Calculating the optimal sphere packing density: with oranges
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- Опубликовано: 10 май 2017
- Check out the corresponding video I made with Steve Mould for his channel.
• 3000 ball bearings sho...
Thomas Hales’s proof of the Kepler Conjecture.
annals.math.princeton.edu/wp-c...
The Kepler Conjecture on wikipedia.
en.wikipedia.org/wiki/Kepler_...
Cubic Close Packing on Mathworld.
mathworld.wolfram.com/CubicClo...
CORRECTIONS:
None yet. Let me know if you spot anything!
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Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Maths book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/ 
Развлечения
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Steve posted a video "with Matt Parker" and Matt posted "with oranges"
+
Mouldy oranges
Steve and Matt play around with lattices
Matt and oranges play around with Steve
+JamesBeanMachine Oh my
Matt is a narcissist
1:25
Normal person: "because your hands are too small"
Mathematician: "because your hands are finite"
When life gives you oranges, make spherical lattices with them
Next life quote
Life is like a box of oranges. You spend all day trying to figure out the optimal method for packaging them.
RUclips comment sections actually inspire me so much
when life gives you oranges, spend months attempting to prove 11 dimensional oranges efficiently pack in not lattice structures
no, don't (hmm, i guess heads are spherical enough that they stack in a lattice...?)
I started watching this video, but the intro made it sound like it was a follow-up to the video on Steve's channel. So I paused and went and started watching the video on Steve's channel and he made it sound like it was a follow-up to this video. The infinite loop made my brain crash, thanks.
Which came first? The chicken or the egg?
I was fine with that because it seemed to me that Steve's video came first, but then my brain crashed when I reached the end of Matt's video and found myself back at the beginning of Steve's.
fruitshuit The egg because the first chicken has to have been born somehow.
b1odome the egg because the chicken's ancestors were borne of eggs
Same! Steve's is the first, though.
The orange companion cube will never threaten to stab you, and in fact, cannot speak.
[♥] [♥] [♥] [♥] [♥]
+Scott Sakurai your comment have only 5 Hearts
if it has 6 Faces (obviously its a Cube (of Companionship) itd have 6 Faces) then itd have 6 Hearts
When life gives you Oranges, don't make Orangade. Make life take the Oranges back! Get mad! I don't want your damn Oranges, what the hell am I supposed to do with these? Demand to see life's manager! Make life rue the day it thought it could give Patt Marker Oranges! Do you know who I am? I'm the man who's gonna burn your house down! With the Oranges! I'm gonna get my engineers to invent a combustible Oranges that burns your house down!
@@1224chrisng You assumed a companion cube has 6 faces with hearts. But have you ever rotated the cube to look underneath it? What if that face is actually missing? What if the cube then really threatens to stab you?
@@sus-kupp yes
"If feel like I've been accepted by your culture."
"You haven't."
LOL that was the best nonchalant burn ever...
very simple and elegant work. "Let me just rotate by tau/2 radians", I could feel the frustration in your voice Matt
"Okay, so this is a bit awkward, but we're gonna try something even more awkward now" Story of my life.
Simon T haha true
I love how us normal people go: "Oh, ok - so this is the best way to pack spheres (in our physical world)." And then end it there, but a mathematician goes: "Ah! But what about n-th dimension? Let's see how they stack in 23 dimensions."
Yeah, but I'm sure it has some application in engineering or science with lots of variables.
@@Speed001 nope. we live in three dimension ya know
@@aryaaswale7316 they're only fourth dimensional but quaternions are a thing. living in three dimensions doesn't stop us from conceptualizing things in higher dimensions (even when it really should)
@@aryaaswale7316 n dimensionnal spaces are quite common everywhere in engineering, or everywhere else. In the physical world, the dimensions for our space may be how much do you like or dislike some things (for example a list of activities), and now suddenly you have a space with hundreds of dimensions and are trying to see whether people are close to each other and how to separate them.
i finally found the guy from my math problems.
XD
I died!
The “A man has forty oranges and has to pack them in a crate as efficiently as possible, how does he do it?” guy?
