Why Do Bees Make Rhombic Dodecahedrons?
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- Опубліковано 29 тра 2024
- You must pre-order Maddie's new book. Several copies. For every young person you know. www.maddiemoate.com/book
And cheers to Maddie for being my number one bee friend. She made a video on the same day which you should absolutely check out. Her whole channel is fab. • 3 Types of Bee in a Hi...
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CORRECTIONS
- None yet! Let me know if you spot any mistakes.
Editing and filming while covered in bees by Alex Genn-Bash
Additional filming and bee angering by Greg Foot
Cardboard models by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b... - Розваги
I'm afraid you're wrong Matt, bees aren't mathematicians, they're engineers. There might be more efficient shapes but some poor bee-geneer has to make the thing. The bee project manager probably got a bulk discount on off the shelf regular rhombii rather than ordering bespoke wonky hexagons and squares. Think of the extra paperwork!!
*beespoke
Wasps are much better suited for paperwork
The bees are engineers in another way. The rhombic dodecahedron is also more structurally sound than the other solutions. They wouldn’t want a collapsing hive now would they?
@@xanderberg3653 Oh, you're damn clever, you are. Take my like, and never speak to me or my bee again.
The truncated octahedron shape seems more like an architect's idea, really... 🙈
"hexagons are really a good shape" is the Parker's Bestagon
Parker square of a bestagon
Matt Parker isn't the only one to think Hexagons are the bestagons. CGP Grey also believes it to be the bestagon.
I rather suspect that “hexagons are ” is meant to evoke us all going “say the line! Say the line!” Only to be disappointed by “a really good shape”. And then afterwards when he *did* say “bestagons” we could all go “he said the line! He said the line!”.
I would have given anything to hear Matt open with "hexagons are the bestagons"
Great comment
You forget the importance of symmetry. I think the reason bees couldn't build truncated octahedrons is because it would require them to choose a direction (for back-to-back assembly), and make sure every builder follows it. While dodecahedrons will always merge perfectly together, no matter how many starting points there are and wherever they are. They are symmetrical. So dodecahedrons is definitely the best shape for distributed workforce.
I think Matt did a good job of demonstrating that bees already have a preference for vertical.
It wouldn't be hard to coordinate, either. Instead of centering a back-side cell on a front-side vertex, you could center it on the middle of the front-side vertical wall, and I think that'd arrive you onto roughly the right shape.
@@SoulSukkur yeah, you really showed us how bees have no reason not to make truncated octahedrons...
And yet, they still don't
So they must obviously have another reason not to
@@aceman0000099 if it ain’t broke, don’t fix it
What spread pollen before bees
@@aceman0000099 I'd say the later half of the video explains what bees are actually doing pretty well, and it has nothing to do with geometry in the first place
I let my bees do freeform comb often. Though tthey do make vertical comb, the symmetry can be rotated in the flat plane in any way, meaning that in nature there would be no universal reference from which they could all build in the same symmetry. The simple rhomboid falls into cadence more easily in a chaotic comb like the one they showed. The major difference is that there arent many straight lines in nature.
Weirdly, I really do complain a lot less when I'm not being actively stung by bees!
Well here's hoping you had no reason to complain much!
The "freestyle comb" honestly looks like an art piece to disrupt wind turbulence/resonance.
Its beautiful. I wonder what caused the run away pattern. Maybe debris that couldn't be removed forced the bees to build over it into this irregular shape?
@@Hyraethian or they wanted to be sculptors since they ain’t the maths guys we thought they were.
@@Hyraethian usually there would bee (see what I did there) another blank frame with wax sheet, or edge of the box in the way. This must have come from a hive that wasn't fully filled with frames. Possibly it was unpopulated, used for storage and a swarm moved in.
@@Hyraethian or maybe noshed on psychotropic (as in trippy) flowers?
reminds me of termite mounds in Australia
I wonder what those bees must think of someone just casually taking the roof off their home, pulling out an entire interior wall, and waving it around. They seem remarkably chill about the whole thing.
