[HN Gopher] The Borsuk-Ulam Explorer
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       The Borsuk-Ulam Explorer
        
       Author : robinhouston
       Score  : 16 points
       Date   : 2023-12-14 11:08 UTC (11 hours ago)
        
 (HTM) web link (julius-ross.com)
 (TXT) w3m dump (julius-ross.com)
        
       | kelseyfrog wrote:
       | Interesting. In practice, what's the distribution of Borsuk-Ulam
       | pairs across the globe? Something other than a Bingham
       | distribution?
        
       | ano-ther wrote:
       | Cool. That's the principle behind why you can stabilize a wobbly
       | table by turning it -- you will find a position where all four
       | legs are on the ground.
       | 
       | Didn't know it had a name.
        
       | dark-star wrote:
       | This is one of the things that, at first, sounds quite
       | unbelievable. Then, when you think about the math involved, it
       | becomes quite clear and almost trivial (well, in this case it's
       | not exactly trivial, but in some other cases it is).
       | 
       | Similar (but slightly easier to prove) mathematical "tricks":
       | 
       | - if you take two pieces of paper, crumple one up and put it on
       | the other, there is at least one point on the uncrumpled paper
       | that is directly underneath the corresponding point in the other
       | paper
       | 
       | - If you have a chair (or table) with 4 legs, and it wiggles
       | because the floor is uneven, then you can always find a way to
       | rotate it around the center so that it doesn't wiggle anymore
       | 
       | - there is no way to comb a hairy sphere ;-)
        
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       (page generated 2023-12-14 23:00 UTC)