THE SCUTOID: did scientists discover a new shape?
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- Опубліковано 2 сер 2018
- Read the Nature paper for yourself:
"Scutoids are a geometrical solution to three-dimensional packing of epithelia"
www.nature.com/articles/s4146...
Thanks to Laura and Clara for helping me with the video!
You can download Laura's model for free or order a print from Shapeways:
www.thingiverse.com/thing:302...
www.shapeways.com/product/L4D...
Laura Taalman, James Madison University
www.jmu.edu/mathstat/people/f...
Clara Grima, University of Seville
personal.us.es/grima/
These are the shows I was doing in Sydney:
www.mansw.nsw.edu.au/student-...
But you can check out the Maths Inspirations shows in the UK:
mathsinspiration.com/
And we'll be in New York on 2 October 2018:
momath.org/upcoming-events/ma...
Images of cells and stuccoed are all from "Scutoids are a geometrical solution to three-dimensional packing of epithelia".
Voronoi demonstration is from here:
en.wikipedia.org/wiki/Voronoi...
Thanks to my Patreon supports who do support these videos and make them possible. Here is a random subset:
Malcolm Rowe
Rhys Johnson
Brian Lynch
Jade Bilkey
John Lewis
Support my channel and I can make more videos:
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CORRECTIONS
- Yes, I pronounce it SCOO-toid, SCOW-toid, SCOE-toid etc. Sorry. It's new! I actually think ES-COE-TOID is the most correct.
- Alex Sweeney noticed that when I describe a prism I say it has rectangle faced sides. But that is only true of right prisms, in general a prism has side faces which are parallelograms. When I later talk about prismatoids I realised I had to be more general and said the sides are faces with three or four edges. But I should have done that earlier.
- Let me know if you spot anything!
This video is not sponsored by Little Creatures Pale Ale or BBQ Shapes but I am totally open to suggestions.
Music by Howard Carter
Filming and editing by Matt Parker
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/ - Розваги
So if I undertand this right: The biologists saw and realized what was happening, described it to the mathematicians, who formalized it as a precisely defined shape, and described it to computer scientists, who programmed that definition as something a something a computer could model, which was analyzed by physicists, who analyzed and confirmed the shape would be stable packed at that scale.
In this story, I'm the chemist
We'll just have to stick to our buckyballs and armchair nanotubes.
maybe the chemists will come up with an application.....
That's what the programmers did.
Drunken Hobo Who's to say we can't make a scutoid of our own?
I‘m sure that there will be some weird crystal formation or an organic compound in scotoid shape
Somebody please market those as salt and pepper shakers.
Someone else watch Stephen Colbert?
www.thingiverse.com/thing:3031063
YES. I saw that episode being recorded at the studio!
I NEED THOSE
They would pack in your cupboard nicely
I'm not a native english speaker. I just noticed how "prism" and "prison" sound alike, and I find it funny when he is building cages :D
Even for us native speakers, those two words sound VERY similar. Almost interchangeable, depending on how it sounds in a sentence
trequor not really...
The only difference is in the n/m
a prison is a group of rectangular prisms
There was a Futurama joke based on that wordplay.
theinfosphere.org/Fulcrum_County_Prism
“generic foreign city”
-pans to most recognizable building in Australia
No need to make up fictional cities now just to sound smart.
Aphrid Gomez yeah, Australia is a social construct
Wait don't you mean Austria?
It's sad that it's acceptable these days to show that kind of thing to kids. My parents used to spank me if I even mentioned a kangaroo so I wouldn't be brainwashed into becoming an Australia. This generation has really lost all morals. 😥 :((
I'm a paid actor from "Australia"
"Matt makes a shape out of things he found around the place he's staying while on the holidays" Best series name ever
Maximum Power can't wait for episode 2
Fabrizio Lungo This is episode 2, he just didn't call it that in the first episode. Edit: This is episode 3
I subscribed for videos like this!
or MMASOOTHFATPHSWOH for short
Sir Mossy Love it, hopefully Matt reads this and calls it that in the next episode
12:20 "It's somewhere between Topology and Geometry"
Oh, so Geology! Wait, no. That's already a thing.
Topometry it is!
