When talking about circles, a "circle" refers merely to a line in the shape of a circle, whereas "disk" (or "disc") refers to a "filled circle". Is there a similar distinction for squares or rectangles?

  • @Adam thanks for the tags, I seriously had no idea how to tag this. – the swine Oct 18 '15 at 15:49

"disc" means "thin, flat, circular object" and is mostly applied to 3D objects. "Circle" is for 2D-ish circular things.

In math, "disc" has its own meaning; the meaning you mentioned, as well as the normal meaning.

Names of shapes cover both definitions you provide ("a line in the shape of X" and "filled X"), except circle (and in non-rigorous talk, they get conflated too).

  • What would be a natural succinct way of referring to the two variants (filled vs. not)? – the swine Oct 16 '15 at 15:30
  • As you draw the line in the shape of a circle, the resulting shape is a circle, with (semantically) blank filling. As a result you get a semantic merger. – Nihilist_Frost Oct 16 '15 at 16:35
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    Try using filled/solid and hollow. – G. Ann - SonarSource Team Oct 16 '15 at 18:42
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    @Nihilist_Frost Note: "Disk" has a distinct mathematical meaning (which I'm pretty sure the question is referring to) that doesn't relate to 3D objects, but rather a circular area on a plane (i.e. 2D): en.wikipedia.org/wiki/Disk_%28mathematics%29 . But I can't think of any such term for any other shape either. – Jez W Oct 16 '15 at 18:43
  • @jezW How about the distinction between annulus, and concentric circles? Perhaps we don't specify a name for "filled square" because topologically, that's the same thing as a disk. – Adam Oct 16 '15 at 18:51

The catch-all term for these is"plane." Circular plane, square plane, rectangular plane etc.

A disk is defined as a plane bounded by a circle. Searching for the phrase "plane bounded by a square" does not yield a single word for which this is the definition.

  • It's worth noting that this is probably because planes are, in fact, rectangular by default. "Rectangular plane" is a redundant phrase. I can't find any nice words for a sub-section of the plane, though. – Crazy Eyes Oct 16 '15 at 19:55
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    I always took "rectangular plane" to mean a finite plane with known bounds since, as you say, otherwise it is redundant. – Yorik Oct 16 '15 at 19:59
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    In my experience (graduate school mathematics in a U.S. university), we would have called them "regions," not planes. Rectangular region. Triangular region. I completely disagree with the idea that "planes" are rectangular. Planes are infinite. – Adam Oct 16 '15 at 20:21
  • Surely you accept that there is a normal plain-english usage that makes fewer fine distinctions than a graduate-level treatise on mathematics without me needing to resort to a link to a dictionary. Also bear in mind that I myself say that planes are infinite. – Yorik Oct 16 '15 at 20:40
  • Doesn't answer the question. – Nihilist_Frost Oct 16 '15 at 20:42

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