Hexagons Are NotSoGreatAgons
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- Опубликовано: 3 май 2024
- Today we're talking about whether hexagons are really the bestagons. I'm sure you've already seen CGP Grey's iconic video, and it is a great video, but he claims that hexagons are the strongest shape and that's just not true.
Outro Music: "Blast" from Bensound.com
(0:00) - Intro
(1:07) - Strength of Materials
(1:57) - Theory 1: Graphene
(3:44) - Hexagons are Unstable
(8:06) - Theory 2: Honeycomb Panels
(13:24) - Bonus Simulations
(14:21) - Outro 
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4:52 I should have mentioned but you only need all of the extra members if you don’t add another joint in the middle. If you add a joint in the middle then you just need the 6 equilateral triangles to keep it stable.
I’ve been trying to get an answer to my question, maybe you can help me?
My idea, hypothetical.
Is there any scenario where…? A person could have large tall cylinder that can withstand both a vacuum and pressure, with a valve at the bottom and top of this vessel. Setting above but next to an open reservoir of water.
Fill the vessel with water just below the valve at the top of the barrel.
From the valve at the top of the barrel connect a small pipe that reaches into the open water reservoir.
From the bottom valve connect another pipe that reaches out… say 12’, but staying above the top of the water in the reservoir.
Is there any scenario in this kind of setup where, when the valve in the bottom of the closed vessel, with the weight of the water in the barrel decrease the atmospheric pressure artificially in the top of the tank, to overwhelm the atmospheric pressure of the reservoir of water and the water weight in the smaller tube connected to the upper valve, So that when the upper valve is opened the water would flow up the tube and into the top of the sealed vessel?
In the 6 equilateral triangle arrangement, could you actually remove one member shared by two of the equilateral triangles and the structure would still be statically determinant? Then there would be 4 equilateral triangles and a rhombus, but three of the rhombus' vertices would be fixed.
I was literally imagining that rocket video before you said it. Algo go burrr.
@@X4R2 possibly except that that would have the possibility of the corner flipping into itself because only fixing the of the corners creates a bistable configuration which is fine if there's not give in the beams but as soon as there is you have issues. Ultimately it makes it more susceptible to bucking on that corner if you have a force from the corner to the centre joint of the hexagon which isn't ideal.
@@ronweber4508 It's been a while since you posted this question but nobody seems to have answered it so here's my two cents:
Short answer no, long answer yes, with certain conditions. The water in the small pipe going to the top of the cylinder would not flow all the way up into the cylinder because the same gravity that affects the water in the cylinder affects also the water in the small pipe. If you open both of the valves the pressure at the top of the cylinder would lower and it would suck up water into the small pipe but only until the level of the water in the small pipe matches the level of the water in the cylinder.
If we start nitpicking we could make the top pipe very small. The capillary force would cause the water in the pipe rise higher than in the cylinder. Even all the way into the cylinder. Capillary force is caused by the surface tension of the water. Water is attracted to many surfaces and wants spread on them even climbing up them slightly. (watch closely at the edges of the water in a glass of water) In a very thin tube the capillary force overcomes the gravity. This is the way how water rises up in tree trunks all the way up to the leaves. It's also how they take a blood sample from you by squeezing out a small drop of blood and touching it with a thin glass tube so the blood just fills the tube "automatically". But in this scenario the water rises up into the top of the cylinder because of the capillary force and not because of the low pressure at the top. Although the pressure difference certainly helps.
If you place the cylinder and the bottom pipe next to the open reservoir but below the level of the water in the reservoir, opening the valves would suck up the water into the small pipe and into the cylinder. The cylinder and the pipes would act as a siphon and would create a flow of water from the reservoir into wherever the the lower pipe ends ups.
Now this is the type of youtube drama between youtubers i like to see
@@arandomgamer3088Don’t even try to compare this to SSSniperwolf
virgin dream v gumball
chad cgp v con hathy
You'll want to check out the feud of ElectroBoom and Steve Mould over the Mould Effect a few years back
Yum
- Can you guess where this goes?
- It goes in the square hole...
Where does the semicircle go?
That’s right, the square hole
Gulp
Chemist turned engineer here. Hexagons ARE the best way to fill the space between 2 strong sheets in a honeycomb for precisely the reason CGP mentioned: they fill an area with the least amount of length. However this is only true for a general purpose (isotropic) honeycomb. If you require more strength in one direction than the other, then a rectangular grid is best per the rocket example you gave. If you have only one sheet, then the other side is subject to buckling, so the best isotropic grid is the triangle one that you showed.
Hexagons are essentially useless for making a rigid structure from beams - for that you obviously need triangles. But if you want to make a 2D atomic sheet it has to be hexagons. Bonds spread out to fill 3d space due to VSEPR. An atom with 3 bonds (and no spare electrons) will be flat with 120 angles as in boron trifluoride (Graphene is a bit more complex, there is a 4th electron on each atom but it is used in a delocalised electron cloud unlike the other 3 which are paired with neighbours into 3 discrete bonds.) if you have more than 3 bonds they make a 3d structure, for example 4 bonds form a tetrahedron as in methane or diamond and 6 bonds form right angles like a cube lattice, as in sodium chloride (ionic bonds) or sulphur hexafluoride (covalent bonds.)
