1, basic formula

In a right-angled triangle on the plane, the square of the length of two right-angled sides adds up to the square of the length of the hypotenuse. If the lengths of two right-angled sides of a right-angled triangle are A and B, and the length of the hypotenuse is C, then the formula of Pythagorean theorem is A? +b？ =c？ .

2. Complete formula

a=m，b=(m？ /k-k)/2，c=(m？ /k+k)/2, where m≥3

(1) When m is determined to be an arbitrary odd number greater than or equal to 3, k={ 1, m? All factors less than m of {

(2) When m is determined to be any even number ≥4, k={m? All even factors less than m/2

3. Commonly used formulas

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

(2)(5， 12， 13)，(7，24，25)，(9，40，4 1)……2n+ 1，2n？ +2n，2n？ +2n+ 1(n is a positive integer).

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

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

Extended data:

Pythagorean array

Pythagorean array is a set of positive integers (a, b, c) satisfying Pythagorean theorem a2+b2=c2, where a, b and c are called Pythagorean numbers. For example, (3,4,5) is a Pythagorean array.

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

3 Pythagorean Theorem uses

The third side is solved by knowing the two sides of a right triangle, or the lengths of the three sides of the triangle are known, which proves that the triangle is a right triangle or proves that the two sides of the triangle are vertical. Using Pythagorean Theorem to find the length of line segment is the most basic application of Pythagorean Theorem.