How do we say "within a kilometer radius spherically"? When we say radius, we think of a circle, so how do you specify that you're thinking of a sphere when you say "within a kilometer radius"?

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  • This is a great question because as an English Language question it has a different context compared to a mathematics question. Thanks! – JBH Jun 8 '19 at 21:31
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    A radius is indifferent of whether its 2D circular or 3D spherical. The context will imply the extra or lesser dimension. – user30379 Jun 9 '19 at 3:59
  • If you communicate with a physicist, you can raise a smile by saying within a 1/300000 second light cone :-) – Jens Jun 9 '19 at 8:44
  • @Jens Light cones are 4D object. Also, they are infinite. Giving a dimension doesn't make sense. – Acccumulation Jun 10 '19 at 15:20

One could say "spherically", or "within a one-kilometer sphere". In some contexts the three-dimensionality will be obvious, as when one is speaking ot the relative position of satellites, say, or stars

  • There are ten satellites within a fifty kilometer radius
  • There are fewer than twelve stars within ten light-years of the sun.

But there is no special word or phrase that I know of for use in this situation, perhaps because it doesn't come up very often in ordinary speech.

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    Technically, a radius is spherical in 3D space. We think of radius of a circle if the space is just planar. – rexkogitans Jun 8 '19 at 16:30
  • @rexkogitans There can still be a circle, and indeed a line, in three-dimensional space (and in solid geometry) and a circle still has a radius. – David Siegel Jun 8 '19 at 16:40
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    Also an ellipse or an Ellipsoid has a radius -- in fact it has more than one (along the major and minor axes). – David Siegel Jun 8 '19 at 16:49
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    @DavidSiegel you're right that this is incredibly rare in ordinary speech. Where is the sphere? Is its equator equal to the surface of the ground? Is the sphere wholly above ground? Even when talking about a nuclear blast, we're only talking about a hemisphere. As you've answered, the context of the statement will be the only solution 99.9% of the time. – JBH Jun 8 '19 at 21:34
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    If you only said "within a one-kilometer sphere" the assumption would be diameter, not radius. – sirjonsnow Jun 10 '19 at 12:30

Pretty much just like that. "Radius" is used for spheres as well as circles.

... anything inside a sphere of one-kilometer radius around the object.

Alternately, just say

... anything within one kilometer of the object

assuming it's obvious you're talking about spatial rather than surface distances.

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You can say:

One kilometer in any direction.

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    This is very context-dependent. If you're on Earth and say "one kilometer in any direction", people will think of the circle surrounding them on the Earth's surface; if you're in the International Space Station, people will think of the sphere surrounding them. (If you're sitting on a train, people might even think one kilometer along any railway line.) – David Richerby Jun 9 '19 at 9:25

I usually say 'within a spherical radius of x from this point'.

In 3d computing and visual effects, this comes up more often than you would think.

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"Radius" is redundant. The term "within" already conveys the concept. If you want to emphasize that it's three dimensional, you can say that: "Within one kilometer, in any of the three dimensions".

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We say this:

Within a ten-foot-square area.
Within a ten-foot-cube area.

The equivalent for a sphere, and extending it to a kilometre, would be:

Within a one-kilometre-sphere area.

Note that you can also add a d to the end of all of these (squared, cubed, and sphered). While the version without a d is more an adjective and the version with a d is more a verb, I've heard both square and squared, as well as cube and cubed, and I couldn't say if one is more obviously (and objectively) natural than the other. I simply used the adjectival version for all three of my examples.

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    The first two statements are ambiguous as it isn't clear if one is referring to 10 feet as being the length of one side, or the resulting square area or volume. Similarly, "one-kilometre-sphere" is ambiguous as to whether 1 km refers to the sphere's radius, diameter, or volume. And although you provide a link to justify the term "sphered", I have never heard this in the wild. All volumes are expressed in cubic terms, regardless of object shape. So not sure if this answer achieves the precision asked for by the OP. – Michael MacAskill Jun 8 '19 at 8:27
  • @MichaelMacAskill I don't think anybody would misunderstand the meaning of the terms 10x10 room or 10x10x10 room, nor would the use of square or cube here normally be thought of as describing something different than that. While square and cube on their own might mean something else (especially, say, a square deal), context—using them in an adjectival noun phrase—should easily determine the intention. Anybody who isn't familiar with sphered would look to a dictionary anyway. (Note that when you mention a 10x10 room, you aren't concerned with height—or volume.) – Jason Bassford Jun 8 '19 at 10:25
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    Indeed, nobody would misunderstand 10 × 10 room, as there is no ambiguity. But "ten-foot-square" is ambiguous. It can easily be though to be "10 square feet", for example, rather than your intended 100 square feet. But again, none of that is relevant to the OP's question, except inasmuch as "one-kilometre-sphere" is still desperately ambiguous. Perhaps not surpassing, as your post refers twice to areas (of cubes and spheres), rather than volumes. – Michael MacAskill Jun 8 '19 at 10:31
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    Cubes and spheres have a volume, not an area. This can hardly be called nit-picking, seeing as it goes to the heart of the OP's question. – TonyK Jun 8 '19 at 11:47
  • @TonyK A cube and a sphere both have both a volume and an area, a surface area. Buit the OP mwas askign about a distance, whioch isn't really either. – David Siegel Jun 8 '19 at 14:38

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