Stereographic Projection Tutorial Using Line Parametrization

An all-in-one tutorial on how to parameterize lines and how to stereographically project a sphere to a plane using a given-find-solution style of teaching. What more can you ask for?

I'm saving topics such as the "point at infinity" and why this projection is a homeomorphism for future videos.

This type of projection is important to me because it serves as a "viewing window" into the fourth dimension. In math, we're allowed to stereographically project between n-dimensional spheres and n-dimensional planes. Because of this generalization, the hypersphere of which is naturally embedded in 4D space can be projected down to the entirety of 3D space.

After viewing the stereographic projection of the 3-sphere's Hopf Fibers down to 3-space, it lead me to believe that this projection's greatest purpose lies in its ability to show them.