Topology introduction:

1. Topology is a subject that studies some properties of geometric figures or spaces that can remain unchanged after constantly changing their shapes. It only considers the positional relationship between objects, without considering their shapes and sizes.

2. The English name of Topology is topology, and the literal translation is geography. First of all, it refers to the study of related disciplines with similar topography and landforms. Geometric topology is a branch of mathematics formed in19th century, which belongs to the category of geometry. Some contents about topology appeared as early as the eighteenth century. Some isolated problems discovered at that time played an important role in the formation of topology later.

Origin:

1. Mathematically, the Seven Bridges in Konigsberg, the polyhedral euler theorem and the four colors are all important issues in the development history of topology. Konigsberg (now Kaliningrad, Russia) is the capital of East Prussia, and the Pledgel River runs through it. /kloc-in the 0/8th century, seven bridges were built on this river, connecting the two islands in the middle of the river with the riverbank.

People often walk on this bridge in their spare time. One day, someone asked: is it true that each bridge can only walk once before it can finally return to its original position? This seemingly simple and interesting question attracted everyone. Many people are trying various methods, but no one can do it. It seems that it is not so easy to get a clear and ideal answer.

3. 1736, someone found the great mathematician Euler with this question. After some thinking, Euler quickly gave the answer in a unique way. Euler first simplified the problem. He regarded two small islands and the river bank as four points respectively, and seven bridges as connecting lines between these four points.

Then the question is simplified as, can you draw this figure with one stroke? After further analysis, Euler came to the conclusion that it is impossible to walk every bridge and finally return to its original position. And gives the conditions that all the drawings can be drawn. This is the pioneer of topology.