Definition:
The fourth-order magic square is a 4x4 matrix, which contains integers from 1 to 16, so that the sum of numbers in each row, column and diagonal is equal. The sum of magic squares is often called "magic sum".
Solution:
A classical solution to construct the fourth-order magic square is the odd number method, that is, the construction method based on odd number. Generally speaking, the fourth-order magic square is obtained by filling continuous integers from 1 to 16 and satisfying the rules of magic square properties.
For example, a simple fourth-order magic square is as follows:
16、2、3、 13、5、 1 1、 10、8、9、7、6、 12、4 1、4、 15、 1
Use:
1, Mathematical Research: Magic Square is often used in mathematical research and discussion. Constructing and analyzing the properties of magic squares is helpful to deeply understand mathematical laws, especially in the fields of algebra and combinatorial mathematics.
2. Art and literature: Rubik's cube is also used in art and literature, and is considered mysterious and artistic. Some artists and writers take the Rubik's Cube as their creative inspiration, which is reflected in paintings and literary works.
Presenter:
The study of the fourth-order magic square can be traced back to the early history of mathematics. Gregory, a famous Italian mathematician, mentioned the fourth-order magic square in his abacus book, which is considered as the earliest fourth-order magic square record in Europe.
Application field:
1, Mathematics: Magic Square is an important research object in mathematics, and its construction and property analysis involve many branches of mathematics, including algebra and combinatorial mathematics.
2. Art: Some artists create in the form of Rubik's Cube and integrate it into paintings and sculptures to show the mystery of art and their understanding of mathematical laws.
3. History: The Rubik's Cube also has certain cultural value in history, and it is considered to be the product of the combination of mathematics and art, which embodies the pursuit of mathematical aesthetics by human beings.
Summary:
The fourth-order magic square is an interesting and challenging mathematical problem. The study of its structure and properties not only involves the field of mathematics, but also has some applications in art and history. The study of the fourth-order magic square by early mathematicians and artists established its position in mathematical culture and became a unique expression of the blending of mathematics and art.