On Wed, Jul 17, 2013 at 9:00 AM, Robert Hansen <bob@rsccore.com> wrote:

On Jul 17, 2013, at 10:46 AM, kirby urner <kirby.urner@gmail.com> wrote:

Dang, I wrote a fine reply last night through the Web interface to math-teach @ Math Forum but it ain't appearin'. 

I am sure it was damn fine, my condolences, I hate that when it happens.

Archimedes, Sommerville, M. Goldberg, Karl Menger...  One ancient greek and a handful of 1900s contributors to this branch point: where mathematics goes off to explore some new territory, like a living organism (STEM students take note).

They say Archimedes was wrong to say "tetrahedrons fill space" but if he meant "not regular" he was right.  Sommerville took up this question, of what tetrahedrons fill space, as did M. Goldberg. 

It's an accessible part of math, fitting right in with tiling and space-filling more generally, elementary school topics.
Was it in agreement that the cube was chosen over the tetrahedron (and sacks of sand) because it MADE MORE SENSE?

Bob Hansen

Does Euclidean geometry make more sense than non-Euclidean? 

It certainly gets more attention and is better developed.  These more recent branches are not surprisingly less trafficked, but that's no reason to avoid them completely.

What we're after is STEM literacy / fluency. 

Right where we talking about 3rd powering as "cubing" we have an opportunity to introduce an alternative that leads to an interesting section of books and other resources in the math and engineering library -- maybe not a huge number, but easily accessible. 

Curriculum writers such as myself, looking to brand, to gain recognition for their work, have a golden opportunity here, to define their material as aligned with the Common Core and yet going beyond it. 

Those that make a foray into "tetrahedroning" (and not just "cubing") will be distinguishing themselves for including more 1900s innovations, that until recently you could only find out about at places like MIT (Dr. Loeb's class for example).