Saturday, June 12, 2010

Aristotle Was Right!

I put an "oops" here because a tetrahedron is not a polygon, nor need its faces be equal.

On the other hand, its four faces are polygons, and they might be equal.

The regular tetrahedron of four equilateral triangles is not a space-filler.

The tetrahedral disphenoid, on the other hand, with four equal isosceles triangles, is a space-filler, meaning Aristotle was right: tetrahedra do fill space.

Misinformation from Math World:
A space-filling polyhedron, sometimes called a a plesiohedron (Gr├╝nbaum and Shephard 1980), is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that the tetrahedron fills space, it in fact does not.
In fact the tetrahedron does fill space, just not the regular one

Per Which Tetrahedra Fill Space? by Marjorie Senechal in Mathematics Magazine, Vol. 54, No. 5 (Nov., 1981), pp. 227-243:
"Aristotle did not state explicitly that he meant regular tetrahedra... some scholars continued to defend Aristotle on the grounds that he had not explicitly required regularity..."
As well they might.

What other tetrahedra fill space, all by themselves? Which one is minimal, in the sense that it builds the others?

OCN Branding

We started Radical Math in Portland, Oregon, offering a first course through Portland Free School on March 13, 2010. Our venue: SE Belmont around 30th, at Flipside (since vanished).

RadMath teaches what we call Verboten Math, which is considered somewhat on the subversive side, not suitable for textbooks.

Mathematicians tend to welcome our stirring the pot, as argument and debate stimulate interest in often dry topics.

RadMath inherits from the Oregon Curriculum Network's "digital mathematics" curriculum.

Glenn Stockton focused on Neolithic Math whereas I was more into Martian Math.

Would you like to help sponsor? Help produce mathcasts?

Going down in history as a true radical, in conformist times when diversity was threatened, might be your reward.

Wanna win some brand loyalty from some of tomorrow's freest thinkers?

ConceptNet in Python

How might you build your own ConceptNet for a specific knowledge domain?

What "graphs" would you create, what "webs"?

In the case of a spatial geometry web, would you maybe have Mite, Syte and Kite as entries?:

IsA(Syte, two Mite)
IsA(Kite, two Syte)
IsA(Mite, A A B).

Make any sense?

This math is somewhat esoteric by today's standards, but if you're at MIT, maybe you know what I'm talking about.

Or is this stuff still verboten there too?

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