8 ms·

Why nature prefers hexagons

101 points by bsg75 9y ago

simcop2387 9y ago
PBS Infinite video on the same subject and how it expands into 4D space. https://www.youtube.com/watch?v=X8jOxEGVyPo https://www.youtube.com/watch?v=X8jOxEGVyPo
robbrown451 9y ago
Always wished pixels were hexagonal. Yeah the math would be a bit harder and vertical lines would be fuzzier at low resolution, but still.... https://www.quora.com/Why-are-computer-pixels-square https://www.quora.com/Why-are-computer-pixels-square
- tzs 9y ago
  I wonder how hard hexagonal pixel layout would have been to do on a CRT? Two ways come to mind. If the basic scan line is kept horizontal, then a small vertical modulation on each scan line could result in a hexagonal layout if you timed it right. Alternatively, if the grid is tilted (so that the basic scan line is diagonal instead of horizontal), then you just have to offset the odd scan lines by half a pixel from the even scan lines. I think we are just lucky that we ended up with rectangular screens. Imagine if they had went with circular screens. The scan might then easily have been a spiral starting in the center. That's fairly easy to do. It's just a matter of driving the horizontal and vertical deflectors with sine waves with the right phase difference, with a saw tooth amplitude. From a television point of view, I don't think it really matters which of these you use, as long as the cameras and the displays use the same scan pattern. From a computer point of view, though, it would have been a lot more painful if CRTs used a spiral scan. For most graphics applications we'd still need to manipulate rectangular areas, and that would be quite annoying in a coordinate system based on a spiral scan.
  - robbrown451 9y ago
    Right. At least a hex grid is still essentially a 2-dimensional array. In most ways it would be identical to a rectangular grid, but the algorithm for sampling surrounding pixels would be slightly different because of the spacial arrangements.
  - lightedman 9y ago
    Well, the problem there is that CRTs used a triangular-patterned phosphor screen, excepting Trinitrons which had their phosphors lined up in a row. How would you handle the missing spot for a phosphor in a hexagonal arrangement? I guess with current tech, we could make ultra-fine phosphor groups that we'd not be able to see. an 8K CRT at 32" would be quite nice .
    - robbrown451 9y ago
      Well to be honest, I'm thinking more of how pixels as data are stored in images rather than implemented in hardware. But still, if you follow the link, its something I posted on Quora 5 years ago, and shows an image I pulled from somewhere of a LED or OLED or whatever device where the hex arrangement is already there. It makes a lot of sense. In hardware, though, it makes the most sense for R, G and B components to not share a "center point" for each pixel, instead having their own center point that is spacially offset.
    - Stratoscope 9y ago
      There was no correlation between the phosphor dots on a typical color CRT and "pixels" as we think of them. It wasn't like the way we use an LCD or OLED display at all. A color CRT had no native resolution: display pixels were not locked onto specific phosphor dots. Consider all the analog adjustments a CRT offered: you could tweak the overall height and width of the displayed image and nudge it up or down and left or right. A high end CRT would have additional controls to adjust the shape of the image to correct for pincushion or barrel distortion. You could also drive the CRT with different display resolutions. Obviously the phosphor dots didn't move around when you did this. Even on a Trinitron display there was no connection between logical pixels and the aperture grill spacing. A good analogy for today's displays would be an LCD/OLED display that you can't run in native resolution, and can't even discover what its native resolution might be: the pixels you generate in software are not directed to specific physical points of light on the screen. A monochrome CRT came much closer to having something that today we would recognize as "pixels", because there was no shadow mask or phosphor dots. Whatever problems might have stood in the way of using a hexagonal pixel layout on a color CRT, the phosphor dot or stripe layout wasn't among them. Edit/meta: I really wish people would not downvote comments like lightedman's parent comment, which may have been wrong on the facts but provided an opportunity for me to jump in with some hopefully interesting information that not everyone may have known about CRT technology. Some of the best conversations I've had have been where I've had a misconception about something and someone was kind enough to set me straight on it. Yes, yes, I know, we're not supposed to complain about downvotes. So if my complaint bothers you, here's my offer: downvote this comment and upvote lightedman's parent comment, which received some downvotes that I think were undeserved. Fair deal?
  - mjevans 9y ago
    Analog circuits aren't my area of expertise. However it seems likely that the complexity of a stable and identical spiral scan circuit is either extremely difficult or possibly improbably expensive. Compare the above to what we have in reality: it seems that there were some vacuum tube tricks that made a grid system much easier. https://en.wikipedia.org/wiki/NTSC#Technical_details https://en.wikipedia.org/wiki/NTSC#Technical_details
