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
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