Monday, May 11, 2009

Back on the Beat

:: museum gift shop toy: instructional booklet ::

I'm doing the usual math teacher beat today, checking in with my sources, one could say "my informants" but that usually means "tattle tales" and I'm not into accusing my peers on the street of such petty crimes. Anyway, I usually don't get to know that much of the picture, at least not from their angle.

I also distribute info (a two way trade), some say "on the sly" but I feel we're pretty up front about it (i.e. open source), we who teach "the Gnu Math" (as some call it, me included).

Today, it's all about this game of "BAT and Ball", an easy mnemonic, reminding of an all-American pass time. In this lesson plan activity, we equate the B, A and T modules (widgets, sliver shapes) in terms of volume, and relate them to our CCP ball of unit radius, a high frequency system (lets say "porous"), maybe spinning (to even out the bumpy bits). Or lets picture a bowling ball, again all-American.

The B & A
build a rhombic dodecahedron (RD) of volume 6 while the T builds a rhombic triacontahedron (RT) of volume 5. We're using tetra-volumes of course, our right as an ethnicity (as buckaneers or whatever). Each RD contains one unit radius ball, tangent to 12 others at the diamond-face centered K-points (kissing points).

What I've been yakking about in review, is our phi/sqrt(2) radius for this other larger rhombic triacontahedron of K-mods (in this namespace), the one that edge-wise criss-crosses the aforementioned volume 6 RD, although not as its dual ("coworker" maybe).

Volume 5 RT
height h of T-module, 1/120th of volume 5 RT
(in tetravolumes)

Its 7.5 volume may be reduced to 5 by a scale factor of course, its radius shrinking by a 3rd root of 2/3 to meet up with the T-module's and an overall volume of 120 * 1/24.

In the meantime, two As (a left and a right) and a B (a left or a right), define our minimum space filler as depicted on page 71 of Regular Polytopes, dubbed "a MITE" in some circus geek gypsy talk but otherwise known as a trirectangular tetrahedron of specific dimensions.

MITE with two Whacks
:: a MITE and two Whacks, on page 71 ::

Given 3 * (1/24) = 1/8, and given our MITEs fill space with no gaps, we have the basis for some excellent gift shop offerings, educational toys, some of which I already have in my collection, for classroom sharing, and/or recording in studio.

Yes, I'm tracking NASA's Atlantis, on an 11 day service call to Hubble, just about 4 hours into it at the moment.

:: roadshow materials, battle scarred ::