[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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