It is true that some of the nicest topics in secondary school geometry are relegated to that optional never-never-land that classes never have time to visit. Sorry about not doing better by the pseudosphere. It's hard to convince someone that it actually has constant curvature when the different parts appear so, well, different. The conviction follows from the equations that give the measure of curvature, and that was unfortunately out of bounds for the Scientific American Library. It does show up nicely in a differential geometry course, but only half way into the semester.
I hope you enjoyed the exploration we carried out on Monday with the regenerating Velcro Moebius band.
Somehow the Kantians of the mid-nineteenth century remind me of some of the ultraconservative figures on today's scene. They were very, very sure that they had the right viewpoint, and they showed remarkably little tolerance for ambiguity, let alone contradictory stands. There is an interesting interchange on Kantian philosophy at odds with mathematical fashion when George Lewes, the husband of Mary Ellen Evans (George Eliot) took on J. L. Sylvester after his presidential address before the London Mathematical Society was published. The topic at issue was whether or nor higher-dimensional spaces could be conceived. I think I have the issue straight--the expert in the field is Prof. Joan Richards in the History Department here.