"When life gives you oranges, make a tetrahedron."
-Matt Parker, Things To Make And Do In The Fourth Dimension
It was basically a FCC lattice
"My studio, my circle constant"
veggiet2009 oh my god it's you again. you, with the profile picture that looks like nerdcubed's eye
Like this guy who tried to define Pi by law...
?
"Let me just rotate through half tau radians"
veggiet2009 James
That cutaway at the end xD
Matt's revenge against Steve for being rude and using the "wrong" circle constant
JamesBeanMachine They pick up in Steve's video.
That cutaway is the transition to Steve's video. Then Steve's cutaway is a transition to this video ;)
I LOLed.
Oooh clever transition.i thought he was being savage 😂😂
The chemistry between these guys always makes me just smile as wide as I can without thinking about it :D
loved that they fumbled with the balls in their hands while having a perfect example in the box.
Matt likes pi so much he's shaved it into the top of his head 1:11
I was gonna like your coment but then I realised how unbalaced the number of likes wold be, that was a close one
Oh, man... That was brutal xD
I thought it's the logo of the channel Real Engineering
that was so brutal that he shaved his head
I like how Steve's video says "with Matt Parker," while Matt's video title says "with oranges."
Says it all, doesn't it?
And points at Steve in the thumbnail
I know Matt's thing is maths, and Steve's thing is physics, but I absolutely love the chemistry between them. It's hilarious to watch them rip back and forth.
And I'm really starting to wonder if that Methodist orange stick lolly candle thing is actually real or not...
Wikipedia seems to think they are: en.wikipedia.org/wiki/Christingle
"Edible spheres"
That's what I'll ask for next time I'm in the grocery store.
MFW I am stuck in a loop trying to figure out which video to watch first because both videos reference the other at the start making me think I should watch the other video first but then the other video references this video at the start making me think I should watch this one first!
The first scene of one is the final scene of the other.
This is true for both videos.
!!!
Moleo And it is wonderful!
Earthbjorn Nahkaimurrao möbius videos
I love how you both cut each other off at the end of your videos.
They did it because they're trying to create an illusion of a loop in the videos. You might notice that the beginning of Steve's video is the same as the end of Matt's video and vise versa where the script suggests that they just did the other person's video. So which video did they do first, really? Hint: One has an obvious insert before going back to the two shot.
FYI the Christingle is a British thing, not a Methodist thing. It's used by many Christian denominations but very few people outside the UK do it.
Yep, I attended a couple in a C of E church when I was little. I still remember toasting grapes over the candle.
I was brought up catholic and i'm pretty sure we did it at school, so it's british not just methodist
The first Christingle was in the Moravian Church in Marienborn (Germany). It's history can be found at: www.moravian.org.uk/index.php/the-moravian-church/moravian-christingle
Oh wow the memories... I forgot the Christingle even existed until he mentioned the sweets on sticks and then it all came back to me. Nostalgia hit hard there (for my childhood, not for the religion).
Looked it up. Christingle is a thing. The orange represents the world, the candle represents Jesus, the red ribbon represents Jesus's blood, and candy represents the fruit of the Earth.
People do weird things.
I used to do them
I never understood them. I'm a Christian, but the church I went to never did them. But the church near my school did. So we did them on school trips. They make no sense.
@@timothybexon6171 we did it in my junior school. We had a bunch of ceremonies at the local church but christingle was the best one, cos you got to eat an orange and 4 sweets afterwards... I was laughing so hard at the jokes they made about it XD
@@timothybexon6171 "they make no sense" so pretty on brand for religion then :p
@@woutervanr True.
I was sitting in my Asphalt Pavement DOT class this morning where we are learning about packing theory for aggregation and all I could think about was this video from 5 years ago. Thanks Matt and Steve for helping me pass my certification.
Now we know how Matt will calculate pi next year. I image some sort of juicer will be involved.
Not only do I love this video because of how interesting and informative it is, but also because of how entertaining it is. Here I am coming back to it 4 years later for the n-th time for the relentless sarcasm and great chemistry. We love you guys!
