Video produced by Douglas Arnold and Jonathan Rogness.

The video demonstrates the transformations in two dimensions but then backs away and adds a third-placing a sphere above the plane and shining light through it. As the sphere moves and rotates above the plane, suddenly all the transformations become linked, in a way that conveys visually in minutes what would otherwise take “pages of algebraic manipulations.

This video has been viewed more than a million times on YouTube, so it is not new, but every time I see it, I am fascinated. Going to higher dimensions and visualizing moebius transformation is just a bonus.

Download the full high resolution wide screen narrated video in QuickTime format (130mb), if you have a fast connection.