Basic Concepts of Arc and Sector Relationships
In circle geometry, there is a very close relationship between arc length and sector area. Imagine a bicycle wheel spinning, the larger the rotation angle of the wheel, the longer the path traced by a point on the edge of the wheel and the larger the area swept by the wheel's radius.
This relationship can be expressed in the form of a consistent proportion. When the central angle of a circle changes, the arc length and sector area will change proportionally with the same ratio to the circumference and total area of the circle.
Fundamental Proportion
The fundamental proportion that connects arc length and sector area to the whole circle can be expressed as follows: