Why Nature Loves Hexagons

[MUSIC] Is nature a mathematician? Patterns and geometry are everywhere. But nature seems to have a particular thing
for the number 6. Beehives. Rocks. Marine skeletons. Insect eyes. It could just be a mathematical coincidence. Or could there be some pattern beneath the
pattern, why nature arrives at this geometry? We’re going to figure that out… with some
bubbles. And some help from our favorite mathematician:
Kelsey, from Infinite Series. Happy to help. [OPEN] A bubble is just some volume of gas, surrounded
by liquid. It can be surrounded by a LOT of liquid, like
in champagne, or just a thin layer, like in soap bubbles. So why do these bubbles have any shape at
all? Liquid molecules are happier wrapped up on
the inside, where attraction is balanced, than they are at the edge. This pushes liquids to adopt shapes with the
least surface. In zero g, this attraction pulls water into
round blobs. Same with droplets on leaves or a spider’s
web. Inside thin soap films, attraction between
soap molecules shrinks the bubble until the pull of surface tension is balanced by the
air pressure pushing out. It’s physics! Physics is great, but mathematics is truly
the universal language. Bubbles are round because if you want to enclose
the maximum volume with the least surface area, a sphere is the most efficient shape. Yeah. That’s another way of putting it. What’s cool is if we deform that bubble,
the pull of surface tension always evens back out, to the minimal surface shape. This even works when soap films are stretched
between complex boundaries, they always cover an area using the least amount of material. That’s why German architect Frei Otto used
soap films to model ideal roof shapes for his exotic constructions. Now let’s see what happens when we start
to pack bubbles together. A sphere is a three-dimensional shape, but
when when we pack bubbles in a single layer, we really only have to look at the cross-section:
a circle. Rigid circles of equal wdiameter can cover,
at most, 90% of the area on a plane, but luckily bubbles aren’t rigid. Let’s pretend for a moment these bubbles
were free to choose any shape they wanted. If we want to tile a plane with cells of equal
size and *no* wasted area, we only have three regular polygons to choose from: triangles,
squares, or hexagons. So which is best? We can test this with actual bubbles. Two equal-sized bubbles? A flat intersection. Three, and we get walls meeting at 120˚. But when we add a fourth… instead of a square
intersection, the bubbles will always rearrange themselves so their intersections are 120˚,
the same angle that defines a hexagon. If the goal is to minimize the perimeter for
a given area, it turns out that hexagonal packing beats triangles and squares. In other words, more filling with fewer edges. In the late 19th century, Belgian physicist
Joseph Plateau calculated that junctions of 120˚ are also the most mechanically stable
arrangement, where the forces on the films are all in balance. That’s why bubble rafts form hexagon patterns. Not only does it minimize the perimeter, the
pull of surface tension in each direction is most mechanically stable. So let’s review: The air inside a bubble
wants to fill the most area possible. But there’s a force, surface tension, that
wants to minimize the perimeter. And when bubbles join up, the best balance
of fewer edges and mechanical stability is hexagonal packing. Is this enough to explain some of the six-sided
patterns we see in nature? Basalt columns like Giant’s Causeway, Devil’s
Postpile, and the Plains of Catan form from slowly cooling lava. Cooling pulls the rock to fill less space,
just like surface tension pulls on a soap film. Cracks form to release tension, to reach mechanical
stability, and more energy is released per crack if they meet at 120˚. Sounds pretty close to the bubbles. The forces are different, but it’s using
similar math to solve a similar problem. What about the facets of insect’s eye? Here, instead of a physical force, like in
the bubble or the rock, evolution is the driver. Maximum light-sensing area? That’s good for the insect, but so is minimizing
the amount of cell material around the edges. Just like the bubbles, the best shapes are
hexagons. What’s even cooler, if you look down at
the bottom of each facet?? There’s a cluster of four cone cells, packed
just like bubbles are. Bubbles can even help explain honeycomb. It would be nice to imagine number-crunching
bees, experimenting with triangles and squares and realizing hexagons are most efficient
balance of wax to area… but with a brain the size of a poppy seed? They’re no mathematicians. It turns out honeybees make round wax cells
at first. And as the wax is softened by heat from busy
bees, it’s pulled by surface tension into stable hexagonal shapes. Just like our bubbles. You can even recreate this with a bundle of
plastic straws and a little heat. So is nature a mathematician? Some scientists might say nature loves efficiency. Or maybe that nature seeks out the lowest
energy. And some people might say nature follows the
rules of mathematics. However you look at it, nature definitely
has a way of using simple rules to create elegant solutions. Stay curious. So that’s how nature arrives at the optimal
solution for three-dimensional bees, but you know mathematicians love to take things to
the next level. What would the honeycomb look like for a four
dimensional bee? Follow me over to Infinite Series and me and
Joe will comb through the math.


  1. Thanks to Kelsey for helping me with this video! For a deeper dive into the math, go watch our collab over on Infinite Series! 📐🤓📏 https://www.youtube.com/watch?v=X8jOxEGVyPo

  2. Haven't seen the video, guessing that the reason is because it's the most structurally sound shape that can create a tiled pattern without the introduction of another shape, which would complicate the pattern, making it harder for life to build.

    Edit: Ok I didn't hit every reason why, but I didn't say anything that was really wrong either, so eh.

