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Orthogonal Systems of Circles on the Sphere
Orthogonal Systems of Circles on the Sphere
This Demonstration shows two families of circles on the sphere such that each circle in one family is orthogonal to each circle of the other family. In the plane these are called Apollonian circles.
As a special example, consider the circles of latitude (cut by planes perpendicular to the polar axis) and the great circles of longitude (cut by planes containing the polar axis). With the exception of the two poles, every point of the sphere is intersected by exactly one circle from each family and these two circles are orthogonal where they intersect (one circle is north-south at the point and the other is east-west). In this Demonstration, the circles are the intersection of the sphere with planes rotating about two axes.