22:20 DENIED
It's incredible how fast your channel has grown. I have loved your channel since the first day I found it a while ago.
"Your hands are finite." may be my new favorite sentence.
I don't care how geeky this sounds, but i genuinely share their enthusiasm.
Love the way you guys made this video as if it were after the one on Steve's channel, then made the one on Steve's channel look as if it was after this one.
I simply love the editing that allowed you to post the two videos in such a way that they cause an infinite loop...
Nicely done with having each video follow the narrative of the other! I never thought of using oranges for this! Diagrams provide fewer sticky fingers (not guaranteed).
Really enjoyed watching this video, guys. Thanks for the collaboration. If more people knew how much math could make you laugh, there might be more engineers in the world. :)
Love that you guys made the videos match up no matter the order you watch the two videos.
Nice job, guys, making the videos link up in a cycle. I'm impressed.
*When you should revise for your physics test that's tommorow but Steve Mould and Matt Parker have both published new videos just 2 minutes after each other*
Close enough
At least one of my exams is on crystal lattices, but I get you.
+Grzegorz Cichosz I also have a Physics test tomorrow. Are you sure we're not all from the same school? Lol
Funny story, my tomorrow's exam includes crystal lattices so this is actually a good review for me
My Physics exam was last week, thank God it was easier than half of the years worth of material we had to learn. Having said that, don't be like me, if it says "End of exam" at the bottom of a page, check the back anyway... I lost 10 marks on it...
I laughed so hard when Matt abruptly cut off Steve's segway into his channel. Love these chaps' banter.
Really great videos. Nice editing, love how you can watch either video first and it works :)
I know little to no math and I'm not that bright BUT you guys are entertaining to watch and the math, references and such go way over my head but you do so nonchalantly and speak of it easy that it doesn't make me feel dumb or hurts my brain, thanks you and have a great day
"Do you have an eighth?" is a real Parker Square of a drug deal. Everyone knows you don't buy partial pills, Matt. That's how you get cheated.
Plus, wouldn't you need the whole needle, not just an eighth of one, to inject a marijuana?
I assume if 7 eights are equally taken off of each separate part of the needle, one might inject an eighth of a marijuana
Not to be the killer of the joke, but an eighth is usually used to describe 3.5 grams of any illicit substance (3.5g is an eighth of an ounce)
fanrco "Any illicit substance"
No one has ever came up to me asking for an "eighth of coke". Usually only marijuana that deals in ounces. Harder drugs are done by grams if purchasing locally and kilos if your importing. I'm European though so I can't speak for imperial measurements. Though I can't recall at any point in my life people asking for an eighth of any substance other than marijuana.
Noremaad You're totally right, I've never heard it used in any other scenario other than marijuana (mostly because I try to avoid anything outside that scope) so I just assumed the phrase spanned to everything else
"I feel like I've accepted by your culture."
No hesitation at all "You haven't."
Very much enjoyed the "working it out" intermission in the video, and rather proud of myself for getting the right answer (even if it is just simple calculation) on my own. Thanks for the great video.
Love it! Thanks for the fun crossover!
I remember working this out in a first-year chemistry lab. Was a good time.
you got to love the cut off at the end. almost an FU to physics vs applied mathematics
awesome vids guys !! Thanks for keeping maths interesting !!
I don't normally do the working out parts of these videos to be honest, but this time I thought I'd give it a go. Turns out I got the right answer. I know it isn't exactly like I've discovered e=mc², but it's always good to know that you have worked something out correctly.
Nice video
*Waits for Steve to try and pour Matt out of a beaker*
These two videos recall all the memories on the metallurgy class back on college.
That "the outro is the intro of the other video" thing in both vids is great. Really great.
14:28
"that is the least cool use of the phrase have you got an eighth"
Damn, wasn't expecting that kind of joke from parker at all lol
"Two guys get together and play with balls"
They try really hard to get their balls to touch.
Mathematicians tried for centuries to kiss as many balls as possible.
