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Topic: Common Core snippet a little distressing
Replies: 73   Last Post: Jul 26, 2013 6:27 PM

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kirby urner

Posts: 1,908
Registered: 11/29/05
Re: Common Core snippet a little distressing
Posted: Jul 18, 2013 6:31 PM
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On Thu, Jul 18, 2013 at 10:36 AM, Joe Niederberger <niederberger@comcast.net
> wrote:

> Kirby says:
> >Here's an unconventional non-XYZ mapping:
> http://en.wikipedia.org/wiki/Quadray_coordinates
>
> I found this to be more enlightening:
> http://en.wikipedia.org/wiki/Synergetics_%28Fuller%29
>
> Which led to places like this:
> http://www.grunch.net/synergetics/ivm.html
>
>

So have you found anything like a "branch" yet? You were saying you
couldn't find one.

Alexander Graham Bell was another pioneer, with those octet truss kites.


> I don't see any applications of these coordinate systems explained. If to
> were to go into business manufacturing geodesic dome kits and such, would
> you use one of these to calculate your material and manufacturing
> requirements, and resulting product specs, or something more traditional?
>
>

One application I'm aware of was I used them to help compute what are
called Waterman Polyhedrons (Steve Waterman found other collaborators after
joining with our group). Watermans are maximally convex shells defined by
IVM nodes of radius X or less from an IVM origin (i.e. some (0,0,0,0)).

Since all IVM vertexes have whole number coordinates (and all formed from
them have whole number volumes vis-a-vis unity -- even the irregular ones)
there was streamlining involved in some of the computations.

But since all the algorithms out there (e.g. for finding a convex hull
given a set of points) use XYZ, I of course needed two-way conversions.

The goal with the iso-matrix may be "conceptual fluency" over "number
crunching" i.e. in tuning in that scaffolding, we're doing what any chemist
would do when imagining an FCC lattice. You can let computers do the busy
work of plotting / rotation / scaling etc. (ala Pymol).

But the presentation along this branch is different (than dwelling on face
centers of cubes) as Dr. Loeb helped point out. Rather than explain the
FCC in terms of a cube, we start with a nuclear ball and pack 12 around it,
to form a cuboctahedron (you have other options -- though only one if all
touching four neighbors plus nuclear with each ball), then another layer of
42, then another of 92... that's an important sequence, accessible to 8th
graders.

http://oeis.org/A005901 (cuboctahedral numbers)

Follow links from there too: you'll get back to the same neighborhood (my
web site, connected topics). See a branch yet?

Kirby

Cheers,
> Joe N
>



Date Subject Author
7/13/13
Read Common Core snippet a little distressing
Peter Duveen
7/13/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/13/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/14/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/14/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/14/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/14/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/14/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/15/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Wayne Bishop
7/14/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Wayne Bishop
7/15/13
Read Re: Common Core snippet a little distressing
kirby urner
7/15/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/15/13
Read Re: [Math 2.0] Re: Common Core snippet a little distressing
Christian Baune
7/15/13
Read Re: Common Core snippet a little distressing
kirby urner
7/16/13
Read Re: Common Core snippet a little distressing
Wayne Bishop
7/16/13
Read Re: Common Core snippet a little distressing
kirby urner
7/14/13
Read Re: Common Core snippet a little distressing
Wayne Bishop
7/14/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/15/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/15/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/15/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/15/13
Read Re: Common Core snippet a little distressing
kirby urner
7/15/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/16/13
Read Re: Common Core snippet a little distressing
kirby urner
7/16/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/17/13
Read Re: Common Core snippet a little distressing
kirby urner
7/17/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/17/13
Read Re: Common Core snippet a little distressing
kirby urner
7/17/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/17/13
Read Re: Common Core snippet a little distressing
kirby urner
7/15/13
Read Re: Common Core snippet a little distressing
CCSSIMath
7/16/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/16/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/16/13
Read Re: Common Core snippet a little distressing
kirby urner
7/17/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/17/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/17/13
Read Re: Common Core snippet a little distressing
kirby urner
7/17/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/17/13
Read Re: Common Core snippet a little distressing
kirby urner
7/17/13
Read Re: Common Core snippet a little distressing
kirby urner
7/17/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/18/13
Read Re: Common Core snippet a little distressing
Wayne Bishop
7/17/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/17/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/17/13
Read Re: Common Core snippet a little distressing
Robert Hansen
7/18/13
Read Re: Common Core snippet a little distressing
Wayne Bishop
7/18/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/18/13
Read Re: Common Core snippet a little distressing
kirby urner
7/18/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/20/13
Read Re: Common Core snippet a little distressing
kirby urner
7/19/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/19/13
Read Re: Common Core snippet a little distressing
kirby urner
7/19/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/19/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/20/13
Read Re: Common Core snippet a little distressing
kirby urner
7/21/13
Read Re: Common Core snippet a little distressing
Joe Niederberger
7/23/13
Read Re: Common Core snippet a little distressing
kirby urner
7/24/13
Read Re: Common Core snippet a little distressing
frank zubek
7/24/13
Read Re: Common Core snippet a little distressing
frank zubek
7/24/13
Read Re: Common Core snippet a little distressing
kirby urner
7/25/13
Read Re: Common Core snippet a little distressing
frank zubek
7/25/13
Read Re: Common Core snippet a little distressing
kirby urner
7/25/13
Read Re: Common Core snippet a little distressing
frank zubek
7/25/13
Read Re: Common Core snippet a little distressing
frank zubek
7/25/13
Read Re: Common Core snippet a little distressing
frank zubek
7/26/13
Read Re: Common Core snippet a little distressing
frank zubek
7/26/13
Read Re: Common Core snippet a little distressing
frank zubek

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