Actually it's odd he said that because geometry and topology are very tied to one another??
Where'd the n come from in topomentry
Matthew Zuelke I actually kind of like the added n. Just my opinion though.
Matthew Zuelke - It came from 5:24
Sebastian Carrier soo... “the shape of altitude/mountains”
I remember seeing something about this, I thought
"what?! you can't just discover a new shape, but whatever"
now that you made me think about it, I came up with
"discovering a new shape is like discovering a new number." It was always there, and there's literally nothing standing in anyone's way of finding/seeing it. They just need the right circumstance to use it or see it in use.
More than discovering a new shape, they discovered a new shape in "nature" concrete and frequent enough to merit his own name, instead of a generic name
Isn't that what "to discover" means? You can't discover something that has not been there before. That would be inventing.
@@goawaygoawaynow I think the most proper to call it is "Scientists gave a new name to an object which they found in nature and which nobody thought about before". But... that doesn't sound aa catchy, admittedly.
I just discovered a new shape. It's 3,907 tetrahedrons arranged in a spiral.
@@official-obama me too, it's 3,907 tetrahedrons arranged in a spiral, but rotating the opposite direction.
I just want to point out that the way you said, “some generic foreign city” while casually showing one of the most iconic buildings in the world in the background was pure genius lol well done
"It's a bit prism-y on one side and a bit atiprism-y on the other side" - sounds an awful lot like a Parker Prism to me
Great minds think alike.
My only thought during that bit is that he called the other faces rectangles... I don't think they are. Maybe one of them is.
Finally another entry in my favourite series “Matt makes a shape out of things he found around the place he’s staying while on holidays”. It has been a while!
Biologists: We're confused. *Inter-disciplinary science team, assemble!*
Four different kinds of scientists, muttering: Okay, so it can't be a regular prism...
Very underrated comment!
“Sc-UH-toid”
“Sc-OO-toid”
“Sc-YOO-toid”
“Sc-O-toid”
I’m screaming Matt, screaming.
Scout-oid?
skeetoid
I don't get it
@@emadgergis6710 -- I think the idea is that Gabe is annoyed by Matt Parker's inconsistent pronunciation of the word "scutoid".
Gabe McKelvy why say it one way when he can annoy everyone all at once?
5:10 it's a Parker prism!
That lady's voice was so adorable 😂
0:46 hi back to you too random lady with an infectious smile :)
Funnily enough, 'scutoid' DOES actually have a meaning, even though it was based on someone's name. It actually means 'scale-like', as the base word 'scute' was derived from the latin 'scutum' (meaning 'shield') and is currently used to refer to the sub-dermal types of 'scale' found on creatures like alligators, though it is often used for the wider and thicker belly scales of snakes and lizards as well.
And now you know.
It is amazing. Interesting mathematically, biologically and etimologically.
I thought I'd heard it somewhere in a biological context. Thanks for making it clear.
"Matt makes a shape out of things he found around the place he's staying while on the holidays" actually everyone's second favorite series after calculator unboxing and reviewing
Matt playing Prism Architect
That pun is so bad I gave you a thumbs up. Kudos to you, sir.
Well I must say, I did find it particularly difficult to escape from this video.
Kids today, and their new shapes.
Thank you so much for not removing that part about OpenSCAD, I've finally found a free CAD software that seems to fit me perfectly!
"Pentagons to the left of thee, hexagons to the right, here Y am, stuck in the middle with scu" - very cute :)
Proposal: a prism with one anti-prism edge is a "first-order antiprism"; two edges make a "second-order antiprism"; an anti-prism is an "nth-order antiprism," with n being the number of edges on the parallel faces
I suppose then a scotoid could be considered a fractional antiprism
That could actually be very correct.
Recategorising maths to make sense?
Get out of here! Don't you know that wannabe Eulers are witches?
You might as well persuade Americans to use SI :)
Triangulate the quads on a prism for an anti-prism. Keep subdividing for higher order anti-prisms?
That still isn’t enough to get a full description. You also need to define which face you use for the shape name (would Matt’s shape be a pentagonal or hexagonal 1-antiprism?), and for 2-antiprisms or higher you also need some way to denote the relative positions of the antiprism bits.
