1, circular area: S=πr? Or s = π (d/2)? . (d is the diameter and r is the radius).
2. area of semicircle: s semicircle =(πr? )/2。
3. Circumference: C=2πr or c = π d..(d is the diameter and r is the radius).
4. The circumference of a semicircle: c semicircle =πr+2r or c semicircle = π r+d. ..
5. The area of the circle where the sector is located is divided by 360 and multiplied by the angle of the central angle of the sector N: S = N/360× π r? .
The area of a circle refers to the size of the plane space occupied by the circle, which is often expressed by S. The circle is a regular plane geometry figure, and there are many calculation methods, such as Kepler method and cavalli method.
Extending Cavoli's point of view, we can also regard curves as unweighted. So the area of a circle is similar to the splicing of countless circumferential curves. The radius of these circles is a continuous point from 0 to r, which can be regarded as a straight line with length r, and the sum of the radii of these circles can be regarded as a right-angled equilateral triangle with right-angled side length r.
Contributions of ancient mathematicians
Zu Chongzhi, an ancient mathematician in China, started with a circle inscribed with a regular hexagon, multiplied the number of sides, and approximated the area of a circle with the inscribed area of a regular polygon. Mathematicians in ancient Greece started with regular polygons inscribed in a circle and circumscribed at the same time, increasing the number of their sides and approaching the area of the circle from the inside out.
Mathematicians in ancient India cut a circle into many small petals similar to watermelons, and then butted these small petals into a rectangle, replacing the area of the circle with the area of the rectangle. Many ancient mathematicians worked hard on the area of a circle and made valuable contributions. It opens the way for future generations to solve this problem.