What exactly is the Pythagorean theorem?

The Pythagorean theorem is a basic geometric theorem, in China, the formula and proof of the Pythagorean theorem are recorded in the Zhou Sutra, which is said to have been discovered by Shang Gao in the Shang Dynasty, so it is also called the Shang Gao theorem; Jiang Mingzu in the Three Kingdoms period made a detailed note on the Pythagorean theorem in the "Jiang Mingzu Sutra" and gave another proof. 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, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c.

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 range a2 + b2 = positive integer array of c2 (a, b, c). (3,4,5) is the Pythagorean number.

The Pythagorean theorem, also known as the quotient theorem and the Pythagorean theorem, is a fundamental 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, strand length) is equal to the square of the hypotenuse (chord length). Conversely, if the sum of the squares 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 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, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a +b = c. 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 range a2 + b2 = positive integer array of c2 (a, b, c). (3,4,5) is the Pythagorean number.

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x,y,z is greater than 0

For a right-angled triangle with x,y as the right-angled edge and z as the hypotenuse, there is x 2 + y 2 = z 2

Conversely, x 2 + y 2 = z 2, x, y, z can form a right triangle.

Pythagorean theorem: In any right-angled triangle, the sum of the squares of the two right-angled sides must be equal to the squares of the hypotenuses.

What is the Pythagorean theorem?

Assuming that the right-angled sides of a right-angled triangle are a and b and the hypotenuse is c, then according to the Pythagorean theorem, it is <>

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.

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 Shang Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean Three Strands, Four Xuanwu".

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.

Summary. The content of the Pythagorean theorem 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.

A common number of the Pythagorean theorem.

The content of the Pythagorean theorem 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 side was the hook, the other long right-angled side was the strand, and the hypotenuse of the state was the chord, so this theorem was called the Pythagorean theorem.

For example, 345, 32+42=52

And so on, what else.

What does 32+42=52 mean?

The square of three plus the square of four equals the square of five.

The commonly used Pythagorean numbers are:

Concept: 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-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 string, so this theorem was called the Pythagorean theorem, and some people called the Shanggao theorem.

Definition: In a right-angled triangle on a plane, the sum of the squares of the sides of the two straight answer corners is equal to the square of the square of the hypotenuse lengths.

Theorem Usage: Solve the third side of a right triangle on both sides, or know the length of the three sides of a triangle to prove that the triangle is a right triangle or to prove that the two sides of the triangle are perpendicular to each other.

Pythagorean theorem: In a right-angled triangle on a plane, the square of the side lengths of the two right-angled sides adds up to the square of the hypotenuse lengths.

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?