:::I've enjoyed playing with the mirror ideas previously, though more in a 3D setting. A friend runs a rock shop and an amateur rockhound group, and I wanted to make the mathematics more accessible. The mirror approach is the simplest I've found in the literature I've examined. So much of what we learn today is based on coordinates and formulae that the pure geometry is lost. 
 :::I'm tinkering (in SVG) with an illustration of translation addition, along with other isometry images; it's pretty to see what can be shown without equations. 
 :::And I think it's good to stimulate that part of the brain. Apparently Hilbert and Cohn-Vossen thought so! Conway, Doyle, Gilman, and Thurston liked the idea enough to use the same title for a summer workshop and a Princeton course, "Geometry and the Imagination". That's pretty good company.  2005 June 28 12:26 (UTC)