Molecules containing an atom with 4 bonds in the same plane do exist, but the atom in question is always a fairly heavy one with a total of 6 electron pairs to maintain that cube-like geometry (the electron pairs that are not used in bonding occupy the poles of the six-sided cube and therefore push the 4 bonds into a flat configuration around the equator of the atom.) To my knowledge nobody has made a flat sheet of atoms in this way - the electron pairs that are not used in bonding (and their corresponding orbitals) would leave the molecule vulnerable to being attacked chemically, even by itself.
If you are stacking long thin objects, a stack of hexagonal prisms is stronger / more stable than square prisms or triangular prisms, because it doesn't have shear planes. A fistful of hexagonal pencils feels quite rigid, but with square or triangular prisms they would tend to slide across each other.
You're right if you restrict your shape selection to regular polygons, and if your core/filler is purely for volumetric (aka non-structural) reasons. However, break those two assumptions for your application and it may no longer be true that hexagons offer the best mass/path length for the situation. For example, an application with negligible radial loads will be theoretically better served with only axially-aligned members, minus a couple radially aligned segments to reduce twist.
"A fistful of hexagonal pencils feels quite rigid, but with square or triangular prisms they would tend to slide across each other."
That's an excellent analogy.
@@felixu95 Isotropic means "equal properties (in this case strength) in all directions." What you are describing is a non-isotropic case. Actually a hexagon grid isn't perfectly isotropic (properties parallel and perpendicular to the sides vary slightly, cycling every 60 degrees) but is more isotropic than a square grid (properties at 0 and 45 degrees vary, cycling every 90 degrees.) I already accepted OP's point that another grid is better if you want more strength in one direction than another, such as the rectangular grid in OP's rocket example. Perfect hexagon grids are rare in practice both because they're not always the best solution, and (as OP mentioned) because of manufacturing. The hexagonal packing insided IKEA table tops is made from strips of card bonded together, for example, and is therefore twice as thick in one direction than in the other two.
@@Joe-sg9ll Bees use hexagons because it optimises storage volume. Actually the bottoms of the cells are made of three rhombuses with diagonals in the ratio sqrt(2):1 (like the corners of a shape called a rhombic dodecahedron) as this further optimises storage volume (it means the front and back sides are offset from each other though.) Bees also seal most of the cells of the honeycomb, and in that state, the structure is also optimised.
thats.... an extreamly narrow area of application. we happen to need that quite a lot, but it's still an extremely weak shape in the plane.
I don’t believe you missed the opportunity to call squares tetragons.
And trigons. We must always push for consistency in our nomenclature. You can't have triangles and hexagons. Either trigons and hexagons or triangle and hexangles.
And the rectangles rectagons
They're all made up of lines, so let's let bigons be bigons.
@@SaHaRaSquad Rectangles are nothing more than right tetragons. Rhombuses meanwhile are equilateral tetragons, and squares are right _and_ equilateral tetragons, or just regular tetragons for short. (Worth noting however that squares and retangles are only right tetragons in euclidean space.)
@@SirPhysics Trigon? Dont mention Trigon dude, Raven from the Teen Titans might hear you talking about her dad.
But hexagons are the bestagons. I joined the cult, sold my soul and pledged allegiance to the almighty hexagonal perfection.
They must be the bestagons. 😩
heretics!
@@Joe-sg9ll i refute that!
Hexagons are the worstagons.
Bro who uses that emoji 💀
@@Nugconhexetic
a hexagon is just 4 triangles
6*
Oh I see what your talking about but it’s 6 IF we are talking about a triagle equal sides
In that case triangles are just broken up hexagons.
Ah yes... a triangle is just 3 triangles
4 triangles is just 12 triangles
I hope cgp gray sees this
Even if the hexagon isn’t the bestagon it still looks good
They are the Coolest of gons.
Good thing they are, in fact, the bestagons!
it's the bestlookingagon
I hope so
Appeal: Triangles don't count because they aren't "-gons", neither do squares because the quadrilateral family is their own mess. Ergo, hexagon still bestagon.
Triangles and engineers.
The best love story.
The only reason bees use hexagons is because they’re circles without the packing density losses. They’re literally just simplified circles with flat sides so there’s no dead space. They’re a packing density optimized circle. It had nothing to do with strength, and everything to do with the efficient use of material to subdivide a given volume
In fact I believe bees actually make their hives out of circles which naturally deform into hexagons because they are the most efficient shape.
when the fuck am i gonna use hexagons for that reason
@@TXA-TXATwhen you can only make roughly cylindrical shapes and need to pack a lot of fluid into the smallest volume possible.
@@ultimatedude5686yep, more or less. Bees shape their honeycomb using their abdomen, which is roughly circular. As the hive heats and cools the wax melts and hardens. Due to most of the combs being filled and/or fully supported, they don't collapse, but they do fuse. Due to the fact that hexpacking is the most space efficient packing for cylindrical tubes this means that the combs create flats on the six sides where they meet and bulge towards the "corners" to maintain their volume. So they actually just form the appropriate N-gon to tile their packing formation.
and?
