What is the explanation of the Pythagorean theorem and what is the definition of the Pythagorean the

The sum of the squares of the two right-angled edges is equal to the sum of the squares of the hypotenuses.

It's very detailed upstairs.

The Pythagorean theorem, is a basic 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 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 chord, so this theorem was called the Pythagorean theorem, and some people called the Shanggao theorem.

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.

In China, Shang Gao during the Zhou Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean three, four strings, five". In the West, the Pythagoreans of ancient Greece in the 6th century BC were the first to propose and prove this theorem, and they 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. <>

Significance of the Pythagorean theorem:

1. The proof of the Pythagorean theorem is the beginning of the argument for geometry.

2. The Pythagorean theorem is the first theorem in history to link numbers with shapes, that is, it is the first theorem to link geometry with algebra.

3. The Pythagorean theorem led to the discovery of irrational numbers, caused the first mathematical crisis, and greatly deepened people's understanding of numbers.

4. The Pythagorean theorem is the first indefinite equation in history to give a complete solution, which leads to Fermat's theorem.

5. The Pythagorean theorem is the basic theorem of Euclidean geometry and has great practical value. This theorem is not only a shining pearl in geometry and is known as the "cornerstone of geometry", but also has a wide range of applications in higher mathematics and other scientific fields.

On 15 May 1971, Nicaragua issued a set of stamps entitled "Ten Mathematical Formulas That Changed the Face of the World", chosen by renowned mathematicians, with the Pythagorean theorem being the first of them.

The Pythagorean theorem: The sum of the squares of the two right-angled sides in any plane right-angled triangle must be equal to the square of the hypotenuse.

For example, in ABC, c=90°, the corresponding edges of a, b, and c are a, b, and c, respectively, so a+b =c. The Pythagorean theorem, a dazzling pearl in the study of several differences, is known as the "cornerstone of geometry", and it is also widely used in advanced mathematics and his pre-blind learning.

In ancient China, the right triangle was called the Pythagorean shape, and the smaller of the right-angled side 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 the most common Pythagorean number was 3, 4, 5, that is, Pythagorean 3 strands and 4 strings 5.

Number of Pythagoreans. The Pythagorean number is a set of positive integers that can form the three sides of a right triangle. (Note that it must be a positive integer!) )

The Pythagorean theorem, also known as the Quotient High Theorem, Pythagorean Theorem, Pythagorean Theorem, and Pythagorean Theorem, is a basic and important theorem in plane geometry. The Pythagorean theorem states that the sum of the squares of the lengths of the two right-angled sides of a right-angled triangle on a plane (known as hook length and strand length) is equal to the square of the hypotenuse length (known as chord length in ancient times).

Conversely, if the sum of the squares of the lengths of the two sides of a triangle on a plane is equal to the square of the length of the third side, then it is a right triangle (the side opposite the right angle is the third side).

The Pythagorean theorem is one of the important mathematical theorems discovered and proven by mankind in the early days.

According to the account in the "Zhou Sutra", in the dialogue between Zhou Gong and Shang Gao on numbers in more than 1,000 BC, Shang Gao explained in detail the elements of the Pythagorean theorem with three specific numbers of three, four, five and three as examples. Second, both outside the square, half a moment, ring and a total disk, to get 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 high as the stock, multiply the Pythagorean by each other, and divide it by the prescription, and get the evil solstice.

Zhao Shuang expressed the Pythagorean theorem in the "Notes on the Calculation of the Zhou Dynasty" as the Pythagorean multiplication of each other, and the combination of them is a string. The square is divided, that is, the chord.

Ancient Egyptian papyrus in 2600 BC had (3,4,5) Pythagorean numbers, and the largest Pythagorean array of ancient Babylonian tablets involved was (18,541,12,709,13,500).

It was Pythagoras who discovered the Pythagorean theorem in ancient Greece, so the Pythagorean theorem is also known as the Pythagorean theorem. It is said that after Pythagoras proved this theorem, he beheaded a hundred oxen in celebration (the Great Sacrifice of Hundred Oxen), so it is also called the Hundred Oxen Theorem. But this claim is clearly based on falsehood, and it is well known that the Pythagoreans were known for their vegetarian diet in ancient times.

The Pythagorean theorem is really very simple, you will learn the function later, and you will find out. The key is that you use the theorem A 2 + B 2 = C 2. The difficulty is not that it is difficult, but that it has many test points, and if you can beat it one by one, then the difficulty will be solved.

