Projecting a Circle on a Sphere to an Enclosing Cylinder
A cylindrical projection maps points on a sphere to a cylinder wrapped around the sphere at its equator.
Several cylindrical mappings are possible, depending on the function that maps on the sphere to on the enclosing cylinder. The most common ones are the equidistant and the equal area cylindrical projections.
This Demonstration shows those two projections of a spherical circle. You can move the circle on the sphere by rotating it about either the or axis.