It's been awhile since I watched Grey's video, but essentially bees use hexagons because the shape is efficient and engineers use triangles because the shape is strong. The shapes are used for different applications. Great.
May we never forget the underappreciated 3rd best shape the square/rectangle, sure its not the best, but its pretty good, and easy to make. Its the Ok-agon
squares are the best because they're easiest to implement in code
It's no accident that it's everywhere.
@@thezipcreator Oh? In what context? You'd think of the flat shapes the cirlce is easiest to implement since it only has one variable: radius. A square has four sides and four angles, which luckily you can compress to one side and one angle as long as you store the shape identifier as well, so that's still two variables more than a circle. Not to mention orientation in any n-dimensional reference frame where n >=2 becomes a whole thing with squares that it simply isn't with circles.
Circle: Distance? Distance to centre minus radius. Collision? Distance to centre minus radius. End of shape? Distance to centre plus radius. Depth? Twice the radius.
Square: Distance? Depends on the angle. Collision? Depends on the angle and rotation speed, if any. End of shape? Again, it depends. Depth? same issue.
@@bramvanduijn8086
rendering squares is easier (with circles you have to pass a bunch of points of the form [centerx+cosθ, centery+sinθ], with squares you can just pass 4 points), collision with AABBs is basically the same difficulty as spheres (although you are right that if a square is rotated it's much harder). also if your entire world is a grid (such as in strategy games), you don't even need to worry about that; making a square grid is just easier than making a hexagonal one (although not by enough that it matters, probably. idk I'm just a lazy developer).
@@thezipcreator easiest in a rectangular coordinate system. Which is most common, so yeah fair enough. 😛
I'm surprised you didn't mention the relatively low surface area of the hexagon fill in the paneling. They're closer to circular so they reduce the amount of materials compared with a triangular mesh -- yet another way in which the hexagon is the cheapagon. Bees use hexagons (well, actually they use halved rhombic dodecahedra) because it minimizes the amount of beeswax needed.
The more pictures of hives I look at, the more I'm convinced they actually use circular tubes that are hexpacked together. If they're hexagons, the corners sure are beveled to hell!
@@BalderOdinson You're right, bees build the tubes of the beehive in a circular shape. The trick is that the wax itself keeps rearranging itself due to the heat of the hive, so it ends to stick together with the walls of the neighboring cells and makes the hexagons.
But the idea of bees making the polygons is a myth, is just a quirk of the material of the hive.
@@EduardoEscarez "The idea that humans melt metal themselves is a myth, it's just a quirk of the tools and materials they use."
I mean, come on. Let the bees have their fame. Maybe they still _intend_ to make hexagons, they simply know that circles will mold themselves into hexagons, so really they're saving energy! :P
Rhombic dodecahedra aren't the best volume to surface area ratio either
Of course the bees are actually creating circular tubes -- they're making them with their own abdomens, which are roughly circular in cross-section.
this is really interesting, i never really understood why some shapes are so much better than others, but this explains a lot!
I guess diffirent shapes are great at handling specific directions of pressure, but triangles are by far the most usefull, since they can handle any direction.
Circles are a funny one i think, since (from my understanding) they're the best at handling pressure from all directions simultaniously, like atmospheric pressure.
But if the pressure is focused, if you were to try and stab one, or a set of circles, it'd be way weaker than triangles.
It'd be cool to see a really simplistic set of physics sims try and demonstrate the strongest shape against stabbing, strongest shape against atmospheric pressure, strongest shape against gravity, etc. etc.
Tbf, I think one of CGPs actual points (outside the jokes) was that hexagons are so good precisely because they have triangles easily in them (compared to triangles in squares I mean)
Like essentially in triangle sheets vs hexagon sheets, the only difference is extra joints in each hexagon (to make it triangles). Compared to a square sheet that uses its own geometry entirely
With squares it's just that you need to use right triangles, which from most bridges we can see isn't as efficient as tiling equilaterals, which tile into hexagons
So triagons are the bestagons
Add 2 Triangles, to form a square, repeat 6 times, join these squares to each other in a t and then join the edges together. Cut the newfound cube along it's 3 dimensional diameter and it's cross section is a hexagon.
Triangle Man, Triangle Man, Triangle Man hates Hexagon Man, they get in a fight, Triangle wins...
@simsom4343 I am of the pro-CGP and pro-hexagon persuasion so keep that in mind when you read this.
You're moving the goal posts in an apologist manner. This video presents valid criticisms of the Holy Hexagon Bestagon. Hexagon = bestagon is no more than a faith based fandom based on a decent, but incomplete/not fully incorrect explanation.
As with any faith based belief, it will not stand up to strict scrutiny, empiricism, and reason. Faith based beliefs can be cool and useful, but I would not lean too hard/center my life/center my personality around anything so flimsy as a faith based system.
