According to legend, a plague broke out on an island called Tyrus in ancient Greece. The local people were so scared that they prayed for the protection of Apollo, the patron saint. After a series of prayers, people got God's will: if the square altar of the temple was expanded to twice its original size, the plague could be dispelled. So people began to build new altars.

However, because they doubled the length, width and height of the cube, the new altar was not doubled, but increased eight times! Everyone is very upset: how can we build a new altar twice as big as the original altar?

This problem may be solved easily now, but the only tools available at that time were rulers and compasses, so it was impossible to solve this problem.

Among the ancient Greek philosophers, there are a group of active thinkers who like to argue with others and can help others win the case in court like lawyers. They are the famous "wise men". In that era when philosophy and mathematics were not separated, these wise philosophers were not only able to skillfully use all kinds of debating skills and philosophical concepts, but also had their own unique views on mathematics, which was one of the famous "three major mathematical problems in ancient Greece" that the wise men thought about.

The other two problems of the three major mathematical problems in ancient Greece are: "turning a circle into a square", that is, drawing a square with a ruler, and its area should be equal to the area of a known circle; And "bisecting any angle" means bisecting any angle with a ruler.

There are two similarities between these three math problems that deserve our attention: first, they are all geometry problems; Second, people can only use rulers and compasses to solve problems. Making such special provisions is related to the way of thinking of thinkers at that time. They pursue simple and ideal figures, thinking that straight lines and circles are some of the most basic geometric figures, so even complex figures will eventually belong to them. In addition, although people at that time liked abstract thinking, geometrically, they insisted that any imaginary image must be drawn in black and white, which also formed the research characteristics of attaching importance to painting at that time.

Summary: Although the "three major mathematical problems in ancient Greece" were proved to be unsolvable in the19th century, mathematicians and thinkers in ancient Greece and even later have been exploring them since they were put forward, and thus many mathematical methods have been developed.