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August 17th, 2005
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Sphere
In general usage, do you consider the word "sphere" to mean just the outside surface, or are the points inside the surface automatically considered part of the sphere (i.e., without having to say "a sphere and its interior")? How about in general mathematical usage (which may be different from the precise mathematical definition of a sphere, which is only the surface and not the interior)?

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From:mabfan
Date:August 17th, 2005 02:04 pm (UTC)
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Whenever I taught geometry and used the word "sphere," I always meant the whole sphere, including the surface and all interior points. So I would refer to the "volume of the sphere." If I wanted to indicate just the surface, I would refer to the "surface of the sphere."

Hope that helps.
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From:jarel
Date:August 17th, 2005 02:08 pm (UTC)
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I'd take "sphere" to include the inside; I'd expect someone to say "the surface of the sphere" or "a hollow sphere" otherwise.
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From:pling
Date:August 17th, 2005 02:10 pm (UTC)
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Ditto.

I seem to be doing that to your comments a lot, recently ;)
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From:pinkfish
Date:August 17th, 2005 02:13 pm (UTC)
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In normal usage, this sort of precision doesn't come into play; "A peach is shaped roughly like a sphere"; of course, the peach includes the interior, but the "shape" doesn't have to refer to one or the other. "The Earth is not really quite a sphere", same thing; the Earth has an interior (of course), the sphere maybe does or doesn't.

Mathematically, the shpere is the locus in three dimensions of points equidistant from a given point, the "center" (at a given distance, the "radius"). The points inside are not equidistant from the center, and hence aren't included.

I suppose one could have defined it as the locus of points at distance r or less from the center, but that's not the definition I ever heard.

Or to be very very terse, x^2+y^2+z^2=1 is the formula for the unit sphere, not x^2+y^2+z^2<=1
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From:magid
Date:August 17th, 2005 02:13 pm (UTC)
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Ditto.
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From:jazzfish
Date:August 17th, 2005 02:35 pm (UTC)
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My vote's for this one.
2D analogy: mathematically, a circle is definitely just its circumference.
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From:queue
Date:August 17th, 2005 02:37 pm (UTC)
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Despite the mathematical definition, it seems that "sphere" is sometimes used to mean "sphere and its interior" in (less formal) mathematical contexts; see mabfan's comment above.

I see your point about normal usage not usually making a distinction.
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From:surrealestate
Date:August 17th, 2005 02:40 pm (UTC)
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The whole thing.

After all, I'd use the phrase "The volume of a sphere" as opposed to "The volume of the space inside the sphere, including the sphere itself" or somesuch.
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From:queue
Date:August 17th, 2005 03:07 pm (UTC)
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Of course, you could just as easily be talking about the capacity of a sphere, since the terms "capacity" and "volume" appear to be virtually interchangeable in common usage, in which case "sphere" might only mean the outside surface.
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From:surrealestate
Date:August 17th, 2005 03:29 pm (UTC)
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That's true. Although does capacity always include the thing itself? If I have a glass whose capacity can be measured as X, the volume of the container plus contents is still more than X.
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From:queue
Date:August 17th, 2005 03:51 pm (UTC)
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True, but a sphere (meaning the locus of points equidistant from a center) has no volume itself.
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From:bitty
Date:August 17th, 2005 02:46 pm (UTC)
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In common usage, doesn't the phrase "sphere of influence" automatically include the space inside? So whether mathematically correct or not, that's certainly what my brain defaults to. All of my brain, not just the surface ;)
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From:spwebdesign
Date:August 17th, 2005 03:09 pm (UTC)
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I'm not qualified to comment on the term's mathematical definition. In common usage, as with many other words and phrases, I think it depends on the context Okay, I just changed my mind. I've considered both the mathematical definition as given by pinkfish above and common usage. In terms such as "sphere of influence," it is correct to say that something is "within," not "in," that sphere. That would imply that "sphere" denotes only the boundary line, that outside surface, and not points within it. To say that something is "in" the sphere, rather than "within" it, strikes me as incorrect.

Isn't there a term for the solid described within a sphere?
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From:queue
Date:August 17th, 2005 03:49 pm (UTC)
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Isn't there a term for the solid described within a sphere?

In computer graphics, I believe they use the term "ball" for this.
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From:zzbottom
Date:August 17th, 2005 05:36 pm (UTC)
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I tend to think of a sphere as just the outside.
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From:mattlistener
Date:August 17th, 2005 08:37 pm (UTC)
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I consider it ambiguous and governed by context. If I wanted to be precise I would say "spherical surface" or whatnot.
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From:hrafn
Date:August 18th, 2005 01:37 am (UTC)
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I think if you are positing a spherical chicken, you are definitely including all the points inside the surface, too.
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