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Many shapes have different terminology for them depending on how many dimensions. For example, a regular quadrilateral in two dimensions is a rectangle, but in 3D it is a box. Compare also circle versus sphere.

Are there different words that can be used to distinguish a line segment with end points in two-dimensional space versus three dimensional space?

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  • $\begingroup$ A line in 2D is also a line in 3D and the terminology doesn't change. The next "step up" by analogy with the circle and the sphere is the line and the plane. Beyond that the pair would be called the plane and the 3-space. $\endgroup$
    – abiessu
    Sep 21, 2013 at 4:37
  • $\begingroup$ Vector, perhaps $\endgroup$
    – Don Larynx
    Sep 21, 2013 at 4:42
  • $\begingroup$ With curves, one sometimes says space-curve. With lines and line segments. I have not seen any distinction made. $\endgroup$ Sep 21, 2013 at 4:47
  • $\begingroup$ Ah...yes, good point on the line and the plane. Hadn't thought of it. I'm working on a piece of software and I was hoping for something more elegant than point2d/line2d and point3d/line3d for my object names, but it might not exist. $\endgroup$
    – lcr
    Sep 21, 2013 at 5:05

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No shape has a different name in 3D than in 2D, including line segments.

Even in a 3D space one can have a rectangle or a circle and by that one means a flat figure. A "box" is a completely different shape?

Would you call a cylinder a "3D circle" or a "3D rectangle"?

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I have never heard any different names, either in mathematics or computer science.

DirectX and OpenGL both use names like Point2d, Point3d, so evidently the folks who designed those APIs didn't have any better ideas. And, anyway, I think it's better to stick with boring commonplace names in public interfaces, to minimise befuddlement among the users of your package.

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