I'm sure you'll find that you can just set the formula when you solve the problem. In general, the test is like this, knowing that in ABC c=90°,BC=5,AC=12, find the value of AB. It's very simple, you just need to follow the Pythagorean theorem and find it directly:

The opposite side of c is ab, so ab is hypotenuse. In ABC, C=90° AB 2=BC 2+AC 2 AB=13 Also, the Pythagorean theorem will be used to determine right triangles during the exam. You have to remember that people ask you:

What is a triangle when it satisfies a2+b 2=c 2? The inverse theorem of the Pythagorean theorem can be found: a right triangle.

I can also give a variant question: What kind of triangle is it if the three sides of a triangle satisfy (a-3) 2+(b-4) 2+(c-5) 2=0? It is easy to solve that it is a right triangle.

There is also a concept of the Pythagorean number, as long as the positive integer that satisfies a 2 + b 2 = c 2 is the Pythagorean number, note that it is a positive integer, if it is a number of tenths of a day, although they can form a right triangle, but not the Pythagorean number. There are skills in judging the number of Pythagoreans, for example, if someone asks you if 15,20,25 is the number of Pythagoreans, you can use a clever way to calculate: 15=5*3, 20=5*4, 25=5*5, 3,4,5 is the number of Pythagoreans, so 15,20,25 is the number of Pythagoreans.

There is also a categorical discussion. People ask you, in a right triangle, one side is 12 and the other is 5, find the third side. This involves the idea of categorical discussions.

Generally, students will definitely find out that the third side is 13, but if you calculate carefully, it is not difficult to find that there is a solution, take 12 as an hypotenuse, 5 as a right-angled side, then the third side = root number 119 The teacher helped you summarize various question types, understand?

The Pythagorean theorem is a junior high school course where the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right sides.

In a right triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse. This is the Pythagorean theorem.

It is the relationship between the three sides of a right triangle, and the sum of the squares of the two right sides is equal to the square of the hypotenuse.

In the simplest way, 3, 4, and 5 form a right triangle.

The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

i.e.: a + b = c

It is the relationship between the three sides of a right triangle.

The sum of squares of the right-angled sides of a right-angled triangle is equal to the squares of the hypotenuses.

What is the definition of the Pythagorean theorem is explained below:

The Pythagorean theorem is a basic geometric theorem that states that the sum of the squares of the lengths of the two right-angled sides (i.e., "Hook", "strand") sides of a right triangle is equal to the square of the side lengths of the hypotenuse (i.e., "strings").

The Pythagorean theorem has now found about 400 ways to prove it, making it one of the most provable theorems among mathematical theorems. The Pythagorean number forms a positive integer array (a,b,c) of a +b = c. (3,4,5) is the Pythagorean number.

The Pythagorean theorem is an elementary geometric theorem, 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.

If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a2;

b^2;c^2;

That is, the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse.

If the three sides of the triangle a, b, and c meet a 2 + b 2 = c 2, for example: a right-angled side is 3, a right-angled side is 4, and the hypotenuse is 3*3+4*4=x*x, x=5. Then this triangle is a right triangle. (The inverse theorem of the Pythagorean theorem).

The Pythagorean TreeThe Pythagorean tree is a fundamental geometric theorem that is traditionally believed to have been proved by the Pythagoras of ancient Greece. It is said that after Pythagoras proved this theorem, he beheaded a hundred oxen in celebration, hence the "Hundred Oxen Theorem". In China, a special case of the Pythagorean theorem is recorded in the Zhou Sutra, which is said to have been discovered by Shang Gao in the Shang Dynasty, so it is also called Shang Gao's theorem; Zhao Shuang of the Three Kingdoms period made a detailed annotation of the Pythagorean theorem in the "Zhou Ji Sutra" as a proof.

France and Belgium call it the donkey bridge theorem, and Egypt calls it the Egyptian triangle. In ancient China, the shorter right-angled side of the right-angled triangle was called the hook, the longer right-angled side was called the strand, and the hypotenuse was called the chord.

In a right triangle, the sum of the squares of the lengths of the two right-angled sides (i.e., "hooks", "strands") is equal to the square of the lengths of the sides of the hypotenuse (i.e., "chords"). That is, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c.

In a right-angled triangle, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse.

What is the Pythagorean theorem?

Concept of the Pythagorean theorem:

In a right-angled triangle on a plane, the square of the lengths of the two right-angled sides adds up to the square of the hypotenuse lengths. If the length of the two right-angled sides of a right-angled triangle is a and b, and the length of the hypotenuse is c, then it can be expressed mathematically:

a²+b²=c²

The Pythagorean theorem is a special case in the cosine theorem.