What if we define 1/0 = ∞? | Möbius transformations visualized

Head to to get started for free with Brilliant’s interactive lessons. The first 200 listeners will also get 20% off an annual membership. 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. This video was sponsored by Brilliant. Video chapters: 00:00 Intro 02:38 Chapter 1: The 2D perspective 08:43 Chapter 2: More about inversion 14:33 Chapter 3: The 3D perspective (1/z) 19:38 Chapter 4: The 3D perspective (general) --------------------------------------------------- SOURCES: [That 2012 paper] Rigid motion 1-1 Möb