"Alex complains a lot less if he's not actively stung by bees" - ugh, such a needy camera man!
If it isn't my favorite 40 year old Australian recreational mathematician, author, comedian, UA-cam personality and science communicator!
Isn't he british...?
@@curiodyssey3867 he is not
He is natively Australian but he does live in the UK.
top 5 at least
if it isn't, then what will happen?
The rhombic dodecahedron seems to be better for stability, as it shares the bottom surface with THREE cells on the other side. The truncated octahedron only shares with TWO cells.
What we can say for sure is that the rhombic dodecahedron outcompeted whatever other mutations that ancestor bees and their lineages had
This is the shape required to reach an evolutionary stable strategy/Nash equilibrium for bees
Surely all exposed (back)sides touch another cell, since it tiles 3D space. Wouldn't that make it share the bottom with FOUR others?
@@funkmonsterjones4753
I’m sad to be a killjoy but natural evolution doesn’t care about any global optimum in regards to anything. If something’s good enough to stay natural evolution will allow it, no matter how ridiculous or obviously inefficient it may look to us.
Just look at C3 vs C4 photosynthesis.
Exactly, it's not just about using the least amount of material, it's also about stability, also it's easier to build because it has perfect symmetry.
A wise man once said: "Hexagons are the bestagons."
HEXAGONS ARE BESTAGONS!!! So glad he got that CPG Grey reference in there!
+
cgp
gcp
I forgot when I heard it that it wasn't Matt's thing
Came here to say it too.
0:12 missed opportunity to say hexagons are the bestagons.
10 seconds later: Why did I ever doubt you Matt?
More like 25 seconds.
Although it doesn't use the optimal amount of wax for the space, perhaps it is still the most efficient shape for them to build, because of the "hardware" they have. It is simpler in it's symmetry, and tiles more naturally than the other solution you presented, so I can imagine it would be simpler, for example, to program a machine to build the rhombic dodecahedron than to program it to build a truncated octahedron...
And the bottoms from other side must fit to bottoms of this side (comb centers are shifted to intersections). There is no better way than what bees do.
@@expioreris yeah, and perhaps there is a better solution that he didn't mention, but I'd guess that for the specific job the bees are doing, the rhombic dodecahedron is probably the best.
Also, the mathematical least amount of material isn't necessarily the strongest structurally for all configurations (eg: where the load is vs where the support is), and like you said, the centre points lining up with the reverse side's walls would add a lot of structural support in a freestanding hive with no precrafted base
Bees don't build hexagons at all, they build tubes, the edge of which melt into more structurally stable hexagons.
@@expioreris Yes, Fitting the opposite side is a strong requirement!
1. There is no rule that millions of years of evolution lead to optimal solutions.
Genetic algorithms have been used to imitate evolution for many decades now and there are much better optimization techniques for most applications. Evolution often converges to good, but not to optimal solutions.
2. I imagine that rhombic dodecahedron based shapes are more stable than most other shapes. Therefor thinner walls might be sufficient to hold the hive, making it actually more Wall-material efficient than the other options mentioned here.
Optimal over what feature space? It could be that the rhombic dodecahedron, while using more wax, provides better structural support, has better thermal properties, etc.
Or that the benifits are marginal enough that there isn't evolutionary pressure.
Please finish watching the video
exactly, for a box-shaped space the optimal shape is cube of course; for an in-the-tree beehive (i.e. rounded undefined volume), a rombii dodecahedron surely fits it better than cubes
@@geurgeury His comment is no less relevant at the end.
Optimal when you have a flexible wall and push backwards and forwards. As he explains.
When you inserted the rhombic dodecahedron into the hexagon, I was stunned to silence! What a beautiful fit for a great shape. Thanks for making models, I'm a visual learner, and your models are helpful.
