A stereographic projection is a mapping that projects a sphere onto a plane. Stereographic projections occur in many areas of math. In fact, this past summer when I was studying minimal surfaces, we used a stereographic projection in the proof of Berstein’s Theorem (a major result in minimal surface theory). More recently, in the topology class I am currently enrolled in, a stereographic projection is used to show that the unit circle is the one point compactification of the real line.

Stereographic projections have a wide variety of uses in the math world, so what? Well, it turns out there are some pretty cool applications of them outside the pure math world. The most practical example is in the making of world maps. Since the Earth is a sphere, in order to project the Earth onto a flat piece of paper, to make a map, a stereographic projection is used.

But this is what’s really cool…

We can go the other way, project a plane onto a sphere. So imagine this, you take a picture, which is flat. We can project that image onto a sphere to get something that looks like this

photo courtesy of wikipedia