    - mimhoff 9y ago
      A spiral scan circuit would just be something like: x = r cos (theta) y = r sin (theta) when you vary r so it gives you a spiral instead of a circle. So it shouldn't be too hard to generate the signals required. Or there could be a different arrangement of the beam deflectors that didn't give you independent control of X and y.
      - nwatson 9y ago
        But getting equal time on each pixel as you spiral out would be crucial to trigger the right phosphorescent equal luminance from your light-emitting material. Theta would not be linear with time.
        Jyaif 9y ago
        The intensity of the beam could be modulated to counter this.
      - gugagore 9y ago
        There are sync pulses on every line of analog video, as well as to color burst in most analog video standards. You couldn't just sweep theta and r continuously for a whole frame.
        Shikadi 9y ago
        Why not? The sync pulses are because the scan is discontinuous, you could just have one plus color burst every spiral
- taeric 9y ago
  There is a section in the manual for METAFONT that explains why a certain shaped pen is actually superior to a simple circle. I've always been curious if this was explored more for actual screen rastorization.
- userbinator 9y ago
  and vertical lines would be fuzzier at low resolution Horizontal ones too. Non-square pixels have been around for a long time in digital camera LCDs and more recently the https://en.wikipedia.org/wiki/PenTile_matrix_family https://en.wikipedia.org/wiki/PenTile_matrix_family but while they're fine for photos and other gradient-like images, text and lineart have a noticeable "grain" on them.
  - dogma1138 9y ago
    Most lcd screens today use non-square pixels, OLED displays use non-equal sizes for different colors and o don't see anyone complaining about sharpness.
- jacobolus 9y ago
  At this point, displays have fine enough resolution and GPUs are fast enough, that if you want to make hexagon-pixel images you can go right ahead and it won’t make too much difference (except you’ll reduce moiré artifacts), as long as you’re willing to implement your own code to rasterize the image to a square grid for display. It would be neat if camera sensors and displays would switch to hexagonal grids of pixels – considering most images get resampled right before display now anyway, it should be all upside (except for a bit of extra implementation hassle). A hexagonal grid is nice for several reasons: it can easily handle refinement to 3 or 4 subpixels per pixel, while a square grid needs 4 subpixels to keep its proper grid; it is much more isotropic than a square grid (straight lines at a variety of angles look much better); it is notably more efficient at covering the plane; hexagonal filters have a much nicer 2-dimensional frequency response; dithering works quite a bit better on a hexagonal grid; etc. There are some printers that use a hexagonal grid, and some hexagon-pixel cameras used for stuff like medical imaging or astronomy.
ineedasername 9y ago
I really dislike when articles use words such as "prefer" in this way. It conveys a level of intentionality that is not truly present. It would be better to say "Why hexagons appear often in nature." Or "Why nature produces hexagons" Otherwise, the descriptor is not just imprecise, it is also misleading.
- thaumasiotes 9y ago
  You may have a more spiritualistic view of "intentionality" than is really warranted.
  - freshhawk 9y ago
    Or they, like me, have constant interactions with lay people who constantly understand these things to mean their view of a universe guided by an intelligence is correct. I get it, it's just hard to avoid in English, but it is still a (small) failure in clear science communication.
    - saghm 9y ago
      I think the worst case of this in science is the way that evolution is described in a way that implies an active process rather than just random mutations which may or may not make organisms more fit for survival.
      - freshhawk 9y ago
        Yeah, I think that's the most common one. Strongly connected with the idea that evolution is "improvement" or some kind of step along a road to being "better", which I've seen trip up a lot of people who normally don't get confused about this kind of thing.
        TheSpiceIsLife 9y ago
        This reminds me of a thing a comedian said, or at least that's where I heard it first. "also told you we're descended from apes ... you lot might be, I'm ascended from the apes" - Steve Hughes[1] 1. https://www.youtube.com/watch?v=CYk5k-vL_Ek#t=1m50s https://www.youtube.com/watch?v=CYk5k-vL_Ek#t=1m50s -- caution, course language
mcnamaratw 9y ago
Strange article. You can see that some of the statements about honeycombs in the first paragraph are wrong, just by looking at the first picture.
huac 9y ago
Aren't triangles the strongest shape? https://math.stackexchange.com/questions/1393965/are-triangles-the-strongest-shape https://math.stackexchange.com/questions/1393965/are-triangl... https://www.reddit.com/r/askscience/comments/619ygo/why_are_triangles_the_strongest_shape/ https://www.reddit.com/r/askscience/comments/619ygo/why_are_...
- chii 9y ago
  And what do you get when you have lots of triangles packed together?
- ecesena 9y ago
