[HN Gopher] A Tower of Conjectures That Rests Upon a Needle
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       A Tower of Conjectures That Rests Upon a Needle
        
       Author : nsoonhui
       Score  : 26 points
       Date   : 2023-09-13 08:03 UTC (1 days ago)
        
 (HTM) web link (www.quantamagazine.org)
 (TXT) w3m dump (www.quantamagazine.org)
        
       | 123sereusername wrote:
       | [flagged]
        
         | sunday_serif wrote:
         | Telling of what?
         | 
         | Not trying to be snarky, I am genuinely curious.
        
           | joelfried wrote:
           | I don't know what parent had in mind, but I was personally
           | disappointed that not one of these conjectures was actually
           | talked about in detail. They had a nice picture of two images
           | of a rotating line and then . . . proceeded to just not tell
           | us what the actual conjecture states. They went on to talk
           | about all the conjectures stacked up but never what any of
           | them say or mean, just that they imply each other.
           | 
           | I wanted some meat, what I got was a photocopy of a magazine
           | picture of some meat.
        
             | xigoi wrote:
             | This is something that Quanta Magazine does all the time
             | and I hate it. You can't just tell us about an interesting
             | conjecture/theorem and then not state it.
        
             | _a_a_a_ wrote:
             | It does say though not brilliantly well. First para
             | 
             | "What is the smallest area that you can sweep out while
             | rotating an infinitely thin needle in all possible
             | directions? Spin it around its center like a dial, and you
             | get a circle. But rotate it more cleverly, and you can
             | cover an arbitrarily small fraction of space"
             | 
             | The animated diagram shows how a naive circular sweep
             | covers a circle of area x, the err.. other one covers an
             | area of x/2.
             | 
             | You can reduce from x to x/2 to x/n for arbitrarily large n
             | (I think, IANAM) thus tending towards arbitrarily small
             | area.
             | 
             | A bit more detail https://www.quantamagazine.org/new-proof-
             | threads-the-needle-...
        
           | mathisfun123 wrote:
           | I dunno what op meant but maybe that people around here
           | aren't good at/aren't interested in analysis? I'd buy that -
           | if you're good at analysis you go into a applied
           | math/econ/stats rather than CS.
        
           | downvotetruth wrote:
           | Censoring
        
       | IvyMike wrote:
       | Mathologer has a pretty decent video showing that the limit of
       | the swept area is zero:
       | https://youtu.be/IM-n9c-ARHU?si=CGlYZelPZmPccKmx
        
       | branperr wrote:
       | Did the website only give you all the option to agree to their
       | privacy policy, and not decline? If so that seems very
       | disingenuous.
        
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