Hacker News Comments on
Hexagons are the Bestagons
CGP Grey
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Youtube
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7
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15
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⬐ O__________OTo be fair, hexagons alone are unable to form a sphere like surface:https://m.youtube.com/watch?v=btPqKAGyajM
And of course the odd response from the UK government to the above petition was to basically say having a realistic football signs would increase the odds of accidents, lol:
https://aperiodical.com/2017/10/standupmaths-petition-has-ha...
⬐ Aardwolf"The purpose of a traffic sign is not to raise public appreciation and awareness of geometry which is better dealt with in other ways."Maybe the petition was done the wrong way:
It's not about geometry lessens. Soccer balls literally don't look like that. There are (most likely) way more people appreciating sports than geometry in the UK, so that'd be a better argument
⬐ O__________OAgree. Video mentions that sports fans likely care and that they only wanted future signed updated, the petition though as far as I am able to tell mentions neither of these points:
⬐ NoneNone
Related - a video on why hexagons are the bestagons: https://www.youtube.com/watch?v=thOifuHs6eY
"Hexagons are the bestagons" according to CGP Grey. https://www.youtube.com/watch?v=thOifuHs6eYPersonally I prefer fractals. A 6-sided hexagon is just 2* 3-sided triangles. Or 6 of them, depending how you prefer to tile the plane.
https://i.pinimg.com/originals/c9/44/99/c94499bb9a0057f8573e...
So how about a day schedule organised by Sierpinski triangles? Lots of space in the middle for resting.
Good idea! Honeycombs are hexagons, and they tile the plane. And they're made of triangles.https://www.youtube.com/watch?v=thOifuHs6eY
We need parks, not car parks! Rather getting zapped on power lines or pooping on cars, the birds can have branches to sit in and flower beds to fertilise.
Mandatory reminder that hexagons are the bestagons.
⬐ ameliusHow does that generalize to three dimensions?⬐ LeifCarrotsonAs a Hexagonal Close Packing lattice, which is the correct way to represent the maximum density arrangement of equal spheres.If you've seen a stack of spheres, with the bottom layer in rows offset by one radius such that each sphere touches six others at the same height, and the next layer nestled in the intersections of this bottom layer, that's a hexagonal close packing.
Also, the "hexagons are the bestagons" attitude generalizes to three dimensions by dismissing face-centered cubic packing as an inferior way to look at the arrangement.
To generalize the Youtube video aspect, see also this Matt Parker/Steve Mould video on spherical packing: https://www.youtube.com/watch?v=3inLMXcetUA
⬐ YajirobeHow does that generalize to four dimensions?⬐ ameliusGiven that the stacking of spheres is built from a stack of planar layers, wouldn't that mean that the stack is prone to shearing forces, sliding the layers over each other?Wouldn't a packing that is irregular in all directions be more robust?
In the "bestagons" video, it is explained that the hexagons win because there are no straight lines in the packing, but I'd expect these to correspond to planes in the 3d case.
⬐ LeifCarrotsonThere are no continuous planes in the spherical packing layers, either - they all nestle down into gaps in the lower layers.
You forgot the reference video!! :-) https://www.youtube.com/watch?v=thOifuHs6eY&t=5s
Worth reminding folks: https://www.youtube.com/watch?v=thOifuHs6eY
so its true....hexagons are the bestagons
⬐ peterburkimsherThe video is great, I wish I saw that back in maths class in school!Hexagons tile the plane very nicely, and are used for choosing where to place phone transmitters!
But they can't be easily divided into sub-hexagons.
Could we instead model them as the combination of Sierpinski triangles?
https://larryriddle.agnesscott.org/ifs/siertri/symmetricZ3he...
CGP Grey: https://youtube.com/watch?v=thOifuHs6eY
On this topic I suggest viewing CPG Grey's video "Hexagons are the Bestagons"
Hexagons are, after all, the bestagons.On the very very low chance you haven't seen this: https://www.youtube.com/watch?v=thOifuHs6eY
And if you don't know who CGP Grey is and are wondering how this comment fits into HN, I can only offer that he's cashing in on his reputation a bit with the fun tone, but IMO the video is also interesting informationally.
CGP Grey did a video about hexagons recently. I mean, there's only so much you can say about hexagons really, but he manages to cover a lot of ground.
For a semi-goofy take (CGPGrey) on hexagons:
⬐ amitpHexagons are bestagons!⬐ smexxymooseCame to the comments just for this link⬐ wummsMore hexagons in nature:Image: "Hexagonal formations on the surface of the Salar de Uyuni (Bolivia, 3,656 meters above sea level) [0] as a result of salt crystallization from evaporating water": https://en.wikipedia.org/wiki/Salar_de_Uyuni#/media/File:Sal...
"During the rainy season (December to March) the salt flat gets covered with a layer of water. As the water evaporates under largely still conditions, the salt forms hexagonal shapes (optimal for heat transfer) on its surface known as Bénard cells, an example of the Rayleigh–Bénard convection [1] phenomena." [2]
[0] https://en.wikipedia.org/wiki/Salar_de_Uyuni
[1] https://en.wikipedia.org/wiki/Rayleigh%E2%80%93B%C3%A9nard_c...
[2] https://commons.wikimedia.org/wiki/File:20170809_Bolivia_158...
⬐ amitpAlso in nature: there is a giant hexagon on Saturn! http://www-cs-students.stanford.edu/~amitp/diagrams/saturn-h...
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Obligatory CGP Grey Video Link - https://www.youtube.com/watch?v=thOifuHs6eY
Coincidence ;-) https://www.youtube.com/watch?v=thOifuHs6eY
⬐ dexwizThe video brings up circles as a viable shape for honeycomb and then throws the option away since they don't pack. When Bees do in-fact make circles, and the hexagons are a product of fluid dynamics. [1] The cause of the hexagonal shape can also been seen with bubbles and other natural materials self assembling. [2][1] https://pubmed.ncbi.nlm.nih.gov/23864500/
[2] http://nautil.us/issue/35/boundaries/why-nature-prefers-hexa...