Not saying this is a bad idea, but in general when something doesn’t have a name, it’s more likely that there’s no need for it than that nobody could think of a good name. :/
How about... you just stressed me out for the day.
Nice, the sciences don’t have to be separate! When they work together amazing discoveries like these can happen. Teamwork is much better than petty rivalries.
the sciences are just applications of math
Rew Rose As long it has Physicist seal of approval
When you said petty rivalries I thought about the classic Probability theorists vs Statisticians and Topology vs Functional Analysis theorists
_Nice, the sciences don’t have to be separate!_
"The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age." - The Call of Cthulhu, Chapter I
It is happening boys!!! Big ol' Cthulhu is soon upon us!!! And beneath us! And to our side! And in directions three dimensional beings can't even begin to imagine, let alone comprehend! He is coming!
Except for the chemists.
"What shape is that shape?"
"It's a Shape-shaped shape."
It’s a shape of shape-shaped shapes that looks like a shaped shaped.
"Traveling through some generic foreign city somewhere in the world"
*Sydney opera house pops into view*
Oh yeah, must be in Tokyo.
@@Milamberinx u sure? seems a lot like Moscow to me
It was obviously a paid actor!
If that were austria, there would be kangaroos kung fu fighting everybody
??? That's the Bengaluru opera house in India
Wall decoration: "PHILADELPHIA"
is -oid mathematical version of -ish?
It's more like the noun form of -ish/-like and it's used outside of just mathematics. For instance, android (man-like) or asteroid (star-like).
its used in all sciences
-oid means it's 3-dimensional (or more exactly more than 2-dimensional). For example a 3D ellipse is an ellipsoid.
Exept for cube which is already 3D, in relation to a cuboid which is a rectangular cube. Is that the case with any other -oids?
Pluto isn't a planet, it's a planet-ish
"In short, there's pentagons to the left of V"
Oh no
"Hexagons to the right"
Matt, please don't
"Here Y Am"
Oh God he's actually doing it
"Stuck in the middle with Scu...toid"
I honestly would have unsubscribed if I didn't love this channel so much.
Jackson DeStefano would've been reason to subscribe for me if I hadn't already.
😂😂😂😂😂😂😂
TootTootMcbumbersnazzle Look up Stealers Wheel.😉
Junky228 I always confuse it with Bob Dylan, myself...
Like an avalanche or a drum solo, you could see it coming a mile off but could do nothing to stop it.
And if you look closely, you can see Matt's lips beginning to curl into a corpsing grin just before the end.
I don't know what's worse: the Stealers Wheel joke or the fact that I saw it coming after the first line...
"Generic foreign city"
*turns to face Eiffel Tower"
No, that's definitely the Eiffel Tower
I could've sworn those were the Pyramids of Giza.
Arthur Morgan I thought that was the golden gate bridge
you guys are all wrong, it's the Grand Canyon
@@antoncid5044 it was obviously the empire state building
Funny, as an Aussie I realised you were at Circular Quay from the sandstone wall before you even turned around to the coat hanger.
PS that Little Creatures is a nice drop.
same
But where was the second outside shot @8:30 onwards? Balmain??
I think so. Those larger ferries don't travel too far down the river. It's gotta be somewhere close to the inner city.
But you export Foster's to the rest of us as your representative national lager, so I can't trust Aussie booze anymore.
Jonathan Charles
We export it because no one here drinks it! I mean have you tried it. Urgh.
It's always inspiring when different branches of the sciences collaborate!
Antifrustrum. There! I invented a new shape!
Frustroid. I'm on a roll!
Scrotum. Dammit! I should have quit while I was ahead...
you must be quite frustrated now
Oddly enough, it doesn’t seem like an antiscutoid is possible. It sort of falls apart if you try to build it in you mind. But antiscrotums do.
@@subzeroelectronics3022 Antiscrotums = kick in the balls
I’ve actually found a scenario where an antifrustum shows up.
If you take 6 points in 3D space and connect them all to each other using exactly 2 different lengths of pipe-cleaner, there are 6 possible arrangements where all the pipe-cleaners are straight:
1. A prism with triangular ends and square sides.
2. An octahedron (aka. triangular antiprism).
3. A short pentagonal pyramid with all edges equal.
4. A tall pentagonal pyramid where the edges to the peak equal the diagonals of the base.
5. A triangular frustum where the ratio of the bottom and top edges equals the ratio of the diagonals to the edges of a pentagon (aka. φ).
