Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume?
01-31-2019, 06:07 PM (This post was last modified: 01-31-2019 06:15 PM by StephenG1CMZ.)
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 StephenG1CMZ Senior Member Posts: 821 Joined: May 2015
Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume?
Over on quora I just saw an interesting question: What is the opposite of a sphere?

My non-technical guess was all the space outside the sphere (like a torus but in 3D). That has the advantage of being easily visualisable in 3D.

But what is the defining characteristic of a sphere that we want the opposite of?
Some answers suggested a negative curvature, and that sounds mathematically interesting, but I'm not yet visualising how that looks.
Other answers picked on the number of corners, but I don't think it has a definite number. It seems to me you can make a case for both zero and infinity.

Another answer suggested that a sphere minimises suface area/volume, so its opposite should instead maximise that ratio...But what shape has that characteristic?

Stephen Lewkowicz (G1CMZ)
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 Messages In This Thread Geometry:what is the opposite of a sphere?& what shape maximises surface area/volume? - StephenG1CMZ - 01-31-2019 06:07 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Valentin Albillo - 01-31-2019, 06:47 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Thomas Klemm - 01-31-2019, 06:56 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - rprosperi - 01-31-2019, 09:29 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Massimo Gnerucci - 02-01-2019, 07:34 AM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Mark Hardman - 02-02-2019, 05:25 AM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Pekis - 02-01-2019, 10:23 AM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - StephenG1CMZ - 02-02-2019, 11:04 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Vtile - 02-05-2019, 11:04 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Massimo Gnerucci - 02-06-2019, 07:08 AM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Thomas Klemm - 02-06-2019, 08:31 AM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - ijabbott - 02-06-2019, 08:54 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Vtile - 02-06-2019, 09:53 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - berndpr - 02-09-2019, 10:43 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - StephenG1CMZ - 02-17-2019, 05:10 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - ijabbott - 02-17-2019, 08:21 PM RE: Geometry:what is the opposite of a sphere?& what shape maximises surface area/... - Thomas Klemm - 02-17-2019, 06:09 PM

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