Date: Dec 30, 2012 4:42 PM
Author: kirby urner
Subject: Re: A Point on Understanding

On Sat, Dec 29, 2012 at 10:35 PM, kirby urner <> 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)

Here it be (a proof), for letter (c):

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: (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)).