Sometimes I see UA-camrs I haven't seen before, and they are smart, talented, charismatic people. Maddie is the first one in recent memory who made me think "Wow, this is indeed a TV presenter". The level of personalism is fascinating
The fly of the Bumblebee by Rimsky-Korsakov was such a nice touch. Once again I'm super impressed by the production quality of this videos. Really, really nice.
They were honeybees not bumblebees though...
I can't imagine a better musical choice.
That impressed you? It's obvious low hanging fruit used for everything bee related ever.
@@FLPhotoCatcher exactly! Completely different animal. In Dutch bumblebees aren't even called "bees". They're called "hommel" while a bee is called "bij". So I'm always surprised to see confusion between the two
Flight* of the bumblebee
Learn the beauty of the Truncated Octahedron space filling shape! Since bees make round 2D combs that settle into a hexagonal lattice due to wax pressures distributing, they're taking a 2D optimization and extruding it into 3D space. If a 4D bee were to take 3D spheres and pack them together -- as they do with hexagons -- then the wax would settle into 3D Truncated Octahedrons extruded into 4D space.
Interesting science, but at the same time I am intrigued/horrified by the concept of a bee in 4D space.
@@lightspiritblix1423 4d bees could be very dangerous to people allergic to them, as they could spontaneously appear and disappear anywhere without warning
@@sebastianjost i wonder how much training it would be to become a 4D pest exterminator
@@benblack5126 That sounds like one of those things where you tailor the genes of the individual exterminators from birth, put them through a rigorous program throughout their childhood, give them a bunch of fancy cutting-edge equipment tailored to their unique biology, and most of them end up dying anyway.
@@Woodledude So its Halo but 4d and private sector. still would make a epic book or movie though
"Hexagons are the bestagons"
- CGP Grey
Vi Hart said it first.
@@sdspivey where
@@sdspivey where?
@@sdspivey CGP Grey said it first.
@@sdspivey It’s a quote from CGP Grey.
As a bee-keeper I loved this video, but you should have used foundationless frames if you're going to look at their cells in this level of precision. Glad you picked up that they're tubes more than hexagons, and rounded bases more than polygonal ones - but bees also build cells in multiple sizes, something that foundation prints try to discourage. If you look at mixed-cell comb, I think you'll find the structure makes more sense. You kind of got there looking at the edges.
Figures it's something as simple as that. Hexagons just have a tendency to pop out when designing parts and more often than not when your trying to connect all the components that make up a given part. They are a fairly easy shape to produce on accident.
I find it more fascinating that they create these shapes by iteratively reshaping the wax! Doing geometry the way we do isn't necessarily the most "natural" way one may say.
I hereby request a collab with CGP Gray to discuss 3D best-ahedras.
Maybe the best tetrahedra also rhymes with best-ahedra. Should narrow the search down a bit.
@@therealcaldini Give that you a raise.
seconded :D
Get Adam Savage on that train, he also have favourite 3D shapes.
One-upping (a pun on going to a higher dimension) "hexagons are the bestagons" is the most on-brand thing for the person who wrote the book on the fourth dimension
11:28 Could you show us how the hexagonal prism into truncated octahedron fit together? What would be the offset arrangement of the two sides of the honeycomb?
Edit: The arrangement is that the hexagons of one side are centred over the middle of an edge on the other side. The peak edge where the two squashed hexagons of truncated octahedron meet is exactly where a wall is built up on the other side. The end to the prism is oriented the same for all the cells so, if you look at only the small rhombi, you see many parallel straight chains running across the pattern.
The CGPGrey reference was really well done! Starting off with a misdirect and then just as this CGP viewer was thinking Matt really should have referenced him, sneaking it in the after all. Loved it!
I think the important part about the end capping isn't the efficiency of the capping, but how it fits together. The shape bees use really obviously slots together with the opposite side of they're just offset. More complicated end cappings may save wax on an individual side, but if it's not the most efficient solution for capping both sides at the same time it's still advantageous to use the rhombus endcaps.