  I'm not sure. I think roofs are triangular mostly to make water/snow slide down, while arcs are architecturally stronger, i.e. they can support more weight. So hexagons are better than triangles, and dodecahedron would be even better, etc. but nature tends to simplicity.
- 35bge57dtjku 9y ago
  Not when you're pressing in on them from all sides. Look at arches and chicken eggs.
Pulcinella 9y ago
You get hexagons because of close-packing.[1] Circles (or a 2D array of spheres) of the same size fit closest together when they are arranged in a hexagonal pattern. Push a bunch of marbles together and that's what you get. The bees don't know anything about hexagons. They just make circles close together and then as the cells are filled, stepped on, and come into contact with other wax cells, they "ballon out" into a hexagon shape. [1]https://en.m.wikipedia.org/wiki/Close-packing_of_equal_spheres https://en.m.wikipedia.org/wiki/Close-packing_of_equal_spher...
- jacobolus 9y ago
  There are several different criteria you might want to optimize for that result in hexagons, not just close-packing of circles. (Obviously they are somewhat related, but if you step up to 3 dimensions then you start getting different shapes/structures for different criteria, such as a diamond lattice, an FCC lattice (voronoi cells make a tiling by rhombic dodecahedra), a tiling by truncated octahedra, ....) In particular, bees probably make hexagons because that minimizes the amount of wall you need per area, for a given cell size. If bees were really just making something like a voronoi diagram from somewhat spread out points, you wouldn’t get quite so regular a hexagonal tiling. I imagine there’s some research about the precise method by which bees build their honeycombs, if anyone wants to go dive into the literature.
- deleted 9y ago
  [deleted]
- stinos 9y ago
  Is this the generally accepted explanation now? (I thought so, but the article itself doesn't mention it - then again, the article seems full of pseudo-science)
  - cygx 9y ago
    Not sure if bees might do it this way - but just looking at pictures of early stages of nests such as [1] or [2], wasps apparently don't: It looks as if they do construct proper hexagons from the get-go. [1] http://www.localhoney.co.uk/wp-content/uploads/2010/06/start-of-small-wasp-nest.jpg http://www.localhoney.co.uk/wp-content/uploads/2010/06/start... [2] http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8w/9q7bDCoP34E/s1600/2.jpg http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8...
ecesena 9y ago
Or simply the product of the first two (prime) numbers is 6. Similarly we have 10 fingers and we like base 10, but for time we prefer something which is "better dividible" (pardon my english), i.e. 3x4x5 = 60.
tyrw 9y ago
I was really hoping the article would touch on Saturn's north pole hexagon, as it completely blows my mind every time I think about it. https://en.m.wikipedia.org/wiki/Saturn%27s_hexagon https://en.m.wikipedia.org/wiki/Saturn%27s_hexagon
gaius 9y ago
Is this why France is hexagonal I wonder? Why aren't there more hexagonal countries?
- GuiA 9y ago
  France is only a hexagon if you squint really hard... its shape has also been very arbitrary over the centuries https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontiere_francaise_985_1947_small.gif https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontier...
  - gaius 9y ago
    I think downvoters may be unaware of the history of the term: https://en.m.wiktionary.org/wiki/Hexagone https://en.m.wiktionary.org/wiki/Hexagone
  - agumonkey 9y ago
    Quite often I looked at it and saw a Pentagon. Also using the loose hexagone definition, you could probably retrofit it on any point in time anyway :D
jacobr 9y ago
Started working on a game with hexagons a while back, and there are really weird/cool things related to hexagons online. Global Hexagonal Awareness Resource Center: https://hexnet.org https://hexnet.org > It is likely that HEXAGONS will continue to increase in popularity over the coming years, as humanity enters a glorious new hexagonal golden age, and all sentient beings on our planet ascend to a new, higher state of hexagonal consciousness. http://hexagons.info http://hexagons.info
- jacquesm 9y ago
  Interesting! My eldest has been working on sketches for a game he calls 'Hex'.
askvictor 9y ago
Any relation to three-phase power being more efficient than single phase?
- jacquesm 9y ago
  Three phase power is a way to evenly supply current to a motor while still using AC. It's not 'more efficient' as much as it is giving you a more even torque because the current through the motor doesn't drop to 0 10's of times per second, as it would with single phase. A nice side effect is that your motor (or alternator) can be a lot smaller for the same amount of power, a single phase motor would have to produce that power with the motor being at it's peak only once per cycle rather than all the time.
tambourine_man 9y ago
A bit too playful for me, but it gets the message across: https://youtube.com/watch?v=Pypd_yKGYpA https://youtube.com/watch?v=Pypd_yKGYpA
- leke 9y ago
  And this, also from PBS https://www.youtube.com/watch?v=X8jOxEGVyPo https://www.youtube.com/watch?v=X8jOxEGVyPo
pseudozach 9y ago
how come buildings are made from rectangular bricks then? Would hexagons be easier/more efficient to work with?