Things are heating up in the shape fandom
Ah yes, the ever vile feud between physics and applied engineering.
As a person who studied construction in a university i think it's a shame teachers didn't properly explained this as good as you did. Wanted me to calculate loads at i-beams etc. without explaining this basic crusial concepts. I might be a bad student if i couldn't think of it myself in a thought experiment, but for sure this would be a good ground to a harder stuff. And it seems like i am not the only person who complain about the education system.
Definitely enjoyed watching it!
I guess hexagons are good for webbing 2D lattices where there is intrinsic repulsion between nodes, such as in graphene or some kind of “tensegrity net” that uses cord/cable for internal triangles and a rigid material for the hexagons.
Honeycomb is also the best shape in terms of both tiling and having a large area to perimeter ratio (which is why bees use it in actual honeycomb). But that's not a strength thing that's a material efficiency thing.
Bees don't actually "use" hexagons. Bees make cylindrical cells in the wax, which become hexagonal due to wax being able to flow when warmed up.
@@SirPhysics it still ends up that way and for the same reasons but that's super interesting thanks for sharing.
@@SirPhysicsyep, and specifically it only forms the N-gon whose tiling best matches the packing used by the bees. If they used square packing instead, the forces acting on the comb would produce roughly square honeycombs. It also means if the packing is uneven, the comb will simply adapt to whatever polygon is best.
@@SirPhysics They do use hexagons. Why would they expend extra energy to "intentionally" create hexagons when the wax will naturally form that way? If another shape was better, they would be using that shape instead. The fact that bees honeycomb ends up as hexagons is BECAUSE hexagons are the best polygon for efficiently tiling a plane.
Being efficient is not the strongest.
the reason graphene's hexagons are strong is kinda several factors, but you did good enough
there's also VSEPR, for example, which is basically lone pairs and molecular bonds repel each other, which is why water forms a bent shape!
so, benzene forming a flat hexagon is a result of that and what you said and maybe a few other things. it pushes itself into that shape, and that sure as heck doesn't happen if you just make any random hexagon on the macro level
Can you develop your point about VSEPR? How does its principle that lone pairs repel molecular bonds more than molecular bonds repel each other factor into graphene’s hexagons being strong?
this answers my question when I saw the smartereveryday ULA tour vid where that (presumably interstage) part was milled in triangular grid and not hexagonal as CGPgrey said hexagons are the bestagons. I believe the physics of packing materials most efficiently (where hexagons are the bestagons) and the physics of static determinance (where triangles are best) is quite different but visually the same and leads to incorrect correlations.
Efficient packing is still triangles. It's just that *neighbors* are in a hexagon.
@@chaos.corner 2D efficient packing, right?
Because in 3D, I think you need a mixture of hexagons and pentagons. Like a soccer ball.
Your body is made up of cells, many of which have hexagonal and pentagonal sides.
@@TheRealE.B. I'm not familiar with cells (which aren't spheres and rave their own raison d'etres for how they are) but for spheres, hexagonal close packing has two different configurations. The smallest arrangement between any four touching spheres is a tetrahedron.
@@chaos.corner Hmm. Maybe it matters if space is the only concern, or if you have to worry about physics like pressure, surface tension, boundary conditions, etc. I don't know. I admit that this exhausts my knowledge on the subject.
@@TheRealE.B. Yes, it's entirely about the space left over by sphere-type objects.(atoms are a bit different as it's about minimizing the energy of the bonds). Boundary conditions can definitely affect things too. Consider that cube-type cells are going to stack in a fairly linear fashion.
CGP Grey: Hexagons are the Bestagons!
Con Hathy: Triangles are the Bestangles!
Your simulations remind me a bit of "world of goo". You get to build structures out of members with various properties. Triangles are the rule of the day. At least in critical points. I may have to dig it out again now.
That was such a great game! I'll have to search for it again
I'm still incredulous that the game's getting a sequel!
I was gonna comment the same thing, especially when I saw that triangle bridge simulation!
@@walugusgrudenburg3068I'm incredulous the game is $15 after all this time. I have a copy somewhere but can't find it.
funny how theres gonna be world of goo 2 now
So knowing that grey obsesses over every single word used, I watched the video back. He never says that hexagons are the strongest shape. He says a hexagon tiling is very strong due to the 120 degree joints which is the most mechanically stable joint.
Chemistry background. They definitely aren't strong in the traditional structural engineering means. Hexagons are really great because of their ability to balance strength with space-filling efficiency - which is really the reason behind the honeycomb tiling and of course, actual honeycomb. Getting rid of that "extra bit" you talked about can be okay in certain situations (like where there will be a backing, like a wall, panel, or floor) but you want walls or compartments. Basically, when there is a single dropplet, a circle is favored because it maximizes volume/area and minimizes surface/perimeter. If you have many dropplets together, hexagons are the shape that provide this ideal ratio.
