
Re: Volume of geodesic "sphere" (project)
Posted:
May 1, 1998 7:15 AM


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 spacefilling of tetrahedra & octahedra", or what ever Bucky saith. true, the hexahedron (and the tetragon) is selfdual (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 threedimensional 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 neato things with it, by now (it seemeth) or have gotten rid of some of the baggage o'hype. so, how about "tripolar coordination" ??
>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 typeanderror 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.unic.dk/~schinst/pres.html) <DELETIVES EXPLETED> http://www.tarpley.net </DELETIVES EXPLETED> *<Brian Hutchings, Living Space Programs, Santa Monica College>*

