Jul 30, 2025
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This is such a delightful opening paragraph for a paper.
(From “Surfaces with Klein bottle topology occur in fusion reactor fields” by C. B. Smiet. Shared with me by my father-in-law, who is a physicist.)
Finally some poetry of interest to me
The space that this male fiddler crab (a chiral object) lives in, a Möbius strip, is non-orientable. Note that the fiddler crab flips to being its own mirror image with every complete circulation (Non-orientable wormhole)
best square gluing diagram shape
disc
annulus
möbius strip
sphere
torus
klein bottle
real projective plane
(show results)
you know, the topology thing where you can pair up sides of a square or a rhombus or whatever and glue them together in a certain direction get a shape? and sometimes the shape only exists in 4 dimensions?
there's lots of sources online that list a subset of these options (like the wikipedia page for fundamental polygons), but i didn't see anything that had all 7 of these options listed, with diagrams, so i did it myself. i think it's exhaustive?
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Nonorientable Magic
this is a cat trying to drink out of a klein bottle
Klein Bottle