6. A triangular antifrustum with that same ratio. (Note that the corners of the top extend slightly beyond the outline of the base.)
I don’t know if it’s useful for anything, but I thought it was neat.
@@NevinBR That's pretty neat. I know the short pentagonal pyramid. It's one of the Johnson solids.
Been months now and it's still my favorite episode of Matt Makes a Shape Out of Things He Found Around the Place He's Staying While on Holidays.
This reminds me of vsauce’s how to make every strictly convex deltahedron
Good to see you, Dolan Dark.
OneWithGoose Heck yes, that's one of my favourite videos ever.
OneWithGoose I wish vsauce hadn't stopped making videos. Oh well, it was a great channel while it lasted
A lot of the more traditional Michael-related Vsauce has moved to DONG for some reason, so he hasn't stopped making videos, he's just made them harder to find for some reason.
Drunken Hobo the DONG videos aren't the same kinda thing. Usually it's just he's bought some gadget and he wants to play with it. It's not the same mind blowing journey kind of thing as vsauce
Business in the front, party in the back. A mathematical mullet.
bonecanoe86 Slightly disappointed they aren't called mulletoids now.
No
My favourite type of prismatoid is the cupola. The two parallel faces have n and 2n sides respectively and they are connected by squares and triangles (or, I suppose, rectangles and triangles in case of non-Johnson versions).
12:30 ...they found "these SHAPES inside LITTLE CREATURES"
Matt that was genius. And that pale ale is not too bad!
It's one of the only beers I actually like to drink.
oh nooo!
"They were able to find these Shapes inside Little Creatures"
well played Matt, well played
BTW, Escudo means " shield" in spanish (Scutum in Latin), and for me, a scutoid actually seems a prismoid with a "shield". Doesn't it?
Marc Gràcia
The “scutum” on a beetle is its hard upper carapace, a.k.a. its “shield”.
Scudo is shield in italian, Scut in romanian
All fun and games, until someone slips an "r" into it.
Lol
Scutum or mesoscutum is the hard "back" part of a certain body segment in many flying insects. It's the triangle in the picture of the beetle, if I'm not mistaken.
Finally another Matt Makes a Shape out of Things he Found Around the Place He's Staying While on the Holidays video!
"these SHAPES inside LITTLE CREATURES"
Thought you'd sneak that one past us eh Matt
When's the last time anyone actually cleaned a pipe?
scarcesense My uncle, several years ago.😅
Can you actually clean pipes with those fuzzy, bendy, sticks ?!?! I thought that was their name & they were for craft making... wow! Mind blown !!!
P.s. great video Matt 🤓
Smoking pipes, yes.
Sewer pipes?
I cleaned my coffee makers lid-pipe with those today! I haven't been able to find a small enough brush to fit, so I use those.
@12:40 - you got me good.. "shapes" and "little creatures".. dammit.. you got me good.
The "Stuck in the Middle With You" joke was solid. Cheers.
Matt, thank you so much for that clear explanation. I always love learning something new! The pipe-cleaners really helped with the visualization, we can spend so much time on computers that we forget model doesn't have to be virtual. :)
Really a fan of the MMASOOTHFATPHSWOH segment
Sir Mossy I'm waiting for the tshirts
I too am a fan of Ma-Sooth-fatf-Woah.
Joseph groves that would be the best merch
"I'm currently traveling through generic foreign city somewhere in the world." *immediately shows one of the most recognizable building/bridge configurations in existance.*
This made me laugh more than it probably should have.
Yet again you’re ability to explain abstract concepts with clear, highly entertaining vignettes inspires me to subject my unsuspecting friends to weird and wonderful maths facts. Thank you for all your work 👍
This is legit my fave segment of yours.
Absolutely! Thank goodness "mathematicians evolved" 9:15!😂😂
congratulations your Theoretical Mathematician evolved into a Practical Mathematician.
*Applied mathematician.
