Next up are the Stereographic and Orthographic projections. These projections have existed for thousands of years. They were even used by the ancient Greeks! These two methods are projections of the sphere onto a plane, resembling what it would look like if you were to view the earth from space. The Orthographic projection maps along straight lines perpendicular to the tangent plane of the sphere (think looking through a window from space) while the Stereographic projection maps each point by constructing a line through a predefined point (like the north pole) and drawing where it intersects the tangent plane (think the image in a mirror that the earth is placed on). Thus, the main difference is that Orthographic takes the projection from infinity while the Stereographic takes the projection from a point on the sphere. This means that the Orthographic projection only shows one hemisphere, where the Stereographic can show the entire sphere (except the pole) but in a more distorted way. For both of these projections, directions are true from the center point. With the Orthographic projection, any line going through the center is a great circle.
There are many more projections to be found online and in books. Indeed, Wikipedia has a stellar list of some of the many different types. These projections all have different uses and are able to convey information in their own clever way, but they share at least one thing in common: they take quite a bit of ingenuity and creativity to come up with and they reflect a deep love and understanding of math in their creators.