On Sat, Dec 29, 2012 at 10:35 PM, kirby urner <email@example.com> wrote:
<< SNIP >>
> In the meantime, lots of important concepts get introduced and we do > some proofs of: > > (a) Descartes' Deficit > (b) V + F == E + 2 (the proof in Cromwell, as he presents it, > attributed to von Staudt, is a fave) > (c) V = 10 * f * f + 2 (I've done one of these -- as Coxeter > exulted, it only takes high school level math) >
But then how does a high frequency cuboctahedron transform into a high frequency icosahedron of the type discussed above? That's less a matter of "proving" than of providing some compelling visuals, which I somewhat get into here:
http://www.4dsolutions.net/ocn/numeracy0.html (encourages use of free software by showing off graphics of the type the curriculum itself leads one to make -- math skills in conjunction with craft skills (not a new idea, though ray tracing software is still relatively not ancient)).