Yeah everything was pretty primitive before that. :)
Mathter Race
bruh read the subtitles
I'm pretty sure I have a picture of one of these that I made when I was younger. I was just exploring what I could do with prisms. I think it's pretty cool that this is a real thing.
Thanks for coming to present to us here in Australia at Sydney Grammar School, it helped many of us gain a better perspective on how to extrapolate from 3D shapes into the much more abstract realm of 4D shapes.
Awesome video, thanks for taking time out of your holiday to make this!
GENERIC SYDNEY
Whoosh
i am so so happy that i found your youtube channel T_T while browsing for exactly this video. i am a fan of you since you appeared on a show at a science channel. OMG so good to see you making videos!
sending love from india!
Phenomenal job explaining the discovery and giving pertinent background information. Nice little bit of trivia thrown in as well; always good to have connections!
This is pretty awesome stuff. What a great merging of technical disciplines to discover new facets of reality!
Is pomegranate packing also example of scutoid?
I was thinking the exact same thing while watching the video... I'm pretty sure I saw something like that while eating pomegranate. One more reason to enjoy them next Autumn!
That's a good point actually.
So now I have to search how to pack pomegranates
Nice. Another productive day.
It approximates Voronoi cell packing, at a guess.
"thrust 'em" is my new favorite shape
👌🏻O O O F👌🏻
Excellent job on making the explanation accessible, informative and entertaining.
11:19
This whole chain of events -- Biologists discover a shape, Mathematicians help define it, Physicists confirm its viability, and finally, the Biologists turn around and use that information to prove the theory -- makes me kind of giddy for some reason. It's like a big, beautiful crossover where everyone uses their particular strengths in a relay race of scientific discovery, and it's beautiful!
"The scutoid derives its name from a bastardization of the song Stuck in the Middle with You, where the famous lyrics are altered to 'pentagons to the left of me, hexagons to the right, here I am stuck in the middle with scu....toid.'" - Wikipedia
...so, was cutting your hair that short the price you had to pay for entering TheMathologer's domain?
He shaved it off to discover another shape!
That's the price he paid for going bald.
Matt Parker doesn't go bald, he Parker Squares growing hair.
TheLimalicious good one
Bald head = Parker Hair (obvious and done before - Parker Original?)
Well done. This was fascinating, and the story arc is brilliant!
Excellent introduction to the scutoid! Thank your for producing and posting this helpful video.
At first he tried it with a hexagon at the bottom and a square at the top. Turns out, that was a Parker Square of a scutioid.
I want more episodes of MMASOOTHFATPHSWOH !
S L A P P
blrrro
Marvelous! Thank you! I had seen the articles, but thanks to this video, I understand the shape much, much better. The wireframe image in most of the articles going around that I saw made it look, to my eye at least, more like a prism with 3 'ends', as if two top faces had both joined to a single bottom face and were somehow fused. That seemed unlikely, especially if it was something that would pack reasonably.
Videos like this make me so excited about geometry!
What about an anti-frustum?
I like openscad.
TheUnnamedGent I thought about that as well... doesn't look like there would be a reason for it not existing...but I guess it was not relevant to explain this series...
Well anti-frustum would be just frustum rotated 180°, so it technically exists, but it's not something new.
No, you would turn the top face half way to the next symmetry point and then have two vertical(ish) edges going from/to each corner, making triangular sides. It's more like an anti-prism with the top squished in.
That makes sense, but I'm guessing there still is a good reason not to make it a shape.
In fact a prism becomes an antiprism as soon as the top and bottom shape are even a tiny fraction out of alignment. The same would apply to a frustum i would think
You should make a video on the geometry of the Sydney Opera House. Many people know the story but most do not.
I feel like I watched a video on that, but I can't remember who it was by :/
He's done that already in /watch?v=zXoJlRFbktw
Thanks! I thought it was Matt, but I wasn't sure if it was Veritasium and I didn't find it with a quick search!
Today by chance I found your videos on the dodecahedron and the scutoid. I love them because I made many shapes based on unfolding with my students at a Dutch high school during art classes. Once I turned a dodecahedron inside out so that a cube appeared.
mind. blown. Love the interdisciplinary connection and a real-world scenario that generates new pure math. Wow!
I love this topic, the inclusivity of biology in this hits close to home for me.
