After 400 years, mathematicians find a new class of solid shapes
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After 400 years, mathematicians find a new class of solid shapes
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Re: After 400 years, mathematicians find a new class of solid shapes
#2Perhaps this submission will get more love than when I submitted it 2 days ago:
Re: After 400 years, mathematicians find a new class of solid shapes
#3It’s hard to know whether or not this is interesting, since the article is very vague and the paper is behind a paywall: http://www.pnas.org/content/early/2014/02/04/1310939111
The claim that Goldberg polyhedra are not really polyhedra is especially puzzling. Presumably the paper explains this better!
Re: After 400 years, mathematicians find a new class of solid shapes
#41. The original article: http://theconversation.com/after-400-years-mathematicians-fi...
2. It actually looks more like a redefinition than a new discovery: "It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces "
Re: After 400 years, mathematicians find a new class of solid shapes
#5Anyone else stumble on that "nasablueshit" typo?
Re: After 400 years, mathematicians find a new class of solid shapes
#61. The original article: http://theconversation.com/after-400-years-mathematicians-fi... 2. It actually looks more like a redefinition than a new discovery: "It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces "
Indeed. A better title may be "After 400 years, a debate over a definition begins among mathematicians."
Re: After 400 years, mathematicians find a new class of solid shapes
#71. The original article: http://theconversation.com/after-400-years-mathematicians-fi... 2. It actually looks more like a redefinition than a new discovery: "It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces "
Goldberg polyhedra: http://en.wikipedia.org/wiki/Goldberg_polyhedron
As far as I can tell, the discovery here (if there is one at all) is a method for constructing those polyhedra and others like them and being sure they're actually polyhedral (no curved or bent faces).
Re: After 400 years, mathematicians find a new class of solid shapes
#81. The original article: http://theconversation.com/after-400-years-mathematicians-fi... 2. It actually looks more like a redefinition than a new discovery: "It may be confusing because Goldberg called them polyhedra, a perfectly sensible name to a graph theorist, but to a geometer, polyhedra require planar faces "
Indeed. A better title may be "After 400 years, a debate over a definition begins among mathematicians."
I don't think that's quite right. They narrowed the definition to strict polyhedral, which hadn't been done before. Then showed that they existed.
"Schein and his colleague James Gayed have described that a fourth class of convex polyhedra, which given Goldberg’s influence they want to call Goldberg polyhedra, even at the cost of confusing others. "
Re: After 400 years, mathematicians find a new class of solid shapes
#9It’s hard to know whether or not this is interesting, since the article is very vague and the paper is behind a paywall: http://www.pnas.org/content/early/2014/02/04/1310939111 The claim that Goldberg polyhedra are not really polyhedra is especially puzzling. Presumably the paper explains this better!
(Non-mathematician here.) Seems the fuss is about getting the faces of the Goldberg polyhedra to be planar.
There's an article at sciencenews.org [1] which has a bit better explanation I think.
It seems "Goldberg polyhedra" as commonly understood encompasses a bunch of shapes which wouldn't normally qualify as polyhedra because some of their faces don't have all of their vertices in the same plane (i.e. the "hexagons" in the picture at the article would not really be flat)
This is what the paper is calling "dihedral angle discrepancy" - a dihedral angle being the angle between two planes.
From the abstract[1], the claim of the paper is to have found a subset of Goldberg "polyhedra" where the planarity of faces is guaranteed.
The resulting shapes also have all edges the same length, but the faces are not necessarily equiangular.
As far as I can tell, they're claiming that only one each of tetrahedral and octahedral Goldberg (or Goldberg-like?) polyhedra exhibits equal edges and planar faces, but that there are infinite icosahedral variations with these properties.
The supplementary info for this paper[2] has more details about their methodology, which seems to included use of molecular modelling software and iterative methods, as well as a few pictures.
[1] https://www.sciencenews.org/article/goldberg-variations-new-...
[2] http://www.pnas.org/content/early/2014/02/04/1310939111
[3] http://www.pnas.org/content/suppl/2014/02/05/1310939111.DCSu...
Re: After 400 years, mathematicians find a new class of solid shapes
#10Anyone else stumble on that "nasablueshit" typo?
Indeed. For the curious, it should be NASA Blueshift [1]
[1] http://astrophysics.gsfc.nasa.gov/outreach/podcast/wordpress...