Mathematics originates from life and is also applied to life. The earliest motivation for people to create numbers is to know the specific numbers of a bunch of objects. In the development of mathematics, there is a maze of wisdom, which is the Rubik's Cube. This game gives 1, 2 ... 2 ... N2. These numbers are required to be arranged in an n×n square, and the sum of all numbers on each row, column and diagonal line should be equal. The sum of the numbers on each straight line is called the magic square constant. But there is a problem how to quickly solve the standard magic square, which is to fill in n2 in the order of natural numbers from 1. First of all, we must determine the magic square constant. For example, the third-order magic square constant is 15 and the fourth-order magic square constant is 34. What is the constant m of the n-order magic square? We can first sum all the numbers of the magic square of order n, and get S =1+2+3+...+(N2-1)+N2 = (1+N2)+(2+N2-1)+(3+N2.
There are also many magic squares, the fifth-order magic square exceeds 200 million, and the seventh-order magic square exceeds 300 million, which makes me lament the flexibility of mathematics.
Another thing that impressed me most in the book was the clever calculation of Pythagoras number. When studying Pythagorean theorem, we will pay attention to the problem of integer Pythagorean number, that is, the positive integer solution group of x2+y2=z2, which is called Pythagorean number for short, for example, (3,4,5). So if A, B and C are Pythagoras numbers and have (a2+b2=c2), then A, B and C are called. Therefore, only the pythagorean numbers of A, B and C are considered, which is called basic pythagorean array. So how do you create a set of Pythagoras numbers? A group proposed by Pythagoras appears in textbooks, that is, if m is any positive integer greater than or equal to 2, then (m2- 1, 2m, m2+ 1) must be a Pythagorean number, because this group is a pair of prime numbers and a basic Pythagorean array. But not all Pythagoras arrays can be given. China's mathematical masterpiece Nine Chapters on Number Theory gives a better method: If two numbers M and N are given, then 1/2 (m2-N2), mn and 1/2 are a set of Pythagorean numbers, and the number of Pythagorean numbers given each time is different. If m and n are coprime, this formula can list all paired pythagorean arrays. So this formula is called the general solution formula of x2+y2=z2.
I only know a little about the wonders of mathematics, and I will have a longer way to appreciate mathematics in the future.