What is the status of the current literature on…
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What is the status of the current literature on generalizing the honeycomb theorem to higher dimensions and what are the potential applications?
I know just enough geometric measure theory to pretend to know what I’m talking about, so if all of this post is nonsense feel free to disregard.
I’ve been on a bee binge recently (likely also drinking far too much mead) as I distract myself from how inadequate I feel trying to do math and stumbled upon the honeycomb theorem.
Read the proof for 2 dimensions and understood slightly more than nothing so then observing the machinery I naively assumed this actually had a lot of applications in industry if you could generalize it.
As far as I could see there have been proposed structures as solutions for 3 dimensions but those aren’t proven and when we get higher than that we know basically nothing.
What interests me is that there is apparently a non trivial link between this and vector quantization.
Is this a real active area of research or am I way off base? The machinery here seems above my pay grade even if the required mathematical maturity may not be
#science
source
I know just enough geometric measure theory to pretend to know what I’m talking about, so if all of this post is nonsense feel free to disregard.
I’ve been on a bee binge recently (likely also drinking far too much mead) as I distract myself from how inadequate I feel trying to do math and stumbled upon the honeycomb theorem.
Read the proof for 2 dimensions and understood slightly more than nothing so then observing the machinery I naively assumed this actually had a lot of applications in industry if you could generalize it.
As far as I could see there have been proposed structures as solutions for 3 dimensions but those aren’t proven and when we get higher than that we know basically nothing.
What interests me is that there is apparently a non trivial link between this and vector quantization.
Is this a real active area of research or am I way off base? The machinery here seems above my pay grade even if the required mathematical maturity may not be
#science
source
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