This theorem is also called "quotient height theorem" at home and "Pythagoras theorem" abroad.
Pythagorean theorem (also known as quotient height theorem, Pythagorean theorem) is a basic geometric theorem, which was discovered by quotient height as early as China Shang Dynasty. It is said that Pythagoras discovered this conclusion and beheaded a hundred cows to celebrate, so it is also called the "hundred cows theorem".
Pythagorean theorem states:
The sum of the squares of the sides of two right angles (namely "hook" and "strand") of a right triangle is equal to the square of the side length of the hypotenuse (namely "chord").
That is to say,
Let the two right angles of a right triangle be A and B and the hypotenuse be C, then
a2 + b2 = c2
There are about 400 ways to prove Pythagorean theorem, which is one of the most proven theorems in mathematics.
Pythagorean array
Positive integer groups (a, b, c) satisfying Pythagorean theorem equation a2+b2 = c2. For example, (3,4,5) is a Pythagorean array.
Because the equation contains three unknowns, there are countless groups of Pythagorean arrays.
range
If the hypotenuse of a right triangle is regarded as a vector on a two-dimensional plane and the two hypotenuses are regarded as projections on the coordinate axis of a plane rectangular coordinate system, we can examine the significance of Pythagorean theorem from another angle. That is to say, the square of the vector length is equal to the sum of the squares of its projection length on a set of orthogonal bases in space.