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Discussion of "tarmrsilondre"

Comment #1: Pathologies
Curtis W Franks (Fri Mar 10 06:09:11 2017)

This includes (half-)infinite cylinders (which may have holes drilled some
of the way down, parallel to their axis), at least some polygons such as
the rectangle and regular octogon, a "U" if made properly, and many other
weird shapes.

It generalizes to some higher-dimensional shapes. For higher-dimensional
cylinders, it selects generalizations which have a linear (2-dimensional,
rather than higher-dimensional linear manifold) axis.

It excludes spheres and tori, and many other shapes of rotation/revolution.

Thus, we may want to refine the definition.

Comment #2: Re: Pathologies
Curtis W Franks (Fri Mar 10 06:11:17 2017)

krtisfranks wrote:
> Thus, we may want to refine the definition.

The current definition is this:

"x1 is a set of points/shape (of any number of dimensions) such that
x1 is connected and there exists a line L such that for any line L' that
is parallel to L, if L' has nonempty intersection with x1, then there
exists exactly one subinterval (line segment, ray, or line) J of L' such
that J has nonzero (Lebesgue) measure and any subset of L' which nonemptily
intersects x1 is contained in J. An axially-perpendicular cross-section
of x1 probably is necessary to specify x2. See also: slanu,

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