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I'm working on sphere packings. When I write, I'm confused with basic definitions. I'm hesitating between the terms "sphere", "ball" or "oriented sphere".

For example, on the wikipedia page of circle packing theorem

A circle packing is a connected collection of circles whose interiors are disjoint.

But rigorously, a circle (1-sphere) is the boundary of a disk (2-ball). A sphere has no interior, a ball has. The interior is important for the definition of packings.

The problem becomes serious if I want to include hyperplanes as generalised spheres, or if I want to use the usual exterior as the interior (negatively curved balls)

I also read in literature definitions like

A sphere packing is a collection of balls with disjoint interiors

I prefer this one, but why not call it a "ball packing" directly as here? I tend to use "ball packing", but since almost every others is using "sphere packing", I'm wondering if I missed something important by calling these objects "balls". (For example, google with "Apollonian ball packing" returns no result.)

Another solution is "oriented sphere", as in Lie sphere geometry. Then my question is, what's the difference (in practice) between a sphere with an orientation, and a ball with an interior?

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Best terminology: :-) – Goldstern Dec 7 '12 at 11:49
I don't think it's the world's most interesting question, but I also don't see why there are votes to close. It seems harmless enough. – Tom Leinster Dec 7 '12 at 12:11
Certainly "ball packing" is a more logical name than "sphere packing" according to modern mathematical conventions, but "sphere packing" is traditional. It doesn't cause any serious confusion, and I prefer the sound of it (maybe just because I'm used to it). It's possible that the community will gradually drift towards "ball packing" over time, but I don't see movement in that direction; if it does happen, it is likely to be pretty slow, especially since there are advantages to using the same terminology as most other people. – Henry Cohn Dec 7 '12 at 14:11
I don't know if the OP is a native English speaker. To me, "ball packing" evokes associations that are distracting ... sort of like the junior high school giggles you get when you talk about Uranus. – Ben Crowell Dec 7 '12 at 15:56
@Ben: if you think that is bad, I heard a talk by a mathematical physicist where he remarked that online searches for information on the hard-core model (of gases, in statistical mechanics) gave, erm, results of a different nature – Yemon Choi Dec 7 '12 at 18:37

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