Trigonometric formulas. The Pythagorean theorem gives me the formula

Pythagorean theoremFor use onlyRight triangle。Expression of the Pythagorean theorem: a + b = c.

The formula of the Pythagorean theorem is: In a right triangle, the square of the hypotenuse side length is equal to the sum of the squares of the two right angle sides If the two right sides of the right triangle are A, Siddly B, and the hypotenuse is C, then the square of a A is the square of b and the square of C.

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 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, causing the first mathematical crisis and greatly deepening the understanding of numbers.

understanding. 4. The Pythagorean theorem is the first indefinite equation in history to give a complete solution.

It 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 and is known as the "cornerstone of geometry", but also in higher mathematics.

It also has a wide range of applications in other scientific fields.

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The formula of the Pythagorean theorem is: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two right sides If the two right sides of the right triangle are a and b respectively, and the hypotenuse is c, then the square of a is the square of b and the square of c.

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Concern. The Pythagorean theorem only applies to right triangles. Expression of the Pythagorean theorem: a + b = c.

The formula of the theorem is: In a right triangle, the square of the hypotenuse side length is equal to the sum of the squares of the length of the two right angles If the two right sides of the right triangle are a and b respectively, and the hypotenuse is c, then the square of a a b is the square of c c

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 link numbers with shapes, that is, it is the first brother to make a theorem that connects 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 non-sideless 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.

The Pythagorean theorem calculates: The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse. a²+b²=c²

The three deformation formulas of the Pythagorean theorem are a=k(m+n), b=2kmn, and c=k(m+n).

The Pythagorean theorem, also known as the Pythagorean theorem, the quotient theorem, the bridal seat theorem, and the hundred bull 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 three formulas of the Pythagorean theorem are a=k(m +n), b = 2kmn, and c=k(m +n).

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.

The number of Pythagorean numbers is:

1. The three positive integers that can form the three sides of a right-angled triangle are called Pythagorean numbers, that is, when a, b, and c are positive integers, they are called a, b, and c are a group of Pythagorean numbers.

2. Remembering the common Pythagorean number can improve the speed of problem solving, such as etc.

3. Use the algebraic formula containing letters to express the number of Pythagorean groups in n groups: (n is a positive integer); (n is a positive integer); (m>n,m,n is a positive integer).

The Pythagorean theorem is a fundamental elementary geometric theorem that states that the sum of the squares of two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse. If the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a+b=c, and if a, b, and c are all positive integers, (a, b, c) is called the Pythagorean array.

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. "Pythagorean three, strand four, string five" is one of the most famous examples of the Pythagorean theorem.

The ancient Babylonians knew and applied the Pythagorean theorem as far back as about the third millennium BC, as well as many Pythagorean arrays. The Pythagorean theorem was also applied by the ancient Egyptians. In China, Shang Gao of the Western Zhou Dynasty proposed a special case of the Pythagorean theorem of "Pythagorean three-strand four-string five".

In the West, Pythagoras of ancient Greece was the first to propose and prove this theorem in the 6th century BC, who deductively proved that the square of the hypotenuse of a right triangle is equal to the sum of the squares of two right angles.

The Pythagorean theorem is a basic geometric theorem, one of the important mathematical theorems discovered and proved by human beings 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. The Pythagorean theorem is a special case of the cosine theorem. The Pythagorean theorem has about 400 ways to prove it, making it one of the most provable theorems among mathematical theorems.

Description: 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 letter indicates: if a triangle is a right-angled triangle, a and b are the two right-angled sides of the triangle respectively, and c is the hypotenuse, then: a b = c

Party A Party B = Party C.

Party A = Party C - Party B.

Party B = Party C - Party A.

a²+b²=c²。

Pythagorean theoremis a basic geometric theorem that refers to a right triangle.

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

of the squared. 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 the formula of the Pythagorean theorem is a +b = c.

The Pythagorean theorem is applied with caution

For example, the roof structure of rural houses can be calculated by using the Pythagorean theorem, and the Pythagorean theorem should also be used in the design of engineering drawings.

There are also a wide range of applications in physics, such as finding several forces, or the combined velocity of an object, and the direction of motion is also mostly used in engineering in ancient times, such as building houses, repairing wells, building cars, and so on.

There is such a record in another ancient book of China's Warring States Period, "Twelve Notes on the Postscript of the History of the Road": Yu governs the flood and breaks the river, looks at the shape of the mountains and rivers, sets the momentum of the high and the low, and in addition to the monstrous disaster, so that the East China Sea is injected, there is no drowning, and the Pythagorean is also born.

The meaning of this passage is: Dayu.

In order to control the flood and make the rivers flow irregularly, the direction of the water flow is determined according to the level of the terrain, and the flood water is injected into the sea according to the situation, and there is no longer a disaster of drowning, which is the result of the application of the Pythagorean theorem.

When doing carpentry work, there should be large boards.

To determine the right angle, use the Pythagorean theorem. The angle ruler is too small, and the right angle error drawn on the large board is large. When doing welder work, the Pythagorean theorem is also used to make a large frame, which must have right angles.

For example, if I want a right angle, I will take a straight corner side of 3 meters, a right angle side of 4 meters, so that the hypotenuse side has 5 meters, then this angle is a right angle.

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

There are about 500 ways to prove the Pythagorean theorem, which is one of the most provable theorems in the mathematical theorem of Pat Lee.

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.

The three formulas are:（1）（3,4,5),(6,8,10)……3n, 4n, 5n (n is.)Positive integer

（2）（5,12,13),(7,24,25),(9,40,41)……2n+1, 2n 2+2n, 2n 2+2n+1 (n is a positive integer).

3）（8,15,17),(12,35,37)……2 2*(n+1), 2-1, 2+1 (n is a positive integer).

4) m2-n 2,2mn, m 2+n 2 (m and n are both positive integers, m>n).

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

Any set of Pythagorean numbers (a, b, c) can be expressed as follows: a=k(m + n), b = 2kmn, c = k(m + n), where k, m, n are positive integers and m > n.

The Pythagorean theorem 3 formulas are:

1）（3,4,5),(6,8,10)……3n, 4n, 5n (n is a positive integer).

2）（5,12,13),(7,24,25),(9,40,41)……2n+1, 2n 2+2n, 2n 2+2n+1 (n is a positive integer).

3）（8,15,17),(12,35,37)……2 2*(n+1), 2-1, 2+1 (n is a positive hail integer).

Pythagorean answer and array:

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

Any set of Pythagorean numbers (a, b, c) can be expressed as follows: a=k(m + n), b = 2kmn, c = k(m + n), where k, m, n are positive integers, and m > n.

Summary. Pythagorean theorem a +b = c The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the squares of the hypotenuses. The number of Pythagorean (a, b, c) of any group can be expressed as follows:

a=k(m + n), b = 2kmn, c = k(m + n), where k, m, n are positive integers, and m > n.

Pythagorean theorem a +b = c The sum of the squares of the two sharply right-angled sides of a right-angled triangle is equal to the square of the hypotenuse. The number of Pythagorean numbers (a, b, c) of any group can be expressed as follows: a=k(m + n), b = 2kmn, c = k (m + n), where k, m, n are positive integers, and m > n.