Orange stacks

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Sujet : Orange stacks
De : qnivq.ragjvfgyr (at) *nospam* ogvagrearg.pbz (David Entwistle)
Groupes : rec.puzzles
Date : 12. Jul 2025, 16:19:27
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <104tudv$274e7$1@dont-email.me>
User-Agent : Pan/0.149 (Bellevue; 4c157ba git@gitlab.gnome.org:GNOME/pan.git)
Possibly going off-topic, but I hope you don't object too much. I have a
question. Please don't spend a lot of time on it, but if you happen to
know the answer, that would be appreciated. The excellent Quanta magazine
have an article about sphere-packing:

https://www.quantamagazine.org/new-sphere-packing-record-stems-from-an-
unexpected-source-20250707

It starts:

"In math, the search for optimal patterns never ends. The sphere-packing
problem — which asks how to cram balls into a (high-dimensional) box as
efficiently as possible — is no exception. It has enticed mathematicians
for centuries and has important applications in cryptography, long-
distance communication and more.

It’s deceptively difficult. In the early 17th century, the physicist
Johannes Kepler showed that by stacking three-dimensional spheres the way
you would oranges in a grocery store, you can fill about 74% of space. He
conjectured that this was the best possible arrangement. But it would take
mathematicians nearly 400 years to prove it".

If I had a grocery store, I think I would stack oranges in a square-based
pyramid, but I assume that a triangular-based pyramid would lead to more
efficient packing. To what does the "74% of space" figure refer, square-
based, or triangular-based? I can't see that they would be the same thing,
but I could be wrong.

Thanks,
--
David Entwistle

Date Sujet#  Auteur
12 Jul 25 * Orange stacks12David Entwistle
12 Jul 25 +* Re: Orange stacks8Carl G.
14 Jul 25 i`* Re: Orange stacks7David Entwistle
14 Jul 25 i `* Re: Orange stacks6Richard Tobin
14 Jul 25 i  +* Re: Orange stacks2David Entwistle
14 Jul 25 i  i`- Re: Orange stacks1Richard Tobin
15 Jul 25 i  `* Re: Orange stacks3David Entwistle
15 Jul 25 i   `* Re: Orange stacks2Richard Tobin
21 Jul08:46 i    `- Re: Orange stacks1David Entwistle
12 Jul 25 +* Re: Orange stacks2Richard Tobin
14 Jul 25 i`- Re: Orange stacks1David Entwistle
16 Jul09:05 `- Re: Orange stacks1David Entwistle

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