The formula for the area of a circle is: S=πr? ，S=π(d/2)？ (D is the diameter, R is the radius, π is the pi, usually 3. 14), and the formula of circular area is constantly deduced by ancient mathematicians.
Zu Chongzhi, an ancient Chinese mathematician, started with the inscribed circle of a regular hexagon, multiplied the number of sides, and approximated the area of the circle with the area of the inscribed circle 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.
Kepler,/kloc-a German astronomer in the 6th century, divided the circle into many small sectors. The difference is that he divided the circle into infinitely many small sectors from the beginning. The area of a circle is equal to the sum of the areas of an infinite number of small sectors, so in the last formula, the sum of the areas of small arcs is the circumference of the circle, so there is S=πr? .
Formula related to circle:
1, area of semicircle: s semicircle = (π r 2)/2. (r is the radius).
2. The area of the circular ring: s great circle -S small circle = π (r 2-r 2) (r is the radius of the great circle and r is the radius of the small circle).
3. Circumference: C=2πr or c = π d..(d is the diameter and r is the radius).
4. The circumference of a semicircle: d+(πd)/2 or d+π r (d is the diameter and r is the radius).
5. Sector arc length L= central angle (arc system) ×R= nπR/ 180. (θ is the central angle) (R is the sector radius)
6. Sector area S=nπ R? /360=LR/2 .(L is the arc length of the sector)
7. Radius of cone bottom surface r=nR/360. (R is the bottom radius) (N is the central angle)
In the sum of infinite small sector areas, so in the last formula, the sum of small arcs is the circumference of a circle, so there is S=πr? .