Interactive Geometry Lessons

The Erlangen Program, Concretely is a short series of interactive lessons built around the idea behind Klein’s Erlangen Program — a geometry is defined by its group of transformations, and different groups give genuinely different geometries on the same underlying space. Nothing to install, no account; open a lesson and start dragging.

Current lessons:

• Groups of translations — drag two generators to tessellate the plane; watch a single tile’s coloring reproduce itself exactly, tile after tile, which is the group’s quotient made visible.
• Groups of spiral similarities — the same idea with a jump-and-rotate generator instead of a translation, a one-parameter slider gliding continuously through the same points the discrete group only hops between.

Released under CC BY 4.0 — copy, adapt, and reuse freely with attribution.