1. Symmetry: A circle has a high degree of symmetry, and the distance from any point to the center of the circle is equal. This symmetry plays a key role in many problems and proofs in mathematics.
2. Pi: The ratio of the circumference to the diameter of a circle is called pi. π is an irrational number with important mathematical properties. It appears in many fields of mathematics and science, such as geometry, trigonometry, calculus and so on.
3. Area calculation: The area formula of a circle is πr_, where r is the radius. This simple formula is very useful in calculating the area of a circle and can also be extended to other geometric shapes.
4. trigonometric function: the angle of the circle is closely related to trigonometric function. In trigonometry, trigonometric functions such as sine, cosine and tangent have established important relations with the angle and side length of a circle.