Stereographic projection

Okay kiddo, imagine you have a ball or a globe in front of you. Pretend you are a bug standing on top of the ball. What do you see? The top of the ball, right?

Now suppose you draw a line starting from the bottom of the ball, going through the middle and coming out of the top of the ball. The line would split the ball into two halves, right?

Now imagine you shine a flashlight at the ball from the bottom, what would happen? You would see the shadow of the ball on a flat surface, like a wall.

In stereographic projection, we do something similar. Instead of the ball being a physical object, we use mathematical equations to create a virtual sphere.

Now, imagine the top of the virtual sphere is the North Pole and the opposite side is the South Pole. We can draw a line starting from the North Pole and going through any point on the sphere.

If we continue that line to the flat surface we talked about earlier, we would get a single point. This is called the projection of that point on the flat surface.

We can do this for every point on the sphere, and we would get a bunch of points on the flat surface that correspond to points on the sphere.

Ta-da! That's stereographic projection! We use it to project 3D objects onto a 2D surface, like a map or a photograph.