In the field of mathematics, there are many great mathematicians who have made great contributions to the development of mankind through their own efforts and wisdom. There is a short story that gives us a deeper understanding of mathematicians' way of thinking and working methods.

The story happened in the18th century, when Europe was in the period of industrial revolution, and various new technologies and ideas were constantly emerging. In this context, a mathematician found a wonderful math problem, which made him unable to sleep. He decided to solve the problem by himself.

The specific content of this problem is: how to put as many circles as possible in a square so that these circles do not overlap each other and the area of the square is filled by these circles. This problem looks simple, but in fact it is very complicated, which requires mathematicians to spend a lot of time and energy to solve.

Mathematicians' way of thinking

Mathematicians have a unique way of thinking. They are good at discovering the laws and characteristics of problems, so as to find solutions to them. In this problem, mathematicians first realized that the size and position of the circle have great influence on the solution of the problem, so they began to study the influence of the diameter of the circle and the position of the center of the circle on the problem.