Circle of a sphere Circle of a sphere A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle. Circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle. In the geographic coordinate system on a globe, the parallels of latitude are such circles, with
Area of a circle formula_53. The calculations Archimedes used to approximate the area numerically were laborious, and he stopped with a polygon of 96 sides. A faster method uses ideas of Willebrord Snell ("Cyclometricus", 1621), further developed by Christiaan Huygens ("De Circuli Magnitudine Inventa", 1654), described in . Given a circle, let "u" be the perimeter of an inscribed regular "n-"gon, and let "U" be the perimeter of a circumscribed regular "n-"gon. Then "u" and "U" are lower and upper bounds for the circumference of the circle that become sharper and sharper as "n" increases, and their average ("u" + "U")/2 is an especially