This shouldve been the title 🤣😂
I thought this was a follow-up video to Steve's, so I watched his first. I couldn't figure out which video his one was following up, so I continued, and then went back to yours.
Well played you guys, well played.
Nicely done with the video looping
21:28 Says "do it properly", but cuts the video anyway xD
This sums up why I ended up in Physics rather than maths too. I always preferred the Mathematical aspect of Physics, but because A) my organisation is an utter mess and B) I prefer the answer to the beauty I went towards Physics. Here we have Steve Mould with a "messy" sheet of working out on all directions (look OCD to mine) and Steve wanting to finish at the result rather than the beautiful simplified result.
Its something I've noticed throughout my career, Mathematicians want utter perfection and Euler's Formula like beauty, physicists would rather take a few assumptions like sin x = x, and any simplification is to ease remembering. And that is also why Mathematical Analysis never agreed with me, a branch of Mathematics so anal as to demand a proof for "1+1=2" with a Physicist's constant reasoning "because it is" for any semi-obvious mathematical assumption. There's your answer, nobody cares why, lets get to the fun stuff.
On a side note, I've always tended towards watching maths videos. Not sure if its because I simply prefer listening to Maths, if its because it gets difficult to find a video with enough Physics left to learn, or if its because the physics I do have left gets a little too in depth for easy watching. Either way, I could watch you two collab forever. Physicist and a mathematician, but you certainly didn't lack any chemistry. Yeah I know, women aren't funny.
As someone who would rather just do the beautiful maths, what you said is pretty accurate 😂. Although it differs quite a bit by field. Applied mathematics like numerics and statistics can be complete abominations, while purer counterparts like analysis and stochastics are generally very pretty.
And if everyone knows that everyone knows how you would prove something, you can leave it out as trivial. You just don't allow early semesters to do that. 😉
I guess most mathematicians end up doing the pretty stuff for fun and the applied counterpart for fun-ding
What!!! these videos are an endless loop!! :o
Turns out the packing of spheres is the basis of an entire engineering branch: materials engineering! The understanding of how (at the atomic level) the packing of spheres/atoms and interactions thereof govern how different materials work! Most commonly studying metals, ceramics, and polymers as materials disciplines. This exact problem is the majority of a intro materials class, crystal structures and lattices! As a materials engineer these videos were lovely to expose this to more people! Well done.
0:21 I thought the video was stuck for a moment there XD
You love to struggle arranging stuff in a square on this channel, don't you ? =D
I really enjoy watching your videos. I met you at Big Bang Fair this year and you said you would take part in my scicomm quiz. Hope you can still do it
I like the illusion that these videos looping with each other.
For both videos, the final scene is the same as the first scene of the other video.
ALL HAIL THE GLORIOUS PARKER SQUARE
...get out... there is nothing parker about that square!
It was created by Matt Parker. So it's Parker's square
Is it now a "Parker Cube"?
It's about 74% of a full cube, so I guess it IS a Parker cube ...
Parker lattices have an amazing 93% packing density... except some of the component spheres are much smaller and others are made of a very malleable clay. Matt still thinks it's pretty great, though.
brb popping down to the shop for some oranges
It kind of both amazes me that this video leads strait into the next one which leads strait into this one, perfect loop.
Props on the never ending loop between videos
I would really love to hear about the properties of the "jumbled packagings" in higher dimensions, it is rather uinintuitive to imagine there are some that are not regular, so maybe the (prime?) properties of the actual dimension play a role in here?
9.2 thousandth view! YYYYYAAAAAAAAAAAAAAAAAAAAYYYYYYYYYYY!!!!!!
I'm surprised this never happened:
Matt: There it is! Pi over root 18!
Steve: Tau over root 72.
Matt: Jerk.
Genuine hilarity when you cut him off in the middle of plugging his own video. And in the video you filmed for your channel in his studio no less. Brilliant!
Totally digging when you bring up some basic 5 minute derivations such as this and the Euler's Disk. This was was a great one because of common familiarity with 45 45 90 triangles and I was able to tackle it with my GF who drew the diagram. As soon as you mentioned the ratical 18 I knew that we needed some right triangles. I wouldn't mind some Calculus problems either, but the Geometry ones are great because I usually suck at drawing pictures and creating equations based on the diagrams without some starting guidance.
