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
Distance from a point to a line formula_39 perpendicular to the line. The distance from the point to the line is then just the norm of that vector. This more general formula is not restricted to two dimensions. If the vector space is orthonormal and if the line ("l" ) goes through point A and has a direction vector formula_45, the distance between point P and line ("l") is where formula_47 is the cross product of the vectors formula_48 and formula_45 and where formula_50 is the vector norm of formula_45. Note that cross products only exist in dimensions 3 and 7. Distance from a point to a