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161 points isaacfrond | 1 comments | | HN request time: 0.221s | source
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matsemann ◴[] No.42724308[source]
> In two dimensions, the answer is clearly six: Put a penny on a table, and you’ll find that when you arrange another six pennies around it, they fit snugly into a daisylike pattern.

Is there an intuitive reason for why 6 fits so perfectly? Like, it could be a small gap somewhere, like in 3d when it's 12, but it isn't. Something to do with tessellation and hexagons, perhaps?

> They look for ways to arrange spheres as symmetrically as possible. But there’s still a possibility that the best arrangements might look a lot weirder.

Like square packing for 11 looks just crazy (not same problem, but similar): https://en.wikipedia.org/wiki/Square_packing

replies(2): >>42724357 #>>42724387 #
1. JKCalhoun ◴[] No.42724387[source]
Three pennies form an equilateral triangle with (of course) 60 degree angles.

Six of those equilateral triangles will perfectly add to 360 degrees. Intuitive enough? (I'm being a little hand-wavey by skipping over the part where each penny triangle shares two pennies with a neighbor — why the answer is not 18 for example.)

For my mind though, the intuitiveness ends in dimension 2 though. ;-)