If you shaped the bags into uniform-sized polyhedrons and fit them together seamlessly, like bricks, to form this growing tetrahedron, then you would be showing what the cube people show. The cube people show smaller bricks making the bigger cube. Here, we have an octahedron and tetrahedron that together fill space.
Another demo would be to take a glass or clear plastic tetrahedron and bury the tip in the sand so it stays upside down. Pour liquid into it using a unit tetrahedron measuring cup. Mark the positions 1, 8, 27, 64... and notice they are equally spaced up the side.
Unlike a cube, when you slice a regular tetrahedron parallel to any side, you still have a regular tetrahedron. Nice property. Slice a cube that way and you have a cube no longer.
On Sun, Jul 14, 2013 at 9:38 AM, Robert Hansen <email@example.com> wrote:
> > On Jul 14, 2013, at 12:05 PM, kirby urner <firstname.lastname@example.org> wrote: > > You have allowed yourself to get side-tracked by a non-issue. It's not > just an analogy, it's a perfectly good model of 3rd powering that doesn't > happen to use a cube. This is what Common Core will lead to, a hardening > of the mental arteries such as you're experiencing now. By adulthood, it > may be irreversible. > > > But that doesn't make any sense. I could just stack bags of dirt in the > order of 1, 8, 27, 64, ... and call it 3rd powering, but where would the > intuition be in that? That is a requirement for teaching, is it not? First > we had a poster that identifies intuition with reason and now we have one > that identifies it with rhetoric. > > Bob Hansen > >