[Edu-sig] RE: Concentric hierarchy / hypertoon (was pygame etc.)

Arthur ajsiegel at optonline.net
Sun Mar 20 14:47:54 CET 2005

> From: Kirby Urner [mailto:urnerk at qwest.net]
> > No major mind damage is going to be done by a different presentation.
> >
> > But I would like to disassociate the notion of geometry and the
> regularity
> > of forms as completely and as early as possible. And this is where I
> seem
> > to be most non-Fullerian.
> >
> > Art
> >
> Not claiming to follow, but yes, we appear to diverge here.

I suspect this exchange is more interesting to you and I than to others on
the list and that it would be most appropriate to table it to a face-to-face
at PyCon breaks - except that my schedule is conspiring against it, it now
looking that I won't be able to make it there.  The best I can hope for at
the moment is attending Friday's sessions.  

> The thing is, we don't disassociate "playing with blocks" from
> architecture,
> and by extension from geometry, at all, in current childhood education.
> We
> most intimately link a rectilinear format, with various cylinders, cones
> and
> balls, into the young (very young) imagination.  Cubes are both prevalent
> and regular, without any doing from me.
> So Fuller's innovation is *not* with respect to linking shapes and
> geometry
> early (regular shapes included, in the form of blocks, toys using them),
> but
> in the particular assortment of shapes and their canonical relationships.
> It's much more 60 degree than we're used to (what with all the equiangular
> triangles everywhere), from a classical western perspective, which is more
> 90 degree, more into post and lintel perpendicularity.

Well certainly Klein presentation makes the (not necessarily regular)
tetrahedron the fundamental space form - so that Klein and Fuller are
thinking in the same manner in some fundamental respects. And I happen to
have a great fondness for 60 degrees - gained via the folding of flexagons,
introduced to me in 4th grade by a brilliant teacher. I still can't resist
making one when I see a roll of adding machine tape.  I think they would be
a great addition to your repertoire.

I think the real competition to the tetrahedron in space is the sphere, and
the real revelation is the perspective that makes the tetra more useful than
it as the fundamental space form.

But I guess I shouldn't forget that Klein's matrix algebra for lengths,
areas, and volumes is working via a regular rectilinear coordinate system.

I know you and others have thought about a coordination of space via a
regular tetrahedron.  *That* I find fascinating, and would probably be my
best way in to more Fullerist geometric thinking.


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