College Math Teaching

April 1, 2013

Fun for my Facebook Friends

Filed under: advanced mathematics, knot theory, topology — Tags: , — collegemathteaching @ 9:59 pm

Fun question one: can anyone see the relation between the following three figures? Note: I made a (sort of subtle) mistake in one of them….the one where the graph lines are showing)

tangle

fundamentallink

order3knot

Fun question two (a bit harder):

What is the relation between these figures?

type1calc

infinprod

And for the win: what is going on here? (this is ambiguous)

bingsling

Ok, I’ll help you with the last one: imagine this process (one solid torus (think: doughnut or bagel) inside a larger one, and repeat this process (think: those Russian dolls that are nested). If you then take the infinite intersection, you get a simple closed curve (not obvious) that is so badly embedded, it fails to pierce a disk at any of its points (and certainly fails to have a tangent vector anywhere).

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