Generally, I wouldn't call them "strong" so much as "efficient." I would like to note of course in chemistry the resonance structures in benzene as well as to some extent the stability of cyclohexane (although technically it isnt a 2D hexagon). These molecules, and benzene in particular, show immense stability, which we colloquially refer to as the "strength" of the bonds. But also, hexagons might not resist compression well, but they do resist expansion (like if you blow up a balloon inside). I think these ideas are where this "strength" idea comes from.
This was really interesting. Great addition to the original video
I'm loving the science and physics, I'm glad I was recommended this video, keep up the good work
I think that Hexagons are almost equal to triangles, but every shape has its own use. One thing hexagons are good at is flexibility in a very light format. When you pull the mesh, it forms rectangles which are under tension, which is, as you mentioned a bit stronger than conpression and a lot stronger than bending. When you stop applying tension to the mesh, it pulls itself together again, something I couldn't see with your simulations because you somehow forget that it could be possible that the rotating force could as well be stronger as the artificial gravity as it could be weaker. If you fix just the sides and the bottom of the sides of the mesh, you can also apply a huge load on the top, whilst saving a lot of material you would have used in triangles. Buildings and such absolutely fulfill these requirements. That being said, I always liked the triangle more, there is nothing it can't do, except flexing. Since the engineering of our world is shifting more and more from trying to make the most rigid structure with mechanical joints to making more elastic ones with newer materials to absorb stress rather than distributing it (which is not ideal in earthquakes to name a simple exanple), flexible meshes are a lot better. Hexagons have just a tiny bit more surface area than a circle, remember that you want the smallest surface area in a shape to use the least amount of material, whilst still being tileable.
I think the biggest problem with the simulation is that the joints are free to move, which is not exactly realistic to life.
In real life there is no joints which can just phase through each-other.
Unfortunately that's not how physics work. Joints, whether they're free to move or fixed, will always be the weakest point in a system if they can't simply pass the force straight to the next side. Remember when Con said materials are strong if you push or pull on them, but not when you bend them? It's basically that.
Found UR channel today !
Looking fwd to more in the future
Hey, chemist here. I want to add some stuff because I think this video misunderstand the foundation of CGP Greys video.
Hexagonal structures are great because they act like triangles in a planar 2D structure without wasting needless material on actual triangles. However, as soon as we go into 3D space, we need a bunch more information.
In nature there are 2 forms of structures that form in 3D space. Cubic, also called octahedral due to its 8 corners, and tetrahedral, which is due to 4 corners. Tetrahedral is, of course, 4 triangles in 3D space. These two types sometimes mix as pyramidal (square plane with 4 triangles), bipyramidal, etc. However, due to hexagonals innate property of "acting like triangles without wasting needless space or energy", some inorganic, or organic, compounds form natural hexagonal crystaline structures, bonded together between triangles. These are often tetrahedral cordinated crystaline structures, whereas the ordinary cubic crystaline structure is formed through octahedral cordinated compounds (this is inorganic chemistry).
However, all this is completely irrelevant. CGP Grey already did mention most of the points of "square being X" and "Triangles being Y" in his video. His point was that Hexagonal structures where the only polygon that could cover a blank space without leaving gaps while maximizing the ratio between area of each hexagon and the surface of each hexagon.
This also works in physics. The reason why hexagons are not used in structural engineering, but that we use triangles instead, is because of pressure differentials within the structure compared to outside. Hexagons minimize the material used for maximum space while holding structural integrity in a packed space. Cells form hexagons. Bee-hive combs, flowers, eyes, etc, all form hexagons because of this differential. The reason why this tidbit isnt useful in construction, is because you dont have a pressure from within. You want the structure to withstand force from the outside without additional force within. So you use triangles instead, which is what hexagons are derived from. Hexagons gets their superb distribution of forces from the triangle. Triangles having the 60 degree angles to form equal distribution of force between 3 equidistant fixture points. This is great for withstanding pressure from outside. Hexagons are great at distributing force from both within and from outside.
While I understand what you are trying to say at 5:00, molecules do most of the time really like specific angles and are a bit more like stiff joints, so even without any repelling/attracting forces of atoms not directly bound to one another the hexagon wouldn't just collapse into a rectangle
came here for 3d printing, stayed for the knowledge. !תודה רבה
Loved this video in love watching those guys video you mentioned and i cannot say anything less you definately earned my subscription
0:28 Correct, I do watch CGP Grey and I saw that video. Actually your thumbnail decision was perfect, it pretty much immediately encapsulates the issue. Thanks for the vid bro, I'm gonna sub now.
Tension is strong, compression is generally stronger. Buckling failures are in a way a type of tension failure where the material fails away from the neutral axis, usually on the side that it is in tension.
Im a firm believer that an Icosikaitetrahexaflexagon made of one way material (like a dielectric mirror or even 50/50 mirrored window tint) are the best '-agons' . Yes!, the joint between topology, logic (state-machine capabilities due to interlocked layers) and geometric optics. We then take that as a shadow of a higher dimensional object of course similar to cube mapped to a hexagon as maximal shadow projection (more interestingly the hexagon is the max shadow for a corner-cube {naturally could be a retroreflector} + more I wont worry you all about here. Yes, and intriguing research field I am the sole freak researching it without funding. Im so poor )': should have stuck to trappin
This is a really cool video. I'm not a professional when it comes to any kind of science, but when I saw that video, I never felt like it made intuitive sense that a hexagon would be stronger than a triangle. I really enjoy your way of explaining things, and I'm very excited to see more of your videos. Subscribed. :3
I just discovered this channel, and I gotta say, the 14 second intro already made me subscribe
Well, hexagons themselves are composed of equilateral triangles, so there might be a point to this video. Plus, triangles are nondeformable, unlike other shapes (except for the circle, I think).
