The three major geometric problems in ancient Greece are both fascinating and very difficult. The beauty of the problem is that it looks simple, but it actually has profound connotation. It is required that only compasses and scaleless rulers can be used for drawing, and only rulers and compasses can be used for a limited number of times. But the basic figures that rulers and compasses can make are: draw a straight line, draw a circle, draw the intersection of two straight lines, draw the intersection of two circles, and draw the intersection of a straight line and a circle.

There are all kinds of geometric shapes in life, and curves and straight lines are the most basic graphic features. So the basic geometric figures originally drawn by human beings are straight lines and circles. To draw a straight line, you must use a tool with a straight edge, and to draw a circle, you must use a tool with one end fixed and the other end rotating, thus producing a ruler and compass.

The rulers of ancient Greece were rulers without scales. They feel from a lot of drawing experience that only two drawing tools, ruler and compass, can draw all kinds of geometric shapes that meet the requirements. Therefore, the ancient Greeks stipulated that painting can only be done a limited number of times with two tools, ruler and compass, which is called ruler and compass painting. With the long-term drawing practice and the requirement of drawing with measuring tools, people have drawn a large number of drawings that meet the given conditions. Even some complicated drawing problems can be skillfully solved through limited steps. Between the 6th century BC and the 4th century BC, the ancient Greeks encountered three cartographic problems that troubled them.

1. Angle trisection problem: bisection of any given angle.

2. Cubic multiple product problem: Find the side length of a cube, so that the volume of this cube is twice that of the known cube.

3. Turn a circle into a square: make a square so that its area is equal to that of a known circle.

These are three famous problems in ancient geometric painting. They were put forward before the publication of Primitive Geometry. With the spread of geometry knowledge, they were later widely spread all over the world.