My second issue of GeekOut! (electronic preprint) features what I've called the Kabul Dome Rant. Like Vol 1. No 1, it has lots of typos, which gave me an excuse to publish a follow-up Addenda and Errata.
The Kabul Dome was a pawn (or maybe higher) on the Cold War chess board, and is a feature of this book, which I'm considering assigning.
Another feature is an essay co-authored by Polya of "How To Solve It" fame, wherein he spends a lot of time on Euler's V + F = E + 2. There's this web cam at an MIT lounge we're using, to make graph theory come alive. An "edge" might mean a one-way "we can see you" spy cam.
You'll have a better understanding of security systems if you know how to read directed graphs (similar to wire bundles in today's aircraft, such as a GS V for $44.5 million -- I might be off on the price tag, a topic @ FNB the other day, with some wealthy gathered; LW thought they were under priced).
As I was recounting on MathFuture (a Math 2.0 OER), this V + F = E + 2 meme has been a part of my generic intro to geometry lesson plan for like 3rd grade and up for some decades. I featured it in Bhutan, along with posters from Peda.com, Lesotho, and in numerous schools around the North American continent (although mostly in Portland). I bring quite a few geometry toyz to the class, as well as slide shows, links to Youtubes.
Schools vary in their ability to accommodate. North Americans tend to lag, when it comes to Internet access (they have the technology, but the bureaucracy gets in the way -- a lot more like India, so blame the UK?).
Anyway, the Kabul Dome was the USAs way of advertising a brighter tomorrow, and it was actually working its magic with the Afghanis, who saw it as a kind of glorified yurt (which it is). The Russians noticed the positive vibe and wisely offered to buy the thing, so they could take it home and reverse engineer. The plans are no longer under patent in any case, and you can find old DEW line radomes on Ebay, as one of my Alaska contacts once alerted me. Domes feature in many playgrounds across the land.
But what about V + F = E + 2. Which textbooks have that? And what do they do about nesting polyhedrons, one inside the other, like Russian dolls? This is a way to show off important relationships, found in nature, in architecture. Many of these were known to Euclid. The Elements is not just about flat stuff. So given Polya was into it, and Euler, a founder of topology, we have a great litmus test for judging the worthiness of elementary, middle and high school geometry textbooks. No V + F = E + 2? No concentric hierarchy of polyhedrons? If you wanna go to MIT, you best develop some critical thinking skills and learn that some textbooks should be derided.
The "gnu math" coming from geek corners involves heaping scorn on various math texts that clearly avoid walking their own talk. They may say they're "constructivist" and yet no real construction goes on. No hands on skills. No camping. No fire starting. They may say they're inspired by Polya, but there's no V + F = E + 2. So as future MIT students, we just laugh and poke fun. How could we possibly take these textbooks at all seriously?
This freedom to rip into books and tear them apart, critically, is encouraged throughout the humanities, is the basis of speech and debate. The Cleveland Cannibals in our district are coached to be ruthless (within the rules of academic propriety of course) in a sportsmanlike manner. The attacks need not be ad hominem.
No sphere packing? Ridiculous. In Vol 1, No 2 follow-up, I find the web page about biomes that shows both the Desert Dome in Omaha and the Garden of Eden domes in Cornwall, and yet does nothing to link to the Dymaxion Projection, House or Car, the house being on exhibit in the very same town as this college or university (Dearborn MI). Talk about lame lesson plans.
Our goal is to have students (MIT students among others) going out over the web and critiquing the math teacher resources they find. Apply various filters and criteria. Establish a ranking. Cosmetics should matter a lot less than content. Don't be shy about questioning authority either. Grade those teachers. Let the world know you have taste and style, not to mention common sense.
I think as a student activity, "grading teachers" is going to be popular. Of course what we're really doing is grading curricula. We're looking for memes like V + F = E + 2, and if we're not seeing much of anything going around that, we're forming a judgment. Not all math texts are equally deserving. Many are ridiculously devoid of relevant content. Lets put those on display. Virtual museums etc.