Area of a circle a formula for the surface area, we can use the same kind of “onion” approach we used for the disk. Area of a circle In geometry, the area enclosed by a circle of radius is . Here the Greek letter represents a constant, approximately equal to 3.14159, which is equal to the ratio of the circumference of any circle to its diameter. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons. The area of a regular polygon is half its perimeter multiplied by the distance from
Circumference in terms of these parameters. One such approximation, due to Euler (1773), for the canonical ellipse, is Some lower and upper bounds on the circumference of the canonical ellipse with formula_5 are Here the upper bound formula_9 is the circumference of a circumscribed concentric circle passing through the endpoints of the ellipse's major axis, and the lower bound formula_10 is the perimeter of an inscribed rhombus with vertices at the endpoints of the major and minor axes. The circumference of an ellipse can be expressed exactly in terms of the complete elliptic integral of the second kind. More precisely, we