Secondly, the science of circle involves many important geometric concepts and theorems, such as central angle, chord length, arc length, tangent line and so on. These concepts and theorems are widely used to solve practical problems and deduce other geometric theories. For example, the tangent theorem of a circle is the basis for solving the tangent problem related to a circle, and the arc length formula is an important tool for calculating the perimeter and sector area.
In addition, the science of circle is closely related and intersected with other geometric disciplines. For example, combined with trigonometry, we can study the properties of inscribed triangle and circumscribed triangle of a circle; Combined with analytic geometry, the problem of circle can be transformed into algebraic equation through coordinate system. Combined with solid geometry, we can study the properties and characteristics of cylinders, spheres and other geometric bodies.
Finally, Xue Yuan also plays an important role in mathematics education. It is one of the important contents of mathematics curriculum in junior and senior high schools. By learning circles, students can have an intuitive perception of geometric figures, master basic geometric reasoning and proof methods, and improve their problem-solving ability and thinking logic.
To sum up, circles play an important role in geometry. It is not only the basis of studying geometric figures and problems, but also a bridge to connect and cross other geometric disciplines, and it also plays an important role in mathematics education.