I've always wondered how cells manage their shapes with minimal information and this seems to hint at some of those answers.
SecularMentat well, I guess it's the same like bees making hexagonal shapes, they build them round and heat them up, until they melt them together to form hexagons. Or how soap bubbles will always form Y shaped structures, when 3 or more come together, it's just the shape with the least surface area compared to it's volume, so they will naturally fall into it.
What would be the equation to figure out the SA and/or volume of the shape?
That was beautifully explained you're an amazing educator Matt.
love this video series! had lots of fun crafting my own hexastick and will proceed to create some scutoids and try to stack them :D
Stuck in the middle with scu.
... toid.
Take five
If Macklemore was a physicist i'm sure he'd be in love with the shape of scu... toid
4:56 I would like to humbly suggest a fitting name . . . .
The Parker Prism!!
I appreciate the appropriate choice of the Shapes box as building material to make shapes
Excellent video! It’s wonderful to have you in Australia again 😋
But how do you find the volume?
Break it down to simpler shapes and add their volumes together or
Do some double integral wizardry or
Build it and fill it with liquid thereafter take the liquid and measure it or
Build it and put it under liquid to measure the volumetric displacement
Displacement method... lol
Oh god the double integral method giving me some bad memories from calc 3. Lol
Split it into simpler shapes , put all their formulas into one and clean that mess up.
You can use Cavalieri's principle aka triple integrals to find out
That moment you wish your were still a high school maths student.
It's incredibly cool that you got someone actually on the team to explain this on the channel!!
Clara's accent was also so cute lol
You find the craziest people, I love them so much
You could say it is a prism in the streets and a prismatoid in the sheets.
Um, Matt? Your links at the end are missing!
Very informative and interesting as always. Thanks for your hard work!
Literally threw my arms in the air during the title card because this really is my favorite segment
Umm. At 0:33 that's the eifel trade centre so you in Berlin fam
Matti Kauppinen suuuure
AndyAndromedaArt Also, at the very beginning he stands in front of the Great Wall of Giza which is located in Berlin as well, right between where east and west russia were which were divided after ww2
Matti Kauppinen good troll 10/10 would fall for again
New form 2b: anti-frustum 👍😁
Awesome vid! So much cool connected information, from math to biology. Very cool.
I had your voice in my head for a moment, but couldn't figure out who it was. Thankfully, the subscription list had me covered
Bit of anti prism, bit of prism, but only a prismatoid? I declare it a neutra-prism!
Your subtitles are slightly off at the end: "escudo" should be "scutum".
Thanks for the update on this shape :D
I actually do love the Matt makes shapes of found things segments.
At the start of the video I was wondering why mathematicians were needed. Why didn't the biologists cut stuff up and look at the cells. That's gotta be the fastest way to see what shape they are. But once you had said by knowing the shape the cells should be, biologists could tell if cells were growing that way for reasons. From that point onwards I started to care about an odd shape. Before that I thought it was just mathematicians making work for themselves.
Maxx B. Cos they're squishy. If you don't realise there's something you need to look out for, the slide preparation could destroy what you're looking for. When the mathematicians said there's something to look out for, then the biologists could use special techniques to see the scutoid
That's kinda what I said.
Not only that but electron microscopes could have been used to verify the shape using laser mapping.
Sometimes the mathematical models that mathematicians discover/invent seemingly when "just making work for themselves" end up eventually actually being used to describe some physical, biological or chemical process in the future in real life. It's not always just useless stuff for "math fun", even when you don't see an immediate purpose to it ;)
There is a new method that doesn't destroy cells but it doesn't matter if the cells get destroyed because there are literally tons of them out there. Also once one scan is done that is it you don't need the original cell after that.
To me, it just looks like a regular old prism with one corner lopped off; well, that's what I first thought...
i think the difference is that it is pack-able. a prism with a corner lopped off wouldn't be.
I didn't expect to see Clara Grima here, so a big like to you and Clara and de Escu-toids
My.
God.
BRILLIANT, Matt. Well done, with that song reference. Absolutely brilliant 😂😂
"pentagons to the left of V,
6:26
hexagons to the right. Here, Y am
6:31
stuck in the middle
6:33
with scu- "