The Pythagorean method of proof, the proof of the Pythagorean theorem

The beauty of mathematics --- the Pythagorean tree.

The diagram of the proof method of the Pythagorean theorem is as follows:

It is known that a square ABCD with a side length of A B, and a point O, P, E, G is taken on each side of the square ABCD to form a quadrilateral opeg. It is known that bo=ap=de=cg=a, oa=pd=ec=gb=b.

As shown in the figure, it is easy to conclude that the quadrilateral opeg is also a square, and if the square is a square, the side length of the family opeg is c. Then, the area of the square opeg is equal to the area of the square ABCD minus the area of the 4 right triangles.

i.e., c = (a b) after 4 ab, c = a b.

Introduction: 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, and the other long straight edge was the strand, and the hypotenuse was the chord, so this theorem was called the Pythagorean theorem, and some people called the Shang Gao 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 proved 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.

Pythagoras was a great mathematician who studied numbers and organized the so-called Pythagoras Brotherhood, Pythagoras had studied odd, even, prime, composite, affinity, and form numbers. He proved the Pythagorean theorem (similar to the Pythagorean theorem with China) and was so happy that he slaughtered more than 100 cattle and celebrated. Therefore, the Pythagorean theorem is also known as the Hundred Bulls theorem.

But Pythagoras also had his failures, for example, when he refused to admit the existence of irrational numbers, and his students asked what is the hypotenuse of a right-angled triangle with a side length of 1. As a result, he was very angry and scolded the student!!

Fermat's theorem.

Master Fermat had a 9-to-5 job of his own, but in his spare time he loved to study mathematics, and he liked to do math problems, especially in the margins of the book. After Fermat's death, people sorted out his math books and math manuscript papers, and found in one book the problem that if the nth power of x plus the nth power of y is equal to the nth power of z, and n is greater than 2, then x, y, and z have no integer solutions.

Next to this question, there is also this sentence: "For this problem, I have given a wonderful proof of one-click fighting, but the blank space in this book is too small for me to write!" And this sentence has troubled later generations of mathematicians for more than 350 years.

Or an extremely complex proof, which is not beautiful at all)

It is said that a man once wanted to commit suicide, he arranged for himself to do something at the end of the time, in which he arranged for himself to go to the library to flip through the book, accidentally turned to Fermat's theorem, so he began to study, and when he came back to his senses, it was past the time he arranged for himself to commit suicide, so this man began a long mathematical research, but unfortunately, this compatriot could not solve the problem of proving Fermat's theorem until he died.

There is no factual evidence to support who proved the Pythagorean theorem.

The Pythagorean Theorem (also known as: Pythagorean theorem, Pythagorean theorem) is a basic geometric theorem, which was first proposed and proved by the Pythagorean school in ancient Greece (6th century BC), and was first proposed by Shang Gao in Xingyanjing China (during the Zhou Dynasty).

The Pythagorean theorem refers to the sum of the squares of the two right-angled side lengths of a right-angled triangle (ancient called hook length, strand length) equal to the square of the hypotenuse length (ancient called chord length). Using the Pythagorean theorem to find the length of a line segment is the most basic application of the Pythagorean theorem.

Benefits of learning math well:

1. Fast calculation. After learning mathematics, oral arithmetic and brain arithmetic in daily life are quite fast, and they will come when they open their mouths.

2. Logical thinking is meticulous and scientific. People who are good at mathematics will generally improve their brain intelligence and logical thinking ability, and they can only achieve a full score without mistakes if they are scientific. To be a person in the world is to do things scientifically, to be careful and careful, but to be a man is not necessarily.

3. Self-motivated, happy with others, proud of achievement, and fun in life. If the math score is good, many people will ask for advice, answer questions for everyone, get along with everyone very happy, very happy and cautious, when it comes to mathematics, they will work hard to learn well, have a sense of pride and achievement, and everyone will be excited, mingle, and have endless fun.

Summary. The Pythagorean theorem is a fundamental theorem discovered by the ancient Greek mathematician Pythagoras and one of the most basic and well-known theorems in triangles. It is led out by an isosceles right triangle:

The sum of the squares of the two right-angled sides of an isosceles right-angled triangle is equal to the squares of its hypotenuses.

The Pythagorean theorem is a fundamental theorem discovered by the ancient Greek mathematician Pythagoras, and it is one of the most basic and famous theorems in triangles. It is drawn from an isosceles right triangle: the sum of the squares of the two right sides of an isosceles right triangle is equal to the square of its hypotenuse acre.

Specifically, if $a$,$b$,$c$ represents the length of the two right-angled sides and hypotenuse sides of an isosceles right triangle, then: $$a 2+b 2=c 2$$ The equation is known as the Pythagorean theorem. This theorem does not apply only to isosceles right-angled triangles, and is true for any general right-angled triangle.

In addition, the existence and uniqueness of the Pythagorean number (i.e., the sum of the squares of two integers $a$ and $b$, i.e., $a 2+b 2$, which is also the sum of squares of another integer), can also be proved. This theorem has a wide range of applications in geometry, physics, astronomy, mathematics, and engineering.

The Pythagorean theorem refers 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 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.

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 first to propose and prove this theorem was the Pythagoreans of ancient Greece in the 6th century BC, 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-angled sides.

Significance. 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 connect 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 dazzling pearl in geometry, known as the "cornerstone of geometry", but also has a wide range of applications in the field of higher mathematics and other sciences On May 15, 1971, Nicaragua issued a set of stamps entitled "Ten Mathematical Formulas That Changed the Face of the World", which were selected by famous mathematicians, and the Pythagorean theorem was the first of them.

Summary. The Pythagorean theorem (Pythagorean theorem) is a basic geometric theorem that was first proposed and proved by the Pythagorean school in ancient Greece (6th century BC) and first proposed by Shang Gao in China (during the Zhou Dynasty).

The Pythagorean Theorem (also known as: Pythagorean theorem, Pythagorean theorem) is a basic geometric theorem, which was first proposed and proved by the Pythagorean school of ancient Greece (6th century BC), and was first proposed by Shang Gao in China (Zhou Dynasty).

There is a mathematical theorem that everyone has to learn in school, this theorem is generally called the Pythagorean Goras theorem in the West, and in China, we are used to calling it the Pythagorean theorem. Therefore, in this article, we sometimes refer to the Pythagorean theorem and sometimes the Pythagorean theorem. **The theorem is generally described as:

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

What is the difference between the Pythagorean theorem and the Pythagorean theorem.

Due to the limited distance between ancient cultures. The "Pythagorean theorem" is the name of the ancient continent of Europe, because this theorem was first discovered by Pythagoras in Europe. In China we call it the Pythagorean theorem.

Because in the ancient arithmetic scriptures, it is recorded that "hook three, strand four, string five" said that Kuan early is the same content as "Pythagorean theorem". In fact, China discovered this theorem much earlier than Pythagoras.

However, due to the distance, this discovery in ancient China did not reach Europe. Therefore, Europeans believe that Pythagoras first discovered this theorem, which is called "Pythagorean theorem".

Hello, we were off work when you asked your question last night, and we apologize for not responding to you in time.

Are the Pythagorean theorem and the Pythagorean law the same thing, and how can they be different?

The content is the same, but the name is different.