What if we define 1/0 = ∞? | Möbius transformations visualised
Defining 1/0 = ∞ isn’t actually that bad, and actually the natural definition if you are on the Riemann sphere – ∞ is just an ordinary point on the sphere! Here is the exposition on Möbius maps, which will explain why 1/0 = ∞ isn’t actually something crazy. And this video will also briefly mention the applications of the Möbius map.
There will also be things like circular and spherical inversion, which are really neat tools in Euclidean geometry to help us establish lots of interesting results, this one included.