The ending was amazing. It threw me all the way back to 2012 when ViHart made a video series on plant geometry (which I will of course rewatch now)
It's fascinating how intricate mathematical patterns arise from very simple instructions.
I was thinking about it - and I suspect there's a simpler explanation. Fundamentally the cells are a stack of cylinders with hemispherical end caps as a circle has a minimum circumference per area and a sphere has a minimum surface area per volume. However, this stack leaves a lot of wasted volume between the cylinders, so the walls are pushed out until they meet - creating the existing cell shape.
I'm glad to see some appreciation for the cinematic masterpiece that is "The Swarm".
Wasn’t it flight of the bumblebee?
@@micahcraine5579 the music was. The movie clips were from "The Swarm".
@@bitequation314 ah, okay
I was expecting to see Nicholas Cage from the remake of THE WICKER MAN.
I thought the movie clips might be from the movie The Swarm. Actually haven't seen it, only know it from Citation Needed.
12:02 it might be possible that another reason for them not using a more complicated packing shape is that their edges have volume- having a face with 5 edges vs 3 edges like in the rddh would mean more wax would be needed for each edge, which might not pack as tightly.
"The bees aren't doing maths; the maths is doing the bees"..... will quote
I was searching for this comment. 👍🏻
I’m totally going to be saying this whenever bees come up on conversation.
@@jessicadaugherty9011 I think this applies to many complex structures in nature. For example, when someone uses a sunflower's pattern as an example of where nature somehow embeds the irrational constant Phi in the plant's DNA (hint: it doesn't). Or the distribution (angle) of branches from a tree trunk to maximize sun exposure of leaves. Again, Phi. But these things keep getting reinforced through genetic algorithm as someone else mentioned. The math is what we apply when reverse-engineering the thing. A sunflower doesn't do a square root calculation! Or is it an analog computer for its own good?
I'm one with the maths and the maths is with me
Love to get your take on the fact that the cells are built with a slight tilt upwards towards the open end, between 9deg to 14deg on average.
Was looking for this comment :)
And are the prisms squashed or is the base elongated?
I'm surprised you skipped over a very important detail. The cells of the comb that they build are not horizontal, they are sloped upwards at between 5 and 7 degrees. Your model presupposed that the cells are aligned parallel to each other on opposite sides of the comb, but that is not the case.
Also, another minor detail, you implied that they build upwards, starting in lower cells and moving on to higher cells. That is also incorrect. They start at the top and build downwards.
would bees accept a hotel with squared cells? (kind of a parker-bee-hive)
Bumble bees make spherical cells that join willy-nilly. So I guess probably yes
When talking about the best shape, you may want to consider that a bee only needs to know 1 shape (the rhombus) and no consideration of orientation to create the cavity (requiring only 1 type of bee) rather than many shapes in particular orientations (or many kinds of bees or some bee micro-manager). The shape may not be the most efficient, but it seems the most practical for simple automatons. Very fun video tho :)
They do not need to know any shape at all, that's the point! They just blindly build a spherically-capped cylindrical capsule approximately their body size. When multiple bees do the same concurrently and try to build as dense as possible, adjacent cells will take a shape of hexagons as an equilibria of opposing efforts. And when they concurrently build two layers cap-to-cap following the same principle, the spherical caps naturally turn into rhombic dodecahedrons, so that comb layers are shifted half period relative each other, and every rhombus makes a shared wall for two cells in adjacent layers, which is very effective.
@@onebronx It's really incredible how many of these comments were clearly being posted before the video ended, and you can easily tell because they're all speculating about what's the proper geometry bees are calculating lol
@@z-beeblebrox The comment stands regardless of the video.
The Swarm! From Michael Caine's "It's A Living" period! Made internet famous by the Technical Difficulties!
Where's Matt's giant jam sandwich?
