A tube of radius of a set is the set of points at a distance from. In particular, if is a regular space curve whose curvature does not vanish, then thenormal vector andbinormal vector are always perpendicular to, and the circle is perpendicular to at. So as the circle moves around, it traces out a tube, provided the tube radius is small enough so that the tube is not self-intersecting. A formula for the tube around a curve is therefore given by

for over the range of the curve and. The illustrations above show tubes corresponding to acircle,helix, and two torus knots.

The surface generated by constructing a tube around acircleis known as atorus.

See also

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• oloid
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References

Bar-Natan, D. "Tube Plot Package."http://www.math.toronto.edu/~drorbn/KAtlas/Extras/TubePlot.m.

Referenced on Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Tube." FromMathWorld--AWolfram Resource.https://mathworld.wolfram.com/Tube.html

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