These Shapes Are Topologically Equivalent

Post by fwlr » Fri, Mar 10, 2023, 2:55 PM UTC

SetTheorist wrote: post #20

fwlr wrote: post #14

Earlier quoted context omitted.

Not quite, since most topological transformations can’t be done on actual physical objects. (I would love to see some of those wood and string puzzles try to implement some of these style of topological puzzles though, that would be awesome if it was possible.) Most of the wood and string puzzles fall under knot theory specifically, rather than topology. The main trick I’ve seen used in those puzzles is they have kno…

I'm not sure exactly what you're trying to say (I'm not sure what you mean by "separate" here), but your assertions seem incorrect. Knots can have even or odd crossing numbers, that alone will not tell anything about whether it is an "unknot" or not. Also, if you have two non-trivial knots and "join" them (ie each a knot in a circle, cut each circle in one spot and join the circles at the cuts) you will _never_ get a…

Post by ouid » Fri, Mar 10, 2023, 3:57 PM UTC

tmhn2 wrote: post #4

The little cartoon shows they are ambient-isotopic--that they are just topologically equivalent is pretty clear already!

Post by OscarCunningham » Fri, Mar 10, 2023, 5:55 PM UTC

vidanay wrote: post #24

fwlr wrote: post #16

Earlier quoted context omitted.

You know the joke about how when you kiss someone, you’re temporarily forming a long tube with an anus at each end? A topologist friend heard that joke and immediately offered a conjecture that that shape is topologically equivalent to the shape you’d get if you connect a mouth to an anus. This got the party discussing if there exists a homeomorphism between making out and eating ass. I agree, you really can’t trust…

Topologically a human is a donut (torus).

Post by ajkjk » Fri, Mar 10, 2023, 10:35 PM UTC

pcrh wrote: post #22

Neat! What are the "real world" uses for this kind of mathematics?

Post by fwlr » Sat, Mar 11, 2023, 4:19 AM UTC

krsrhe wrote: post #19

fwlr wrote: post #16

Earlier quoted context omitted.

You know the joke about how when you kiss someone, you’re temporarily forming a long tube with an anus at each end? A topologist friend heard that joke and immediately offered a conjecture that that shape is topologically equivalent to the shape you’d get if you connect a mouth to an anus. This got the party discussing if there exists a homeomorphism between making out and eating ass. I agree, you really can’t trust…

It doesn’t exist, because there is no homeomorphism that takes a distance of 0 to non 0, so you can’t change the connections.