You guys should make an infinite number more collab videos together!
Which came first?
The "Calculating the optimal sphere packing density: with oranges" or the "3000 ball bearings show crystal defects with Matt Parker"?
The circular videodesign is fab!
These guys are answering questions literally no one has asked before
Steve x Matt I ship these 2
Serene Grace oh gosh the shippers have arrived
lol it's fun when i write a comment, then scroll down and see that others feel the very way i do :D
The square base is not the same as the tetrahedron on its side (though the spacing is the same) as a tetrahedron is platonic and so is the same when placed on any face. There are no Square faces, and the square base has one, so the two shapes aren't congruent.
True, a square based pyramid is not congruent with a tetrahedron, but how is that relevant to the video?
The tetrahedral arrangement has 6+3+1 or 10 spheres, the square one has 9+4+1 or 14 spheres. Take four spheres out of the square arrangement without moving any of the others and you get the tetrahedral arrangement.
Brilliant how you managed to somehow make two separate videos that blend seemlessly with no actual beginning or ending. #Mindblown
Cand you do a video on continued fractions? I just stumbled upon these, didn't know they existed. It's a pretty cool subject!
15:45 NOICE
this is the most adorable math vid ive ever seen. boys playin with balls and fumblin around. yall r cute
Love the hard cut at the end :D
Working it out worked. I'm satisfied. I'll watch the rest of the video anyway :)
Sweets on a Christingle? Bah! In my day we had to make do with cloves!
hypertetrahedral = simplexal?
lol I just watched Steve's video, and I love how both of you cut off the other person at the end before they could talk about their channel.
Good paint job on the red pipes. Look really super.
So, can we call this 6:12 a Parker-Packing?
Please watch this video on 0.5 speed and try not to laugh.
This works for every video actually. You can turn anyone stoned as fuck.
jesus they sound drunk and stoned hahaha
two guys high as a kite working out how best to stack oranges LMAO
Yes it does but if you take a look at the content you get not only two stoned guys but two stoned guys playing with balls and stacking Oranges.
This is the second infinite video loop I've watched today. I just finished the vsauce/minutephysics one and now im here.
this actually is very relevant in what i study at university, as in chemistry you need to know and calculate that kind of stuff. and to simplify for us we actually have graphics that are very close to your orange build. but youre actrually beeing very understandable. i wish this video came some semesters earlier.
anyways. doubt someone cares what i wrote, just felt like letting you know.
greetings from germany.
The amount of spheres that can touch a sphere in any dimension is:
n^2 + n
0: 0^2 + 0 = 0
1: 1^2 + 1 = 2
2: 2^2 + 2 = 6
3: 3^2 + 3 = 12
4: 4^2 + 4 = 20
...
No. For n=4, it's 24, and in higher dimensions your terms are lower than the known lower bounds. Look up "kissing number".
god i want to ship them so hard. they're both gorgeous, personable, funny, and smart, and they both totally make it a fun way to pass the time thinking about mathematics. i love it when they show up in videos together! that chemistry and banter that they have, so delightful and dreamy. *faints*
i know the comment is more than a year old but omg i thought the same and saw no else talking about it e_e they are cute together
I'm stuck in a loop of watching matt's video then Steve's video then back to matt again
A rhombic dodecahedron (such as Matt built with Adam Savage) that circumscribes a unit sphere, is a space-filling polyhedron with a volume of sqrt(18). The ratio of the volume of the unit sphere to the volume of the rhombic dodecahedron is pi / sqrt(18), equal to the packing density of the hexagonal close packing lattice.
pi > tau
pi > 2pi? There is something off with your logic :P
therefore, 1>2
tau > pi ;)
how is 1/2 turn greater than 1 turn?
I agree with the principle, not the mathematics.
That was a glorious Parker cube!
That cut off was perfect.
That spontaneous conversation about the Christingle was hilarious!