Circles are weird, they're non-deformable if they're a single line, but if they're infinitely many points they're the most deformable shape.
That's actually what causes honeycomb to become hexagons, as bees just hex pack cylindrical tubes they make with their abdomens, which are incredibly structurally sound, right up until the wax heats up and becomes less rigid, the cylinders push on each other and buckle out into the gaps, forming a hexagonal tiling in the process due to how the cylinders were packed. As the rigid lines return to a bunch of points, they deform.
It's still the best-a-gon compared to Pentagons, Octagons, and the other agons. The triangle is the strongest but I don't remember CPG saying it wasn't. Good video though!
I'd be really interested to see a video discussing what -agon is the bestagon, given the constraint of the -agons starting from pentagons and rising in number of sides!
I think one way (I've thought of it like this in the past & seen it brought up) to describe how Hexagons are 'the best' *still*. Is by discerning how they can be broken up/have internal triangles added to them which is 'intuitive' & on a large scale. Putting together many many many triangles is potentially daunting when looking at the scope of a problem, whereas using a hexagon & conceptualising what to take away/adapt is a more reasonable task.
You can adapt a hexagon's shape too and still have it be a hexagon right... so you can fit essentially any major type of triangle within them.
It all comes down to hexagons as volumes versus hexagons as a system of struts. Different things.
"Hm I wonder why a short, showy video can't elaborate on its points and ends up misleading tons of people"
This is why long form content always wins
Cool video. Happy Christmas!
I cant believe this video has only 5600 views.
Keep up the very good work and quality videos and soon your channel gonna exploded. :)
Oh wow, yeah
I assumed it would be way more!
It's hit the recommendation stream now. Hope Con is ready for virality!
The main real advantage of hexagons is that they approximate a circle and thus are the tileable polygon that requires the least perimeter for an area, which is why they're good for honeycomb paneling
One of the only commercial products I've ever personally handled in my life with a hexagonal pattern is chickenwire - a fine mesh fencing material used for low-strain applications.
If hexagons are superior, consider: why are nets and chain link fences always made with a square pattern? Why are fabrics made with a square pattern in the textiles?
Basically, if hexagons were the best shape for everything, we'd bother using them more often. Most of the time, they're more effort than they're worth - but sometimes they do get used, because there are times when hexagons are the best solution!
Regarding fabrics, they are not always made in a square pattern. Most fabrics used to be square because of the ease of manufacturing them (weaving), but there's also non-square fabrics like Jersey, which is knitted. If you take an old T-Shirt or a knitted scarf, give it a good stretch and look at the holes, you'll see that they'll actually form some kind of hexagonal lattice. Which perfectly aligns with the point of the video.
Hexagonal (knitted) fabric = Stretchy in all directions
Square (woven) fabric = Rigid along the X and Y axis, but stretchy if you apply diagonal tension (this turns the squares into rhombi)
Nets are generally made in a diamond pattern, not a square pattern.
Yeah, it seems pedantic, but it's significantly easier to keep everything consistent if you're tying them in a diagonal lattice because each knot is in the middle of two other knots, so you can control the height of the diamond by using the width of the netting needle (they're much wider than the name suggests) and once the first row is established it's comparatively easy to place each knot between two knots in the previous row (tension and gravity do much of the work).
The reason they're not hexagons or triangles is primarily because each knot weakens the load capacity of the line, so minimizing the number of knots is a very desirable property and diamonds are a good balance between ease of manufacture and minimization of the number of knots.
Easier to make that way + cheaper + people who make fabrics/nets/fences are not mathematicians or physicists.
It's faster to replace damaged fabric rather than making super strong hexagonal fabric
People defending the hexagon from a gaming perspective are kind of missing the forest for the trees.
The real value of the hexagon in mathematics comes from its synergy with the unit circle and the real value in practical applications from from its synergy with polar coordinates (which is often expressed in gaming).
The mathematics makes it super easy to calculate because of native relationships with sin and cos.
Polar coordinates have the advantage over grid systems of natively expressing distance as the radius from the origin (no cutting corners and getting 1.4+ units of diagonal movement. It also has a pretty elegant system of vector addition but that's getting into the nuts and bolts.
Good video and very informative to this non-MechE.
This video is AMAZING. thank you.
Out of curiosity, what software are you using for your physics simulations?
This was just something I threw together in Matlab and eventually it turned into this video. Definitely not the fastest way to do it but it works
@@ConHathy Figured it was matlab, but I would like to see how you simlated the physics. If you could somehow make the code public for us to try... I would really like to learn from it.. Thanks in advance
I came here because I saw hexagons are being question!