This one is going to live in my warmed heart for a while now. I adore this
4:10 "I've worn a bee costume before, but it was different... I was literally dressed up as a bee ! " - Matt
I instantly knew what movie the clips were from, since I've watched one of the early episodes of Citation Needed!
From the "it's a living" stage of Michael Caine's career
I was wondering who else would pick up on that. At least this time, it's not a swarm of didgeridoos.
giant Jam sandwich!
I always wondered what a "natural" way of filling 3D space would be.. and yes studied some foam experiments I did. As far I can tell.. there isn't a clean winner, it's always kind of chaotic contrary to 2d space (like on the surface of a fluid) where it will create hexagons. So I guess this means there are a lot of possiblities to fill 3D space, but almost as good, so chaotic shapes are created.
I wonder how gravity affects substances trying to build in freeform style
I only have 360p as an option. Might only be me.
Me too. My eyes hurt.
Same
same
it takes a while for the higher resolutions to appear
@@muhilan8540 I’m almost 5 mins in and still just 360p
Looking forward to the second channel video with the Bee-roll footage.
+
Maddie has such an infectious smile
There's nothing more awesome than watching standup maths in 360p
Me : *Grabs a bee*
Me : Why are you making Rhombic Dodecahedrons?
Wasp : *Visibly confused*
Me : Your tricks won't work on me, fool.
Jokes aside. Grabbing a wasp is a very bad idea. More like the wasp would instantly attack you.
I want to see an ultra-low-budget sci-fi film with those beekeeper suits for spacesuits. ;)
I love that math didn't come up with it. It was a goal and a process that ended up being what math can describe. The bee's goal is to get in there and cull out material while making the largest volume, and what comes out is what math can describe. Now I'm thinking of entropy and baby steps.
Oh god, a clip from The Swarm right off the bat? Man after my own heart
Would be interesting to slowly rotate the frame, or in increments to see how much they use gravity. Could you get a swirl?
The regular dodecahedron is my favourite of all the dodecahedra, because the regular pentagon is a very elegant shape, I think. The only problem: The regular dodecahedron doesn’t tile Euclidean 3D-space, by itself.
The 120 degree angle occurs naturally because it minimizes the surface energy. The bees actually make circles but the the wax is a flowing solid which minimizes the overall energy when all intersections are 120 degrees. This is also how crystal grains grow is solids such as when metal is annealed.
As Matt and Maddie approach the hives at 4:48 the background music is “Flight of the Bumblebee”
I wonder how many viewers caught that Easter Egg?
I was a little bit disturbed by it.
Fist thought was "It is a bumblebee, a completely different insect, why Matt are you trying to confuse me"
@@TheNadOby maybe somebody could perform and record their own version of the tune and name it “Flight of the Honey Bee”
Most of them, I assume.
I don’t think a single person didn’t notice that.
Just looking for information about Hexagons in hives for a school project and found this, thank you man
Stuff like practical geometry is really fun. Polyhedra like those can be found also in crystals an crystal lattices, and the rhombic dodecahedron is also the Wigner-Seitz cell of the face centered cubic laatice, one of the two most dense arrangement of spheres in 3d (the other being the hexagonal lattice, hcp)
I like what you did with the patreon names. It looks like no one else has commented it. But I noticed! Was worth the effort Matt. :)
17:15, Matt, you gotta start normalizing the volume in your videos mate. Your aside was so quiet, and then you come back in yelling. Idk if you use Final Cut, but I know at least if you use Premiere Pro, you can run a loudness report on the export screen and it will give you an impression of your maximum loudness. You can help a lot by adding a bit of compression, a limiter, or even just watching your video back one last time with the audio level visible to make sure you aren't peaking when you have your volume set to a place where the preceding most important parts of your explanation are actually audible.
I can't believe Matt missed the opportunity to reply to "You happy?" with "Absolutely buzzing!"
Imagine what shape a 4D hypebee would make their hypercomb. The hole would approximate a rhombic dodecahedron and I can't conceive what fantastic shape the back of the tube would be.
