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Regarding:I suppose I had better bring the usual note of practicality to this amusing idea. Masking tape these days may be purchased in a form that can mask quite small radii. This is NOT the tape for this demonstration.
The key idea is to use /masking tape/ to construct geodesics.This is an excellent suggestion. I would only warn that in order for the analogy to work properly the tape needs to be *carefully* laid down on the surface locally straight/even with no bunching/wrinkling or stretching/tearing of the tape material as it is laid down. If the surface has significant curvature over a length scale comparable to the width of the tape and the tape *can't* be laid down without local distortion, then the tape needs to be laid down in a way that any unavoidable stretching or binding is laterally symmetric across the centerline of the tape. (But maybe this caveat is included in one of JD's lurid details.)
You can apply tape to surfaces that have zero or nonzero
intrinsic curvature and see what happens.
David Bowman
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