I’m honestly surprised this video doesn’t have more views !
To this day, I do not understand how certain people refuse to learn anything ! Let alone go out of their way!
great work, subscribed!
Very cool, thanks. Hadn't seen CGP Grey, glad to see your reaction. Any thought about how this related to Fuller geodesic domes?
I guess the wouldn't work in a simulation without collisions ...
So they don't work in real life because collisions don't exist in reality ...
Hexagon is best for optimizing wall length compared to area when tiling. That's all. Every problem might need a different optimization.
This really highlights how important context can be.
Fun and informative, many thanks!
Thank you for this!
Hexagons are useful additionally for these reasons:
- They have good packing properties
- They are good at retaining their shape after elastic compression
- They are good at resisting internal pressure.
Basically, they're circles.
That's the real benefit of hexagons. They're the best approximation of a circle that monotiles the plane.
The point of hexagon making a great spacer material between two strong sheets made me think of cardboard. Would a hexagon lattice between two fiberboards be stronger per material used that the corrugations?
Yes and it is sometimes done but more complex and expensive
Yep, it doesn't have long lines where it buckles easily, making it much stiffer and harder to compress. Not really great for making boxes though.
I've seen it and it's been living rent free in my head and driving me nuts
5:02 I expect you say "and it looks like this... And.... Look ! Bunch of triangles !"
The real reason hexagons are the bestagon is because they look cool and are great for RPG terrain.
Triangles are the SECOND strongest shape, the strongest shape is actually a circle but circles are really hard to make so we've just made things out of triangles because they are much easier to produce.
It doesn't help that the strength of a circle is way more dependant on its precision than any other shape, and given that a perfect shape can't exist outside of theoretical modelling, a circle will always have some point of failure in practice.
A circle is only strong when the force is equally distributed around the circle and is orthogonal to its edge. Any other load configuration will cause it to buckle. That’s why arches only work when loaded at their apex with the force parallel with gravity. This is also why gas tanks are cylinders because gasses expand to fill a volume and exert equal force on its surface.
homie you make an amazing point that I agree with. also, i may copy your facial hair...tbd. good video and communication skills
I didn't watch CGP's hexagon vid, but am nonetheless glad that I found this corner of the internet where people nerd out about materials engineering & physics
CGP Grey specifically states that they are the strongest shape *for the least amount of materials* because you need more wall to make triangles than hexagons
Adding the extra members doubles your weight but easily more than doubles the strength
Except you can do the same thing AGAIN for less and still get the same result so@@ConHathy
I just think they are pretty...
What program do you use for the physical simulations?
When you simulated the bridge it looked a lot like polybridge ahah.
I can't believe it's been two years already
Ok, but the claim that ‘hexagons are the best “-agons” ‘ is still true. Name a better “-agon”. I’ll wait.
trigon
The one that bothered me was that Grey said that bees make it because reason that I forget. Turns out, as Matt Parker found out, they make as a side product of how they make shapes.
Packing efficiency, circles leave space unused.
No shit, they have evolved that way specifically for the packing efficiency
Verry interesting, great content 👍
Tell it to the bees. Well the beehives. Agree. Triangles for strength, but hexagons for filling area uniformly. Storage option in other words. Basically, a bunch of tightly packed circles (Minimum perimeter for volume optimization) but without all the unused space between the circular cells.
7:15 to be fair, Grey was talking about hexagons in a flat plane and not a vertical plane
If the vertical plane collapses because gravity pulled down on it, what will the horizontal plane do when something pushes across it?
@@bryananderson688pretty sure you can overlap layers and make the structural integrity amazing
Makes you wonder...
If hexagons are not, in-fact, "the bestagons", what else could CGPGrey have lied to us about?
I haven't seen CGP Grey's hexagon video or any of his video for that matter (unless he has a video on flag colors, I may have seen that), so the RUclips algorithm suggested this video more out of nowhere. You still have my interest though.
Honeycomb panels use hexagons not because they're the best _structurally,_ but because they're the best tiling perimeter-to-area shape we have; hexagons are known to have the most sides of any regular, tessellating polygon.
In other words, it's not a geometric consideration so much as an economic one. And that's why bees use them: because it's really just circle packing and filling in the corners. Honeycomb matrices are nothing more than approximating circle packing with straight lines, for material efficiency.
Hexagons are great for tiling glass because it is the most round tileable polygon, and round is better for glass because corners are its weak point. Thus thing with glass tiles (eg. space station windows) are hexagons, because it maximizes viewability. This also means hexagons are common choices for force fields in media, hence the idea that they are strongest.
So does this then mean that force fields are weak at the corners as well?
always hilarious that when the hexagons are left to themselves they try to turn into rectangles, shapes grey seems to dislike :P
I'd like to mention that bees and wasps end up with hexagons not because they are the best to keep two sheets apart and wasp nest is nothing like honecomb, yet still consists of hexagonal shapes. What they trying to do is to fit as many cylindrical containers of similar size as close as possible and hexagonal pattern is the natural result of this. As for example, lookup NBC News "Bees don't do math".
