This is what a Riemann sphere is. https://en.wikipedia.org/wiki/Riemann_sphere Some ideas for graphing on the Riemann sphere: https://www.mathematica-journal.com/2008/11/14/graphing-on-the-riemann-sphere/ I had this idea as a shower thought, and realized that people haven't had this idea yet. Here is a tangent function graphed on the Riemann sphere. Noticeable details: - Undefined points are represented here as points at infinity. - The feature of the function diverging close to undefined points is shown here as the shown segment of the function speeds up near infinity, while slowing down near the origin. - The line getting longer is just the range of the graphed region of the function increasing.
