Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Common Core snippet a little distressing
Replies: 73   Last Post: Jul 26, 2013 6:27 PM

 Messages: [ Previous | Next ]
 kirby urner Posts: 2,472 Registered: 11/29/05
Re: Common Core snippet a little distressing
Posted: Jul 17, 2013 1:23 PM
 att1.html (2.6 K)

On Wed, Jul 17, 2013 at 10:06 AM, Robert Hansen <bob@rsccore.com> wrote:

>
> Primarily, because it isn't intuitive (at all) as an illustrative aid for
> students learning volume and cubing. That is the reason it didn't nor will
> ever catch on.
>
>

It did catch on, in the 1900s, and there's a branch of mathematics
exploring this new territory.

The tetrahedron (simplex) is a topologically minimum volume in having the
fewest edges of any edge-built structure. The cube has 12 edges and 6
faces compared to the tetrahedron's inventory of 6 and 4.

For an alien civilization to think a topologically minimum volume could
also serve as a unit of volume does not seem that far fetched -- great
science fiction could be made from this.

The tetrahedron arises more naturally when you consider sphere packing, a
topic that got a lot of attention in the 1900s as well, especially in
n-dimensions.

Three spheres (equal radius) make a triangle (connect their centers) and a
fourth sphere, nesting in the valley, above or below, makes a tetrahedron
(connect centers again).

That's the first time we get the edges to enclose a volume (the edges
define an inside separated from an outside).

The octahedron we get, of four balls in a square, one above, one below, has
a volume of 4, relatively speaking.

Young students have no problem with these concepts.

The tetrahedrons and octahedrons fill space together, to make even bigger
tetrahedrons and octahedrons.

Playing with this skeleton is worthwhile because it's what we call the
iso-matrix, also CCP and FCC (same thing).

It's of core significance in chemistry and crystallography, a kind of
"holodeck". Molecules may be (are) defined with reference to it.

Kirby

> But when its oblique coordinate system applies to a problem, then by all
> means use it. Once you learn all the math to apply it.
>
> Bob Hansen
>
>

Date Subject Author
7/13/13 Peter Duveen
7/13/13 Robert Hansen
7/13/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/14/13 kirby urner
7/14/13 Robert Hansen
7/15/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 kirby urner
7/14/13 Wayne Bishop
7/15/13 kirby urner
7/15/13 Robert Hansen
7/15/13 Christian Baune
7/15/13 kirby urner
7/16/13 Wayne Bishop
7/16/13 kirby urner
7/14/13 Wayne Bishop
7/14/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Joe Niederberger
7/15/13 Robert Hansen
7/15/13 kirby urner
7/15/13 Robert Hansen
7/16/13 kirby urner
7/16/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/15/13 CCSSIMath
7/16/13 Joe Niederberger
7/16/13 Robert Hansen
7/16/13 kirby urner
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 Robert Hansen
7/17/13 kirby urner
7/17/13 kirby urner
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/17/13 Joe Niederberger
7/17/13 Joe Niederberger
7/17/13 Robert Hansen
7/18/13 Wayne Bishop
7/18/13 Joe Niederberger
7/18/13 kirby urner
7/18/13 Joe Niederberger
7/20/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 kirby urner
7/19/13 Joe Niederberger
7/19/13 Joe Niederberger
7/20/13 kirby urner
7/21/13 Joe Niederberger
7/23/13 kirby urner
7/24/13 frank zubek
7/24/13 frank zubek
7/24/13 kirby urner
7/25/13 frank zubek
7/25/13 kirby urner
7/25/13 frank zubek
7/25/13 frank zubek
7/25/13 frank zubek
7/26/13 frank zubek
7/26/13 frank zubek