"The maths is doing the bees" has to be one of my favourite quotes from you lol xD
😯
11:28 Is the claim of more efficient filling just for rhombic dodecahedron *(without hexagonal prism)* vs truncated octahedron *(without hexagonal prism)* at the goal of *fully filling 3d space?* Or is that claim for *hexagonal cells* with rhombic dodecahedron shaped backing vs *hexagonal cells* with truncated octahedron shaped backing at the goal of *being built upon the two sides of a plane with all the cells open to be able to be accessed?*
Edit: the efficiency boost is for the bee cells, but the area saved is only 0.35% of the mouth of the cell, it assumes the area of 0-thickness walls is a good measure, and losses could be introduced by 'crystal grain boundary'-like inefficiencies.
'crystal grain boundary'-like inefficiencies: When the bees start to make cells on side B, to get the truncated octahedron shape, they would start with a cell centred on an edge of the hexagonal grid of side A. But there are 3 possible phases. So, unless they had a plan of where to start building, if multiple starts are made on side B, when these growing honeycomb 'crystals' meet, there would be a 2/3 chance of misalignment.
Clearly Matt is a Latinophile. He goes with the Latin plural "rhombi" but not the Greek plural "dodecahedra."
My favorite mythical beast was the Dodecahydra.
@@silverXnoise every time you cut one head, 12 more appear!
I was so not expecting that mention (and slight teasing dig) at CPGrey but MAAAAN in was glorious!
I keep bees too!
If you take some old dark comb and leave it to weather in the sun the wax cells will delaminate from each other and you'll be left with many individual cells of the shape he made from paper! They really are amazing!
0:40 hexagons are the bestagons!
CGP converted you to the religion as well. I hope he will watch this video!
All hail the bestagons! ONE OF US! ONE OF US!
@@lemonice one of us, best-a-gons, one of us, best-a-gons!
Much bigger fan of the pentagon IMO
I was worried when he didn't say bestagons the first time, but he quickly correct himself.
@@megaing1322 I really had this inner fear, that he misses the oportunity to say it. I was such a relieve xD
I haven't believed in bee-made "hexagons" for many decades now. After thinking about it. They are merely circular / tubular cells, stacked like you would cut firewood logs. The negative volume of which. The walls separating the cells are the natural gaps between the circular chambers. If you thin those walls out they will eventually transform into more evenly thickness surfaces / walls, which at a distance resemble hexagons.
Matt covers this thinning out or pressure from adjacent chambers. It's not that bees are clever architects but more about cells or soap-film like geometric efficiencies manifesting naturally. Equilibrium. Again, Matt mentions soap film after I got to that part.
bees do in fact just stack spherical wax cylinders that melt into hexagons and a few pentagons and a few rhomboid spheroids. This works with next to no planning.
@@ollllj Indeed. They are stacking their chambers and working alongside or within naturally forming efficient minimum-area seeking membranes. I find a much more interesting example of clever bee behavior is how they communicate food source direction and distance using "dance" or repetitive walking movements primarily in the direction of polarized light from the sun - and adjusting for the sun's position throughout the day even while it's overcast. That and it's performed vertically, further transposing their coordinate system.
Bees are great! They're so fascinating; everything from their wiggle dances to communicate the location of flowers, to their honeycomb. I like to watch them at work sometimes when I chance upon flowers with busy bees around.
Facinating. I was reading a beginnner beekeeper's handbook, and didn't realize before the 20th century people had to kill the bees to get the honey. The whole hive. The removable frames made it possible to reuse! Crazy
For someone who likes maths and bees, and works at a factory that packages honey, this was interesting.
Matt - you should get that small bit of wax structure set in a block of epoxy as a desk ornament👍👍👍
this answers so many questions I had never looked into
Thanks!
11:52 "This isn't even the best solution!" -- Strong Dave Gorman vibes there.