  3. This is the most fundamental law of reality.
    It's known as the Law of Least Resistance / Law of Greatest Efficiency.

    You can practice it by maximizing your internal effort and optimize your external effort.
    From there your only limitations are relative to your beliefs.

    You only exist in physical reality because you chose to believe your sensory input data.
    But existence is more or less an illusion.

    You (generally) don't question if a dream is real when you're experiencing one.
    You (generally) don't question if your world is real when you're experiencing this one right one.

    When you're dreaming you are accepting the illusion.
    When you're awake, still, your are accepting an illusion.

    So "dead", "awake", "unconscious" and "asleep" are just labels we use to try and make sense of our relative awareness. : )

  4. سبحان الله وبحمده، سبحان الله ربي العظيم، وما أوتيتم من العلم إلا قليلاً، صدق الله العظيم

  5. 138 ФolLOWs path 6
    Alphabet waves of shaLOW shadow(sing Y) waters. XYH

     https://www.youtube.com/watch?v=I_ECjs8YeEI inverted bubbles
    Don't disturb the circles( tubes, cyllinders, music of the spheres)

    B Fuller mentioned 3 simplex as way better than square structures where we live in.

    ФX scale(1.61803) of nonlocality follows triangular squares.

    https://www.facebook.com/watch/?v=505856030242251 x^2+1=0 Euler
    https://www.youtube.com/watch?v=0jEj5cTJzZ0 Design Matters: Doing Better with Less

  6. You didn't cover how triangles, squares or other shapes would have different degrees in their angles and how that would affect the structures or be inferior
    This video is just you arguing for the hexagon and providing support for what you like without adequately explaining why the alternatives wouldn't work
    This video is biased to personal preference while briefly mentioning and then quickly moving away from any alternatives and how they would be different

  7. I was cooking pasta this week and remembered this video. There's a kind of pasta, sold in Brazil with the name "Ave Maria", that is shaped like a tiny hollow cilinders.

    When you cook them, they form a honeycomb pattern in the bottom of your pan, just like the rocks and the bubbles. I found that fascinating.

  8. In conclusion, the hexagon has the smallest perimeter out of the only three 2D shapes that can place next to each of their own kind without any empty space in between each unit.

  9. Or there was an intelligent designer who was all knowing and just made things the most efficient way possible… but you don’t want to believe that

  10. Only biology creates hexagons everything you mentioned except for rocks is biological. But guess what- those rocks you showed is biological- Permineralized biology

  11. The people who say nature seeks out the lowest energy are right XD.

    Mathematics are us explaining what we see in nature, so you could say that nature was the first mathematician

  12. Mathematics follow the natural laws, rather than vice versa, since the mathematics is a construct of human consciousness trying to idealize and rationalize the natural phenomena.

  13. If you are smart bro, why just you don't thincking that nature couldn't create every this miracles by itself ?! God create everything and he instituted every law and rule for nature and every thing.

  14. you say nature decided to choose hexagon like it really has a free well and a mind of its own, I say GOD decided.

  15. Left me unsatisfied. I might have missed something, but it sounds like circular and deferred reasoning. The actual "why" is never told. :'(

  16. That's basically what Chinese and Indian engineering is….maximum efficiency with minimum cost and resources…..yet they call it cheap in the west !!!

  17. It's just amazing how hexagonal areas are useful for covering telephone coverage areas. I never got it until today.. wonderful!

  18. Asking if nature is a mathematician is like asking if nature is a physicist 'cause it follows the rules of physics.

    Every science is just an observation of the patterns of nature. It's like asking if a person is a psychologist because they follow observations of human behavior. .

  19. I don't agree with the proof he did. He needs a smarter proof. I think he could repeat the same thing with a Pentagon. You can see he is intentionally blowing the bubbles to their desired locations and this discredits the proof

  20. how do you think we call math signs, by only using the math language? HOW DO YOU THINK WE SAY THE WORD BROOM WITH MOUTHS BY ONLY USING MATH?!
    broom= brum. is saying broom in math is "50+(60+(-))(90-90+300000=30%)"?

  21. We invented math to explain nature in writing.

    That’s why functions are also called mathematical expressions.

    If we were not around, the world will still ‘function’ under the same rules of nature.

    We did not discover the number 5. We came up with it to represent a quantity of 5

    We came up with 5xn so we don’t write 5+5…. n times

    And 5^n so we don’t write 5×5 n times.

    We come up with a function to describe the motion on an object, just like we invented words to describe emotions and things.

    Math did not exist before humans. Math however ‘discovers’ relationships in nature, say the Pythagoras theorem, but math itself is not a discovery.,

    Sorry for the long winded comment. It’s lust a list of different examples .

  22. Romans 1:20 will help you understand how this came about. Genesis 1 will show you the first time light broke down the thick gas clouds which started life.

    How sad these little dummies are afraid to admire this is by pure design and not by chance or evaluation OOOORRRRR little bees figuring out by process of elimination by trying different shapes and then deciding on a circle that turns into a hexagon. The same reason why birds now how to fly! It’s inate

  23. Well, naturally Nature follows the most efficient way… since we live in an Simulation. They have to save some computing power somewhere and use those they have efficiently ^^

  24. So if my battery is hexagonal shape than my phone will use less energy? 😂😂😂

    Edit: or is it the other way around 🤔🤔

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