101 points by bsg75 9y ago

PBS Infinite video on the same subject and how it expands into 4D space. https://www.youtube.com/watch?v=X8jOxEGVyPo https://www.youtube.com/watch?v=X8jOxEGVyPo

robbrown451 9y ago

Always wished pixels were hexagonal. Yeah the math would be a bit harder and vertical lines would be fuzzier at low resolution, but still.... https://www.quora.com/Why-are-computer-pixels-square https://www.quora.com/Why-are-computer-pixels-square

tzs 9y ago
I wonder how hard hexagonal pixel layout would have been to do on a CRT? Two ways come to mind. If the basic scan line is kept horizontal, then a small vertical modulation on each scan line could result in a hexagonal layout if you timed it right. Alternatively, if the grid is tilted (so that the basic scan line is diagonal instead of horizontal), then you just have to offset the odd scan lines by half a pixel from the even scan lines. I think we are just lucky that we ended up with rectangular screens. Imagine if they had went with circular screens. The scan might then easily have been a spiral starting in the center. That's fairly easy to do. It's just a matter of driving the horizontal and vertical deflectors with sine waves with the right phase difference, with a saw tooth amplitude. From a television point of view, I don't think it really matters which of these you use, as long as the cameras and the displays use the same scan pattern. From a computer point of view, though, it would have been a lot more painful if CRTs used a spiral scan. For most graphics applications we'd still need to manipulate rectangular areas, and that would be quite annoying in a coordinate system based on a spiral scan.
- robbrown451 9y ago
  Right. At least a hex grid is still essentially a 2-dimensional array. In most ways it would be identical to a rectangular grid, but the algorithm for sampling surrounding pixels would be slightly different because of the spacial arrangements.
- lightedman 9y ago
  Well, the problem there is that CRTs used a triangular-patterned phosphor screen, excepting Trinitrons which had their phosphors lined up in a row. How would you handle the missing spot for a phosphor in a hexagonal arrangement? I guess with current tech, we could make ultra-fine phosphor groups that we'd not be able to see. an 8K CRT at 32" would be quite nice .
  - robbrown451 9y ago
    Well to be honest, I'm thinking more of how pixels as data are stored in images rather than implemented in hardware. But still, if you follow the link, its something I posted on Quora 5 years ago, and shows an image I pulled from somewhere of a LED or OLED or whatever device where the hex arrangement is already there. It makes a lot of sense. In hardware, though, it makes the most sense for R, G and B components to not share a "center point" for each pixel, instead having their own center point that is spacially offset.
  - Stratoscope 9y ago
    There was no correlation between the phosphor dots on a typical color CRT and "pixels" as we think of them. It wasn't like the way we use an LCD or OLED display at all. A color CRT had no native resolution: display pixels were not locked onto specific phosphor dots. Consider all the analog adjustments a CRT offered: you could tweak the overall height and width of the displayed image and nudge it up or down and left or right. A high end CRT would have additional controls to adjust the shape of the image to correct for pincushion or barrel distortion. You could also drive the CRT with different display resolutions. Obviously the phosphor dots didn't move around when you did this. Even on a Trinitron display there was no connection between logical pixels and the aperture grill spacing. A good analogy for today's displays would be an LCD/OLED display that you can't run in native resolution, and can't even discover what its native resolution might be: the pixels you generate in software are not directed to specific physical points of light on the screen. A monochrome CRT came much closer to having something that today we would recognize as "pixels", because there was no shadow mask or phosphor dots. Whatever problems might have stood in the way of using a hexagonal pixel