What is the Pythagorean theorem and what is the Pythagorean theorem

In China, the sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the hypotenuse is called the Pythagorean theorem or the Pythagorean theorem, also known as the Pythagorean theorem or Pythagoras theorem. In mathematical formulas, it is often written as a +b =c

If the two right-angled sides of a right-angled triangle are a, b, and the hypotenuse is c, then a2+b2=c2 ; 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 lengths. The ancient Egyptians used this method to draw right angles.

If the three sides of the triangle a,b,c satisfy a 2 + b 2 = c 2; There is also a deformation formula: ab = root number (AC 2 + BC 2), for example: a right-angled side is a, and another right-angled side is b, if the sum of the squares of a and the squares of b is equal to the square of the hypotenuse c, then this triangle is a right-angled triangle.

The inverse theorem called the Pythagorean theorem).

In any right-angled triangle, the sum of the squares of the two right-angled sides must be equal to the square of the hypotenuse lengths.

The Pythagorean theorem states.

The sum of squares of the two right-angled sides of a right-angled triangle (i.e., the "hook" and "strand" for the short one is the hook and the long one is the strand) is equal to the square of the side length of the hypotenuse (i.e., the "string").

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

The square of a + the square of b = the square of c a 2 + b 2 = c 2 The Pythagorean theorem has now found about 500 ways to prove it, which is one of the most provable theorems among mathematical theorems.

The property that the sum of the squares of the two right-angled sides of a right-angled triangle equals the squares of the hypotenuse is called the Pythagorean theorem or the Pythagorean theorem.

In a right-angled triangle, there are two right-angled sides and an hypotenuse, so that the right-angled sides are a and b, and the hypotenuse is c, then the square of a plus the square of b is equal to the square of c. Thank you.

right triangle trilateral; a 2 + b 2 = c 2 (c is the longest side).

A right triangle is equal to the square of the hypotenuse of the two right-angled sides.

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 square of a b is equal to the square of c.

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.

1. 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.

Second, the use of theorems.

The third side of a known right triangle is solved, or the length of the three sides of a triangle is known, proving that the triangle is a right triangle or is used to prove that the two sides of the triangle are perpendicular to each other. Using the Pythagorean theorem to find the length of a line segment is the most basic application of the Pythagorean theorem.

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

What is the formula for the Pythagorean theorem.

What is the Pythagorean theorem?

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. 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.

"Pythagorean four strings five" is the most basic formula of the Pythagorean theorem. Pythagorean array equation a2+b2

C2 is a positive integer (a, b, c). (3,4,5) is the Pythagorean number. That is to say, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a2+b2=c2

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.

Assuming that the two right-angled sides in a right-angled triangle row are a and b respectively, and the hypotenuse is c, then a 2 + b 2 = c 2 and conversely, if a 2 + b 2 = c 2, then the triangle is a right triangle.

The former sentence is the Pythagorean theorem, and the latter is the inverse theorem of the Pythagorean theorem.

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. 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 beheaded 100 oxen to celebrate, so it is also called the "100 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 to say, if the two right-angled sides of a right-angled triangle are a and b, and the hypotenuse is c, then a2+

The Pythagorean theorem of b2=c2 has been found to have about 400 ways to prove it, which is one of the theorems with the most ways to prove it in mathematics.

Pythagorean array. Satisfy the Pythagorean theorem equation a2+b2

C2 is a positive integer (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.

GeneralizationIf the hypotenuse of a right-angled triangle is regarded as a vector on a two-dimensional plane, and the two hypotenuses are regarded as projections on the coordinate axes 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.

Only for right triangles, the sum of the squares of the two right-angled sides is equal to the square of the hypotenuse, e.g. 3 squares plus 4 squares = 5 squares.

Literal formulation: In any right-angled triangle, the sum of the squares of the lengths of the two right-angled sides is equal to the square of the length of the hypotenuse (it can also be understood as the square of the two long sides minus the square of the shortest side).

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^2+b^2=c^2

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

The property that the sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse is called the Pythagorean theorem or the Pythagorean theorem, also known as the Pythagorean theorem or Pythagorean theorem, and is often written as a 2 + b 2 = c 2 in mathematical formulas

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. i.e. a2+b2=c2