Circle, that is, geometry, is an important branch of mathematics, which is of great value to mathematical research.

First of all, Xue Yuan is a science that studies the relationship between space shape and size, which is the basis of many other branches of mathematics. For example, algebra, calculus, probability theory and so on all need to use geometric concepts and methods to understand and solve problems. Without geometry, the study of these branches of mathematics will be greatly limited.

Secondly, some basic concepts and theorems of circle science, such as point, line, surface, angle, circle and triangle, are important tools to describe the real world. For example, we can use geometric methods to measure the length, area and volume of objects, calculate the trajectory of objects, and design the structure and shape of buildings.

Thirdly, some theories and methods of circular science, such as Euclidean geometry, non-Euclidean geometry, analytic geometry and topology, have great influence on other scientific fields. For example, mechanics, electromagnetism and optics in physics are inseparable from the support of geometry; The analysis of molecular structure in chemistry also needs geometric knowledge; Genetics and ecology in biology also need geometric methods to study and solve problems.

Finally, some thinking methods of Yuanxue, such as abstract thinking, logical reasoning and proof methods, are also of great help to cultivate people's thinking mode and problem-solving ability. By studying geometry, people can learn how to abstract general laws from specific practical problems and how to verify and establish these laws through logical reasoning and proof, which is very important for improving people's scientific literacy and innovation ability.

Generally speaking, the value of Xue Yuan's research on mathematics mainly lies in its foundation as other branches of mathematics, as a tool to describe the real world, and as a method to cultivate people's thinking mode and problem-solving ability.