Talk:Sphericity

The derivations for the volume, area, and sphericity of the dodecahedron are correct, but the numerical value for the sphericity should be about 0.910. I stopped my derivation for its sphericity at an earlier stage and erroneously concluded that the formula given was wrong without using it. If you don't believe the original numerical value given is incorrect, try substituting numerical values for the volume and area into the defining formula.

The discoverer still deserves a full citation: Hakon Wadell, “Volume, Shape and Roundness of Quartz Particles,” Journal of Geology, Vol. 43, 1935, pp. 250-280. I know that 1935 is correct because I copied“Systematic Packing of Spheres,” by L.C. Graton and H.J. Fraser, Journal of Geology, Vol. 43, 1935, from the same volume at a library.

The author of the sphericity entry should also write one for the circularity of closed planar areas, deriving a formula for it in a similar fashion. It would have been logical for Wadell to have done it in his 1935 paper, but I don't know if he did.

The problem with this article is that it is not always possible to derive simple algebraic formulæ for volumes and sphericities. As a result Coxeter and other mathematicians have tended to ignore the Archimedean and other regular-faced polyhedra. Computer science becoming a separate specialty has not helped any. It seems to have made mathematicians have even more difficulty accepting that an algorithm is every bit as good as a formula.

Numerical values for the sphericities of many more polyhedra may be found at http.//geocities.com/freasoner_2000/spheric.htm

Error in formula for a hemisphere?
On this page - http://en.wikipedia.org/wiki/Sphericity...

The equation provided for the volume of a hemisphere produces a value half the value of the equation provided for the volume of a sphere, but the equation for the surface area of a hemisphere produces a value 3/4ths the value of the equation for the surface area of a sphere. Both should be half. This problem can also be seen by thinking of the area formula as the derivative of the volume formula. That's the case for the formulas provided for the sphere but not for the formulas provided for the hemisphere.

Gregory A. Miller University of Illinois at Urbana-Champaign —Preceding unsigned comment added by 74.134.248.240 (talk) 17:51, 4 November 2007 (UTC)

I posted the note above, then realized a complication.

The complication is that, in the areas of science in which I work, "the area of a hemisphere" would refer to the area of the curved surface only, not also ncluding the area of the flat surface that bisects the full sphere as part of "the area of a hemisphere". On that view, my post is correct (that there is an error in the wikipedia page). On the other hand, for some purposes one would indeed want to include that flat surface, in which case the wikipedia page entry is correct.

Statistical Part
The statistical part is very bad and should probably just be removed. This talks about very specific sphericity. —Preceding unsigned comment added by 142.3.103.20 (talk) 01:54, 18 November 2009 (UTC)

fractals?
Is there an alternate definition applicable to bodies that have well-defined volume (and finite convex hull) but not well-defined surface area? —Tamfang (talk) 20:16, 24 December 2011 (UTC)

ideal cone
The examples given include "ideal cone (h=2√2r)", "ideal cylinder (h=2r)", "ideal torus (R=r)". What's ideal about these arbitrary choices of aspect ratio? —Tamfang (talk) 23:10, 20 May 2012 (UTC)
 * Perhaps they are the values which maximize sphericity?--Salix (talk): 08:06, 21 May 2012 (UTC)

Link broken
The link at the bottom of the page: Grain Morphology: Roundness, Surface Features, and Sphericity of Grains http://people.uncw.edu/dockal/gly312/grains/grains.htm Is broken... Edwardando (talk) 15:01, 10 September 2014 (UTC)

Merge proposal
Over on Talk:Roundness (geology), that withdrawn merge proposal led to the proposal for a new merge between Sphericity and Sphericity scale. Given the unreferenced stub at Sphericity scale, I support the idea of merging it here. Perhaps continue the discussion here. Klbrain (talk) 12:31, 12 June 2018 (UTC)

Formulas for sphericities of Platonic solids with rational denominators
The following are the formulas for sphericities of Platonic solids with rational denominators: Tetrahedron: $$ \Psi{=}\frac{\sqrt[6]{432\pi^2}}{6} $$ Cube: $$ \Psi{=}\frac{\sqrt[3]{36\pi}}{6} $$ Octahedron: $$ \Psi{=}\frac{\sqrt[6]{27\pi^2}}{3} $$ Dodecahedron: $$ \Psi{=}\frac{\sqrt[6]{21060000\pi^2+9396000\sqrt{5}\pi^2}}{30} $$ Icosahedron: $$ \Psi{=}\frac{\sqrt[6]{25380000\pi^2+11340000\sqrt{5}\pi^2}}{30} $$ —Jencie Nasino (talk) 05:37, 22 July 2019 (UTC)

Particle?
I'm confused by this. Is this talking about molecules, atoms, hadrons, leptons, quarks, bosons, rishons, etc.? Or a mathematical abstraction occupying a single point in space? The latter would necessarily have zero surface area and zero volume, so the ratio would be 0 : 0, which is somewhat meaningless. If it's talking about particles in chemistry/physics, I can't see why the definition should be restricted to these. Furthermore, the Sphericity of common objects section doesn't seem to be talking about particles in either of these senses, so it must be some other definition I haven't come across. Can anyone shed light? — Smjg (talk) 23:17, 17 July 2023 (UTC)


 * You are trying to make it too complicated. In colloqiual English, a particle is a small piece of matter. A dust particle. A particle of food. A piece of stuff. A thing. See Wikt:Particle, definition 1. —David Eppstein (talk) 00:28, 18 July 2023 (UTC)
 * Why a small piece of matter in particular? What is the sphericity of a medium-sized or large piece of matter, if not the same?  What is the sphericity of a geometric shape (which may not have a definite size or be made of matter), which the article goes on to talk about? — Smjg (talk) 12:10, 18 July 2023 (UTC)
 * I don't know why whoever chose that word did so. I would think sphericity would be more relevant for ball bearings, bowling balls, etc., which might be a bit too large to call particles. I'd be open to rewording. —David Eppstein (talk) 17:26, 18 July 2023 (UTC)
 * Whoever chose that wording was apparently following the cited reference, whose abstract refers to "the volume, shape, and roundness of sedimentary quartz particles." I agree that a rewording is in order. Perhaps we should change "particle" to "object." Doctor Whom (talk) 14:44, 20 July 2023 (UTC)
 * I thought myself "object" would be better. I haven't changed the sentence about Hakon Wadell's definition, as I would guess he defined it in terms of particles, so we may need to think a bit more about how to link talking about particles to talking about objects or geometric shapes more generally. — Smjg (talk) 16:23, 20 July 2023 (UTC)