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.
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.
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.
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.
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[ 2.1 ms ] story [ 103 ms ] threadNot trying to be snarky, I am genuinely curious.
I wanted some meat, what I got was a photocopy of a magazine picture of some meat.
"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-...