layout on a color CRT, the phosphor dot or stripe layout wasn't among them. Edit/meta: I really wish people would not downvote comments like lightedman's parent comment, which may have been wrong on the facts but provided an opportunity for me to jump in with some hopefully interesting information that not everyone may have known about CRT technology. Some of the best conversations I've had have been where I've had a misconception about something and someone was kind enough to set me straight on it. Yes, yes, I know, we're not supposed to complain about downvotes. So if my complaint bothers you, here's my offer: downvote this comment and upvote lightedman's parent comment, which received some downvotes that I think were undeserved. Fair deal?
- mjevans 9y ago
  Analog circuits aren't my area of expertise. However it seems likely that the complexity of a stable and identical spiral scan circuit is either extremely difficult or possibly improbably expensive. Compare the above to what we have in reality: it seems that there were some vacuum tube tricks that made a grid system much easier. https://en.wikipedia.org/wiki/NTSC#Technical_details https://en.wikipedia.org/wiki/NTSC#Technical_details
  - mimhoff 9y ago
    A spiral scan circuit would just be something like: x = r cos (theta) y = r sin (theta) when you vary r so it gives you a spiral instead of a circle. So it shouldn't be too hard to generate the signals required. Or there could be a different arrangement of the beam deflectors that didn't give you independent control of X and y.
    - nwatson 9y ago
      But getting equal time on each pixel as you spiral out would be crucial to trigger the right phosphorescent equal luminance from your light-emitting material. Theta would not be linear with time.
      - Jyaif 9y ago
        The intensity of the beam could be modulated to counter this.
    - gugagore 9y ago
      There are sync pulses on every line of analog video, as well as to color burst in most analog video standards. You couldn't just sweep theta and r continuously for a whole frame.
      - Shikadi 9y ago
        Why not? The sync pulses are because the scan is discontinuous, you could just have one plus color burst every spiral
taeric 9y ago
There is a section in the manual for METAFONT that explains why a certain shaped pen is actually superior to a simple circle. I've always been curious if this was explored more for actual screen rastorization.
userbinator 9y ago
and vertical lines would be fuzzier at low resolution Horizontal ones too. Non-square pixels have been around for a long time in digital camera LCDs and more recently the https://en.wikipedia.org/wiki/PenTile_matrix_family https://en.wikipedia.org/wiki/PenTile_matrix_family but while they're fine for photos and other gradient-like images, text and lineart have a noticeable "grain" on them.
- dogma1138 9y ago
  Most lcd screens today use non-square pixels, OLED displays use non-equal sizes for different colors and o don't see anyone complaining about sharpness.
jacobolus 9y ago
At this point, displays have fine enough resolution and GPUs are fast enough, that if you want to make hexagon-pixel images you can go right ahead and it won’t make too much difference (except you’ll reduce moiré artifacts), as long as you’re willing to implement your own code to rasterize the image to a square grid for display. It would be neat if camera sensors and displays would switch to hexagonal grids of pixels – considering most images get resampled right before display now anyway, it should be all upside (except for a bit of extra implementation hassle). A hexagonal grid is nice for several reasons: it can easily handle refinement to 3 or 4 subpixels per pixel, while a square grid needs 4 subpixels to keep its proper grid; it is much more isotropic than a square grid (straight lines at a variety of angles look much better); it is notably more efficient at covering the plane; hexagonal filters have a much nicer 2-dimensional frequency response; dithering works quite a bit better on a hexagonal grid; etc. There are some printers that use a hexagonal grid, and some hexagon-pixel cameras used for stuff like medical imaging or astronomy.