So the bees aren't trying to make hexagons per se, they're just trying to stuff the most holes into a limited space and that's just how it shakes out. Very interesting.
Bees who made less efficient use of the area died for some reason or another, the bees who made this shape are the survivors, that's the way I prefer to frame it at least, it helps me parse it
The clips from The Swarm killed me, Matt
I was muttering soap bubbles under my breath for the whole video. Made me happy when you used it as an example at the end!
Now I'm imagining someone watching a video intensely whilst whispering "Soap bubbles... Soap bubbles... Soap bubbles..." constantly.
Amazing video
I can see the passion you have for the math in this
Cant remember who it was that mentioned your channel, but I'm glad I subscribed to it
I’ve been a part of the “hexagons are the bestagons” cult for a good while; I am now happily a part of the “rhombic dodecahedrons are the bestahedrons” cult.
Where can we order _those_ T-shirts?
I love Bees
me and my fiancee went to a bee farm the day we got together. over 4 years ago.
when i proposed I actually used a beeswax candle charm that I ordered from the exact farm that we went to. and I was really corny and said "will you BEE my wife"
Do you call each other honey?
@@baksatibi yes. yes we do. I call it honey bean. (my fiancee uses it/its pronouns)
@@BleachedBlackSocks that's extremely sweet, but also it brings the thought of the famous bean toast, now with honey!
@@fabiob7261 I'm.. I actually have a phobia of baked beans. I have no idea how or why, but im terrified of them.
@@BleachedBlackSocks Are you sure you're not Pythagoras?
Also, happy to find another it/its pronoun user! :)
CGP Grey had already convinced me, but man, this video really confirms that hexagons are indeed bestagons
I'm pretty sure that Charles Darwin wrote about bees 'homing in' on the shape of their honeycombs by simultaneously working side by side and on opposite sideds of the comb simultaneously.
Hexagons are the bestagons!
I've been waiting for this video my whole life. I was the 66th like. I love you Matt. In a platonic way.
Been thinking this forever. They're hexagonal by accident, but they're basically modified circles. Or spheres.
My dad is a bee keeper, so growing up these shapes were regular affair but never knew they got any name fancier than a hexagon!!
Hexagons are bestagons
Come on Matt, you could have gone with "A-Level Knowledge" as well, for "Apiarist"
Thank you, Matt, for this birthday present!!
I'm not that into bees, but this video is wholesome. Thank you.
Of course they're suboptimal in 3D space they are only B's, if they solved it optimal they would be A's
Really, it's a rhombic dodecahedrons on one end, hexagonal prism on the other... has anyone named that shape yet?
"honeycomb cell shaped" 🙃
9:46
I think Matt has reached his lifelong peak for gratification
One can buy honey with comb at the store (expensive) , and then examine more closely.The cells of the front and the back are offset by one half in three 120-degree differing directions. Note that each rhombus at the bottom of one cell is shared with one of the three back-wall neighbor cells. You can see that more clearly with the stamped wax foundation of a new frame.
Why is the video quality maxed out at 360p?
Uploaded and published immediately?
I thought it was just me. It's supposed to be 4K according to the thumbnail.
"Hexagons are..."
"Come on, say it!"
"a really good shape"
*angry viewer noices*
"However, hexagons are bestagons."
*happy viewer noices*
a) love matts visual aids
b) second video I’ve watched this week to reference The Swarm
Your videos are such good mathematical concept education. Thank you for teaching over my life!
Hexagons are the bestagons!
Except when you need to make a spherical object (such as a soccer ball), in which case you'd need to add some pentagons into the mix. But I don't think Matt would know anything about that. _Right?..._
Nah, you can tile a whole soccer ball with just hexagons. Saw it on a road sign once.
Maddie is smart, sharp and charming. Just like you, Matt!
"Flight of the Bumblebee" playing in the background. Nice.
You can hear the offset phasing of the frequencies of Matt's voice reflecting off his paper sculpture at 18:25 as he pulls it away from his face.