1. Euler diagram: Euler diagram is a graphical model used to represent network structure, which was put forward by mathematician Euler in18th century. It can be used to solve the traveling salesman problem, that is, how to find a shortest path that passes through each city once and returns to the origin.
2. Four-color theorem: Four-color theorem is a problem about map coloring, which requires that the map on the plane be divided into four areas, so that the colors of adjacent areas are different. This theorem was put forward in the19th century and was not proved until the 20th century.
3. Fractal: Fractal is a geometric shape with self-similarity, and its local structure is similar to the whole structure. Fractal can be used to describe many phenomena in nature, such as mountains, clouds and rivers.
4. Topology: Topology is a branch of mathematics that studies the shape and properties of space. It can be used to solve some problems related to continuity, such as judging whether two shapes can be transformed by stretching or compression.
5. Triangulation: Triangulation is a method of dividing a polygon into several triangles. It can be used to calculate the area and perimeter of polygons and other related calculations.