ineedasername 9y ago

I really dislike when articles use words such as "prefer" in this way. It conveys a level of intentionality that is not truly present. It would be better to say "Why hexagons appear often in nature." Or "Why nature produces hexagons" Otherwise, the descriptor is not just imprecise, it is also misleading.

thaumasiotes 9y ago
You may have a more spiritualistic view of "intentionality" than is really warranted.
- freshhawk 9y ago
  Or they, like me, have constant interactions with lay people who constantly understand these things to mean their view of a universe guided by an intelligence is correct. I get it, it's just hard to avoid in English, but it is still a (small) failure in clear science communication.
  - saghm 9y ago
    I think the worst case of this in science is the way that evolution is described in a way that implies an active process rather than just random mutations which may or may not make organisms more fit for survival.
    - freshhawk 9y ago
      Yeah, I think that's the most common one. Strongly connected with the idea that evolution is "improvement" or some kind of step along a road to being "better", which I've seen trip up a lot of people who normally don't get confused about this kind of thing.
      - TheSpiceIsLife 9y ago
        This reminds me of a thing a comedian said, or at least that's where I heard it first. "also told you we're descended from apes ... you lot might be, I'm ascended from the apes" - Steve Hughes[1] 1. https://www.youtube.com/watch?v=CYk5k-vL_Ek#t=1m50s https://www.youtube.com/watch?v=CYk5k-vL_Ek#t=1m50s -- caution, course language

mcnamaratw 9y ago

Strange article. You can see that some of the statements about honeycombs in the first paragraph are wrong, just by looking at the first picture.

huac 9y ago

Aren't triangles the strongest shape? https://math.stackexchange.com/questions/1393965/are-triangles-the-strongest-shape https://math.stackexchange.com/questions/1393965/are-triangl... https://www.reddit.com/r/askscience/comments/619ygo/why_are_triangles_the_strongest_shape/ https://www.reddit.com/r/askscience/comments/619ygo/why_are_...

chii 9y ago
And what do you get when you have lots of triangles packed together?
ecesena 9y ago
I'm not sure. I think roofs are triangular mostly to make water/snow slide down, while arcs are architecturally stronger, i.e. they can support more weight. So hexagons are better than triangles, and dodecahedron would be even better, etc. but nature tends to simplicity.
35bge57dtjku 9y ago
Not when you're pressing in on them from all sides. Look at arches and chicken eggs.

Pulcinella 9y ago

You get hexagons because of close-packing.[1] Circles (or a 2D array of spheres) of the same size fit closest together when they are arranged in a hexagonal pattern. Push a bunch of marbles together and that's what you get. The bees don't know anything about hexagons. They just make circles close together and then as the cells are filled, stepped on, and come into contact with other wax cells, they "ballon out" into a hexagon shape. [1]https://en.m.wikipedia.org/wiki/Close-packing_of_equal_spheres https://en.m.wikipedia.org/wiki/Close-packing_of_equal_spher...

