The axis of revolution passes through the hole and so does not intersect the surface.
2.
Such surfaces includes all surfaces of revolution, where the degenerate curve is the axis of revolution.
3.
The parameter " c " is the distance from the intersecting plane to the axis of revolution.
4.
This is in contrast to disk integration which integrates along the axis " parallel " to the axis of revolution.
5.
Without loss of generality, choose a coordinate system so that the axis of revolution is the " z " axis.
6.
I only call them a " torus " or " toroid " if the section which is rotated is a full circle in the plane of the axis of revolution, but not touching that axis.
7.
:: If we are to be rather pedantic, this is somewhat ambiguous, since if the axis of revolution does not go through the center of the annulus, then you get something else.
8.
But I'm a little stumped and I have about five problems left to finish, all of which involve the same twist in the normal solid of revolution process . . . the regions we are rotating contain the axis of revolution.
9.
"' Shell integration "'( the "'shell method "'in integral calculus ) is a means of calculating the volume of a solid of revolution, when integrating along an axis " perpendicular to " the axis of revolution.
10.
Light rays within a plane through the axis of revolution ( the " z " axis ) of the torus are refracted according to the smallest radius of curvature, " r ", which means that it has the greatest refractive power, " s ".
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