One note about the Smarter Everyday video, the triangles were their old pattern and the rectangles are their new pattern.
I would sure love to tell Grey about this, if only there was a method to comment on his videos
We need video responses back
Hexagons may not be strongagons, but they are still bestagons
How could you? I was indoctrinated into the bestagon cult three years ago, and have been a faithful believer all this time! How dare you shatter my faith like this?!
The start of the video sounds like “we use steal now, that’s why steal is best, and wood is old school. But it’s wrong”. But it all just different things we talk about.
And later: “These are not physical connections, these are just forces…”.
It all sounds very strange to me.
P.S. I hope readers understand what I mean.
Finally the video I wanted to see: *Hexagons are NOT the bestagons.*
You know, this video completely missed CGP grey's point.
What struck me the most is the argument that hexagons are best for games. When there's so many fantastic games on squares and so few games that actually are on hexagons.
But ehh I'm glad to see any video complainig about worstagons, including the material physics ones I guess
The problem with squares is whether you allow diagonal movement, like a bishop in chess. Since they're right next to each other, it feels like you should, but then diagonal movement is faster than lateral movement (by a factor of sqrt(2)), which might problematic. Hexagons don't have that problem.
I've always thought triangles were a bit better for games than hexagons.
@@TheHenryFilms The thing is that having those two types of movement makes it easy to make gameplay more interesting and varied than more uniform hexagons.
@@TheHenryFilmsunless you are playing a game with a realistic distance system, that doesnt matter. Hexagons also have a MASSIVE problem that squares dont: you cant move in all 4 cardinal directions
Cope harder, square peasant.
Your video is really cool and interesting, however, I returned to the video Hexagons are the bestagons, and at no point does CGP Grey say that hexagons are the strongest shape. He speaks about how great they are at being able to tile the plane, and how strong they are compared to how little material they require when building, but he never says they are the strongest shape. Even when he speaks about graphene, he says that it is the strongest known material, and he says that it is made of hexagons, and that it does make graphene pretty light and sturdy at the same time, but he doesn't say that hexagons are the strongest shape. The closest he goes to saying something like that is "hexagons are strongagons", but even then, not "THE strongagon".
The Order therefore declares you a heretic, for Hexagons are the bestagons.
I'd say for the rocket panels, a hexagonal "reinforcement" of the tank would be not just heavier, but also a lot worse in both vertical compression and horizontal tension, just like diagonal squares. So here the alignment does matter quite a lot.
ONE caveat:
Hexagons are the "strongest" shape for the specific case of an array of VOLUMES under PRESSURE in a 2D plane. If you stack cylinders on top of each other perpendicular to their axis of rotation, then they will tend to deform into more stable hexagons. Or, rather, into hexagonal prisms.
Of course, the world is not 2D, so it seems like in practice you get a lot of "scutoids", a shape that can (among other things) look like a compromise between a hexagonal prism and a pentagonal prism. Vihart has done videos about them before. Your body contains a lot of scutoid-shaped cells, which are volumes under pressure. I'm not aware of any engineering applications for them, though.
1. Area to perimeter ratio
2. Strength
3. Atoms
4. Tiling
5. Boards
6. Saturn
These are some of the points that other video made. Invalidating the strength point alone doesn’t invalidate that hexagons are the bestagons
A thing that I mentioned in the comments of the original which I haven’t seen mentioned here is another argument that Grey made, which is also wrong.
Saturn’s polar hexagon _is_ understood, and we’ve created a variety of regular polygons in simulations using the same mechanism. It’s basically just rossby waves interfering constructively when near a pole. Hexagons are the shape with the fewest number of sides that’s easy to make (with less, the winds need to be far more intense, which means extremely high gravity and way faster rotation) but lots of shapes are possible.
I spoke with one of the authors of a paper looking into this when I was in uni. His explanation was extremely confusing until he showed me the model, then it all clicked 😅
11:42 "I know it's no square-agons it's 4 the bit"
Best unintended pun ever
I have NOT seen the video from CGPgrey you are referencing and yet youtube was still shoving this in my face insistently despite me not really showing much interest in structural engineering. That said, while this is the first i've heard about "Bestegons" this was still interesting.
*gasp*
There's some drama going on in the shape fandom
...however, I remain loyal to CGP grey.
I love Greys video but i also love that this respectfully counters it. Scientific debate for the win.
I was under the impression that "strength" usually refers to how much force an object can take before breaking, not deforming. by that definition, strength and rigidity would be 2 separate things, but they're used synonymously in this video. is "strength" actually a clearly defined term across science and engineering, or can it refer to multiple things?
With regards to materials you are right but I would argue that they are very much linked when looking at large structures. For example, the bridge at 8:00 didn’t fail in the material sense where a member broke from stress, but if an engineer tried to argue that the bridge was perfectly strong you probably would disagree because it collapsed under its own weight.
Also in terms honeycomb, triangles would actually be stronger because they are supporting some of the load unlike hexagons which are too flexible to really support the skin under tension or compression.