History of Pythagorean Theorem: Pythagorean Theorem is a special case of Cosine Theorem. This theorem is also called "quotient height theorem" at home and "Pythagoras theorem" or "hundred cows theorem" abroad (Pythagoras discovered this theorem and beheaded hundreds of cows to celebrate, so it is also called "hundred cows theorem"), and the French and Belgians also call this theorem "donkey bridge theorem". They discovered Pythagorean theorem later than our country, and they were the first country to discover this geometric treasure. At present, the proof method of learning textbooks for junior two students is Zhao Shuangxian's map, which proves to be Zhu Qing's access map. Origin: Pythagoras tree is a basic geometric theorem, which is traditionally proved by Pythagoras in ancient Greece. It is said that after Pythagoras proved this theorem, he beheaded a hundred cows to celebrate, so it is also called "Hundred Cows Theorem". Pythagoras recorded the formula and proof of Pythagorean theorem in China. According to legend, it was discovered by Shang Dynasty's quotient height, so it is also called quotient height theorem. During the Three Kingdoms period, Zhao Shuang made a detailed annotation on Pythagorean Theorem in Zhou Bi suan Jing and gave another proof [1]. France and Belgium are called donkey bridge theorem, and Egypt is called Egyptian triangle. In ancient China, the shorter right-angled side of a right-angled triangle was called a hook, the longer right-angled side was called a chord, and the hypotenuse was called a chord.

Content: If two right angles of a right triangle are A and B and the hypotenuse is C, then A 2+B 2 = C 2; That is to say, the sum of squares of the lengths of two right angles of a right triangle is equal to the square of the length of the hypotenuse. The ancient Egyptians drew right angles in this way.

If the three sides A, B and C of a triangle satisfy A 2+B 2 = C 2; There is also a deformation formula: AB= root sign (AC 2+BC 2), for example, one right-angled side is A and the other right-angled side is B. If the sum of squares of A and B is equal to the square of hypotenuse C, then this triangle is a right-angled triangle. (called the inverse theorem of Pythagorean theorem)

Fermat concentration: when the integer n > 2, the indefinite equation x n+y n = z n about x, y and z has no positive integer solution.

Real number: including rational number and irrational number. Among them, irrational number is infinite acyclic decimal, and rational number includes integer and fraction. Mathematically, real numbers are intuitively defined as numbers corresponding to points on the number axis. Originally, real numbers were just numbers, but later the concept of imaginary numbers was introduced. The original numbers were called "real numbers"-meaning "real numbers". Also called quadratic root, for non-negative real numbers, it refers to real numbers whose result of self-multiplication is equal to [√], in which the square root belonging to non-negative real numbers is called arithmetic square root.

Square root: