plane Cartesian coordinate system, the significance of the Pythagorean theorem can be examined from another perspective. That is, the square of the length of a vector is equal to the sum of the squares of the length of the projection on a set of orthogonal bases in the space in which it is located.

The Pythagorean theorem, a dazzling pearl in geometry, is known as the "cornerstone of geometry", and it also has a very wide range of applications in higher mathematics and other disciplines Because of this, several ancient civilizations in the world have discovered and carried out extensive and in-depth research, so there are many names

China is the oldest country to discover and study the Pythagorean theorem Ancient mathematicians in China called the right-angled triangle the Pythagorean shape, the shorter right-angled side called the hook, the other right-angled side called the strand, and the hypotenuse called the string, so the Pythagorean theorem is also called the Pythagorean string theorem In more than 1000 BC, it is recorded that Shang Gao (about 1120 BC) replied to Zhou Gong and said, "Gou Guang three, stock repair four, Jingyu five", which means that in the right triangle, "Hook three, strand four, string five" Therefore, the Pythagorean theorem is also known as the "Shang Gao theorem" in China In the 7th and 6th centuries B.C., a Chinese scholar Chen Zi once gave the trilateral relationship of any right-angled triangle, that is, "take the sun as the hook, the sun height as the strand, and the hook and the strand each multiply and divide the square to get the evil solstice."

In France and Belgium, the Pythagorean theorem is also called the "donkey bridge theorem" and some countries call the Pythagorean theorem the "square theorem".

One or two hundred years after Chen Zi, the 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 to reward the gods, so this theorem is also called the "Hundred Oxen Theorem".

The Pythagorean theorem is also known as the Pythagorean theorem.

The Pythagorean theorem formula is that the square of a plus the square of b is equal to the square of c. If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then the formula is: a2+b 2=c 2.

The Pythagorean theorem now has about 500 ways to prove it, making it one of the most provable theorems in mathematics. The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days, one of the most important tools for solving geometric problems with algebraic ideas, and one of the links between numbers and shapes.

Extended Information: Introduction to the Pythagorean Theorem:

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, and the other long right-angled side was the strand, and the hypotenuse was the chord, so.