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Topic: Volume of geodesic "sphere" (project)
Replies: 21   Last Post: Aug 15, 2001 3:09 AM

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Brian Hutchings

Posts: 635
Registered: 12/6/04
Re: Volume of geodesic "sphere" (project)
Posted: May 1, 1998 7:15 AM
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In a previous article, rjc@maths.ex.ac.uk (Robin Chapman) says:

oops; forgot alt.skeptics!... as for "triangled", yes,
that is a Buckyism, although I favor "trigonned" or "trigonated",
or wome thing better will arise. I mean,
the triangle is *special*, but why privileged to ungreek naming?

>But you still wrote a^2. How do you say this? a triangled?
>What about a^3?


the following is not a dysadvantage, so much as a lack
of practice with the "always complimentary space-filling
of tetrahedra & octahedra", or what ever Bucky saith. true,
the hexahedron (and the tetragon) is self-dual (ditto), but
that also happens to be related to the other lattice,
which Bucky calls the Isotrpic Vector Matrix (IVM),
for some reason o'be.

>Anyway there is a subtle disadvantage with using the regular tetrahedron
>as the model for measuring volume, as opposed to the cube and
>indeed either the equilateral triangle or the square for measuring area.
>One can estimate area of a plane figure, by superimposing a fine square grid
>and counting the number of little squares in your given figure. You
>can do the same with equilateral triangles. In three-dimensional space
>one can do the same with cubes, as we can tessellate space by cubes,
>BUT it is impossible to do the same with regular tetrahedra.


personally, I dyslike the quadray stuff, but
they may have done some neat-o things with it, by now (it seemeth)
or have gotten rid of some of the baggage o'hype. so,
how about "tripolar co-ordination" ??

>coordinate system for the problem at hand (Cartesian, affine, projective,
>trilinear, polar, spherical, etc.) while no doubt you as liberated from this
>sterile dogma are free to use quadray coordinates for any problem whatsoever.


I recall this dyscovery;
Gerald did it by type-and-error on his laptop,
somewhat mysteriously inducing Euler's old formula, although
in terms "normal" to Bucky, or precessional, he might have saith.

>It is misleading not to call them equivalent too.

oh; le'see.

>I presume the formula is something like the square (SORRY triangle) root
>of x^2 + y^2 + z^2 + u^2 - xy - xz - xu - yz - yu - zu which must be
>easier to work with than the Pythagorean expression: the square (no apology)
>root of x^2 + y^2 + z^2.


Fink Haplloyd maketh me puke!

>Weren't they some popular beat group? Did they have a donkey fixation
>(I thought it was pigs)?


--
member, African Civil Rights Movement -- extirpate retrocolonialism!
(No **** is good ****; eh?... http://inet.uni-c.dk/~sch-inst/pres.html)
<DELETIVES EXPLETED> http://www.tarpley.net </DELETIVES EXPLETED>
*---<Brian Hutchings, Living Space Programs, Santa Monica College>---*







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