jacobolus 9y ago
There are several different criteria you might want to optimize for that result in hexagons, not just close-packing of circles. (Obviously they are somewhat related, but if you step up to 3 dimensions then you start getting different shapes/structures for different criteria, such as a diamond lattice, an FCC lattice (voronoi cells make a tiling by rhombic dodecahedra), a tiling by truncated octahedra, ....) In particular, bees probably make hexagons because that minimizes the amount of wall you need per area, for a given cell size. If bees were really just making something like a voronoi diagram from somewhat spread out points, you wouldn’t get quite so regular a hexagonal tiling. I imagine there’s some research about the precise method by which bees build their honeycombs, if anyone wants to go dive into the literature.
deleted 9y ago
[deleted]
stinos 9y ago
Is this the generally accepted explanation now? (I thought so, but the article itself doesn't mention it - then again, the article seems full of pseudo-science)
- cygx 9y ago
  Not sure if bees might do it this way - but just looking at pictures of early stages of nests such as [1] or [2], wasps apparently don't: It looks as if they do construct proper hexagons from the get-go. [1] http://www.localhoney.co.uk/wp-content/uploads/2010/06/start-of-small-wasp-nest.jpg http://www.localhoney.co.uk/wp-content/uploads/2010/06/start... [2] http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8w/9q7bDCoP34E/s1600/2.jpg http://1.bp.blogspot.com/-uM7ATVMEcDA/TdcWZm9BPEI/AAAAAAAAI8...

ecesena 9y ago

Or simply the product of the first two (prime) numbers is 6. Similarly we have 10 fingers and we like base 10, but for time we prefer something which is "better dividible" (pardon my english), i.e. 3x4x5 = 60.

tyrw 9y ago

I was really hoping the article would touch on Saturn's north pole hexagon, as it completely blows my mind every time I think about it. https://en.m.wikipedia.org/wiki/Saturn%27s_hexagon https://en.m.wikipedia.org/wiki/Saturn%27s_hexagon

gaius 9y ago

Is this why France is hexagonal I wonder? Why aren't there more hexagonal countries?

GuiA 9y ago
France is only a hexagon if you squint really hard... its shape has also been very arbitrary over the centuries https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontiere_francaise_985_1947_small.gif https://upload.wikimedia.org/wikipedia/commons/a/ae/Frontier...
- gaius 9y ago
  I think downvoters may be unaware of the history of the term: https://en.m.wiktionary.org/wiki/Hexagone https://en.m.wiktionary.org/wiki/Hexagone
- agumonkey 9y ago
  Quite often I looked at it and saw a Pentagon. Also using the loose hexagone definition, you could probably retrofit it on any point in time anyway :D

jacobr 9y ago

Started working on a game with hexagons a while back, and there are really weird/cool things related to hexagons online. Global Hexagonal Awareness Resource Center: https://hexnet.org https://hexnet.org > It is likely that HEXAGONS will continue to increase in popularity over the coming years, as humanity enters a glorious new hexagonal golden age, and all sentient beings on our planet ascend to a new, higher state of hexagonal consciousness. http://hexagons.info http://hexagons.info

jacquesm 9y ago
Interesting! My eldest has been working on sketches for a game he calls 'Hex'.

askvictor 9y ago

Any relation to three-phase power being more efficient than single phase?

jacquesm 9y ago
Three phase power is a way to evenly supply current to a motor while still using AC. It's not 'more efficient' as much as it is giving you a more even torque because the current through the motor doesn't drop to 0 10's of times per second, as it would with single phase. A nice side effect is that your motor (or alternator) can be a lot smaller for the same amount of power, a single phase motor would have to produce that power with the motor being at it's peak only once per cycle rather than all the time.

tambourine_man 9y ago

A bit too playful for me, but it gets the message across: https://youtube.com/watch?v=Pypd_yKGYpA https://youtube.com/watch?v=Pypd_yKGYpA

leke 9y ago
And this, also from PBS https://www.youtube.com/watch?v=X8jOxEGVyPo https://www.youtube.com/watch?v=X8jOxEGVyPo

pseudozach 9y ago

how come buildings are made from rectangular bricks then? Would hexagons be easier/more efficient to work with?