Great post! Here's one from Keith Peters with some interactive code examples: https://www.bit-101.com/blog/2022/01/circle-inversion/
What is the inverse of a circle?
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Re: What is the inverse of a circle?
#42I did some wacky inside-out pics of planets years ago, inspired by the inside-out Mandelbrot set looking like a leaf/teardrop. https://www.adamponting.com/inside-out/ Related: Not Knot , 1991 Thurston-ish short film about knots and knot complements - "the space where the knot isn't". https://www.youtube.com/watch?v=zd_HGjH7QZo https://en.wikipedia.org/wiki/Not_Knot https://en.wikipedia.org/wiki/Knot_complement
To me, inside out would mean the core on the outside with the crust in the middle. ;-)
Re: What is the inverse of a circle?
#43The dymaxion projection of the globe is one of my favorites and is essentially what an unbroken singular peel/shell of an orange would look like, centered on the North Pole
Re: What is the inverse of a circle?
#44The dymaxion projection of the globe is one of my favorites and is essentially what an unbroken singular peel/shell of an orange would look like, centered on the North Pole
Take Away: 'Is a "smoke ring" also possible as an accustic phenomenon ?' (-;
Re: What is the inverse of a circle?
#45imo it would be helpful if the interactive visualizations indicated that they are interactive—I skipped right over the first one!
Re: What is the inverse of a circle?
#46Otherwise know as a Möbius transformation...how is this terminology missing from the article?
Re: What is the inverse of a circle?
#47IMO the opposite of a curve is an angle. One is smooth, the other disjoint such that zooming in on a curve flattens it, but zooming in on an angle makes no change. A circle is a curve that comes back around to the starting point, closing itself. The opposite of closed is open.
Therefore I propose that the inverse of the unit circle is something like the (open) region around two intersecting line segments at the origin.
Re: What is the inverse of a circle?
#48I was really hoping the answer was some input/output dad joke along the lines of: I/O...
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Re: What is the inverse of a circle?
#49This article is interesting but not rigorous I think. * The inverse of a geometric shape makes no sense. We only inverse operations. * aa^-1 = 1 only if you consider the multiplication over reals. * 1/0 is not equal to infinity. Because the article is interesting but some people might be put off by the first few sentences, I suggest to had a disclaimer that this article lean on edutainment to the detriment of rigorou…
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Re: What is the inverse of a circle?
#50Great post! Here's one from Keith Peters with some interactive code examples: https://www.bit-101.com/blog/2022/01/circle-inversion/
Sorry: meaning this one copied from that earlier one, without attribution? yuck.