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In defining geography objects within software, I have things such as a City Area, which is an area defined by the bounds of a city, or a County Area, defined by the county boundary.

What is the proper term for an area defined by a center coordinate pair with a radius?

I thought circle might be appropriate, but wasn't sure since that circle is bent along the earth's surface. Is there a proper name for this?

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Circle sounds fine to me. You could also call it a buffer, depending on your target audience. – BradHards Oct 22 '12 at 22:52
@BradHards, Sounds good, thanks Brad! I thought there was a chance I was over-complicating this. – Brad Oct 22 '12 at 22:54
up vote 3 down vote accepted

"Circle" is overloaded and therefore ambiguous. Most often, this term refers to a circular boundary: a one-dimensional object. Mathematicians--who need to make careful distinctions like this--typically use "disk" (or its multidimensional generalization, "ball") when denoting the circle with its interior. The concept is very general: it applies to any metric space. This includes standard models of the earth's surface (including the sphere and ellipsoids).

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