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I am interested in this unanswered question Pipe-fitting conditions in 3D and so I was trying to find information about it.
If the 3D curve $f(x(t), y(t), z(t)) = 0$ is a line I think that the pipe of diameter $D$ around it can be called the surface of a cylinder, but what is a proper mathematical term for describing that surface when $f$ is not a line? Tube? Pipe?
I believe in this case, the proper mathematical term for the region would be tube (or tube domain, depending on your focus), so the corresponding surface would be the surface of the tube. While pipe is not (to my knowledge) a formal mathematics term, it is used as a physical example in enough problems (both real and created) that the meaning would be just as clear.
Consider: Mathworld definition of 'tube'
With reference to a curve $C$ with continuously turning tangent in a metrical space of any number of dimensions, we define a tube as the locus of points at a fixed distance $\theta$, called the radius, from $C$, the distance being measured in each case along a geodesic perpendicular to $C$.
HOTELLING, Harold. Tubes and spheres in n-spaces, and a class of statistical problems. American Journal of Mathematics, 1939, 61.2: 440-460.
