It's a very useful shape when you want to 3D print something but you don't have any filament :P
@Nusma8 жыл бұрын
+Gergely H It depends. If you want to 3D print a Menger Sponge in reality then you have to fill the "empty" spaces with something since a total vacuum is rarely practical. So lets say you use plastic A for the sponge and plastic B for the space in between. You would end up with a solid block of plastic B wich, with some abstract thinking, could be rightfully called a Menger Sponge. (Or an inverted one if you are picky)
@gery498 жыл бұрын
Nusm4 :'D
@ciarfah8 жыл бұрын
+Nusm4 you, I like you.
@JNCressey8 жыл бұрын
+Nusm4, Nah, in reality, you'd just have to accept that you're forced to have a limited resolution and have to print one of finite level.
@iqbaltrojan8 жыл бұрын
+Gergely H 181 likes on your comment no reply's intill this one XD
@Box-of-hats8 жыл бұрын
To this day, I'm still finding myself laughing at all of the little jokes you throw into your videos. Thank you for bringing so much humor to the world of mathematics!
@standupmaths8 жыл бұрын
My pleasure. Thank you for watching the videos.
@jonahvanke50028 жыл бұрын
+standupmaths You probably won't see or answer this, but is there another fractal to get Tau?
@secularmonk51768 жыл бұрын
+Jonah Vanke Not sure if this will be satisfying for you, but ... Draw a diagonal from opposite corners of the current square. Use this length as the sides of a new, larger square, and perform the Wallis sequence on that new square. All areas will be twice as large, compared with the original square.
@peter77188 жыл бұрын
+standupmaths You need to make some videos about τ. =P
@trobin8 жыл бұрын
+Laurelindo he supports pi not tau
@54m0h75 жыл бұрын
The second form square having the area of a circle, and 3D a sphere, actually makes perfect sense if you visualise it right. Picture a square. Now cut a square out of each corner. Now cut another square out of the new corners. More and more cuts will define a more and more accurate circle. When you get to infinity you get a proper circle. The same squares you just cut and the same squares you cut out in the other example, just a different location.
@esyrim6 жыл бұрын
The Menger Sponge is WITHOUT A DOUBT the scariest fractal in 3D and the friendliest fractal in 2D.
@imacds8 жыл бұрын
Time to build a level 5! Let's get other planets into this project...
@lavaande7 жыл бұрын
and after a while it would be great to announce that all the multiverses are now united :D
@firefish1115 жыл бұрын
@Whited Out Black holes
@vasudevraghav21094 жыл бұрын
@tshrpl level 12: different timelines Level 13: different timelines clusters with different physics. Oh wait isn't q3 dimensions related to string theory....
@ChrisLuigiTails4 жыл бұрын
Level 5! = Level 120
@R1ckr0114 жыл бұрын
@Whited Out they just make them out of unit square crystal materials and you can probably get do level 14 or something
@TheNdoki8 жыл бұрын
I feel cheated. I really wanted to see a level 4 actually assembled.
@YouTubist6668 жыл бұрын
Ditto. I was hoping Matt would say something like "and we asked everyone to ship their assemblies to us, and we put it together and here it is ..."
@azuritet37 жыл бұрын
if they keep up the tradition for 20 years in a row then we could have a level 5
@maxnullifidian6 жыл бұрын
I'm trying to visualize in my head what it would look like...
@skydivingisfun6 жыл бұрын
Lol let's see a level grahams number
@brcoutme6 жыл бұрын
Walt F. it shouldn't be too hard to visualize it would look exactly the same but bigger, well very slightly different but by a level 4 the difference from a level 3 would be minor enough to not be very visually noticeable. From a level 4 to 5 it would more so just look bigger. Still I would love to see one level 4 even never mind level 5.
@GeekyAsItGets8 жыл бұрын
I've build a level 4 Menger sponge by hand several years ago in Minecraft. A few years ago, I used the ComputerCraft mod to program a robot to build all possible levels that can fit in Minecraft, level 0 to level 5.
@MasterC20128 жыл бұрын
This is why I love fractals so much. They always have a weird quirk hidden somewhere that blows your mind away. My favourite fractal is the dragon curve. It's really fun to draw and see how the shape of the curve evolves each step.
@BlightVonDrake7 жыл бұрын
Someone had to say this. "Dojyaaa~~n!"
@Decimator694203 жыл бұрын
D4C’s favourite puzzle cube
@Periwinkleaccount8 ай бұрын
What’s this a reference to?
@tacobor6 жыл бұрын
It was this video that inspired me to build a magnitude 5 Menger sponge in Minecraft. It took the better part of 4 months. I calculated a level 6 would take just over 2 years.
@denascite20298 жыл бұрын
the fact that I like most about the menger sponge: if you have one right in front of you(so that the line of your sight makes a 90º angle with the surface (I hope you can understand what I mean)), you can look through it (you don't see it at all) but if you want to go through it you will hit a hard surface. and if you turn it a little bit so that you don't look directly at it you can't see through it anymore.
@ValanceJ8 жыл бұрын
Level 3 Menger Sponge... Am I the only one imagining a cube going through an RPG dungeon, beating up enemies, and progressively getting more complicated while it levels up?
@anthonycourte13846 жыл бұрын
A gelatinous cube is a fictional monster from the Dungeons & Dragons fantasy role-playing game. It is described as a ten-foot cube of transparent gelatinous ooze, which is able to absorb and digest organic matter. Thanks wikipedia. They're really nasty things btw.
@rewrose28385 жыл бұрын
No, eventually the cube will get an option to change its class and become a Sphere Knight... where it's volume would remain unchanged but it unlocks a new skill tree involving spherical geometry! (for the sake of completeness, it'll also unlock unique skills- Squaring The Circle & Squeezing Pie)
@grassy5564 жыл бұрын
Good idea for a video game
@KryssAA8 жыл бұрын
"Send money for researches, please, we need more, for project GigaMenger !"
@SaHaRaSquad8 жыл бұрын
+Christophe Abi Akle But why stop there? TeraMenger is just a bit larger!
@lawrencecalablaster5688 жыл бұрын
+SaHaRaSquad I prefer the great new dawn of human-fractal understanding, YoctoMenger.
@DomenBremecXCVI8 жыл бұрын
+Christophe Abi Akle Lets just make a Menger Sponge from a cube big enough to fit the wholr Earth in, it shouldn't be that hard.
@Crlarl8 жыл бұрын
9:53 Shouldn't it be "80/81" not "63/64"?
@Henrix19988 жыл бұрын
Probably
@DaveScottAggie8 жыл бұрын
+dimmddr1 Yes I searched on using the Wallis products, and all of the denominators are squares of odd numbers: 3², 5², 7², 9², 11², 13², ... Here is the site I found, which I believe is the same one that Matt scrolls through in the video community.wolfram.com/groups/-/m/t/822984
@juggernaut938 жыл бұрын
+dimmddr1 Yeah, I thought the same thing and checking on Wikipedia it seems so.
@jesusthroughmary8 жыл бұрын
+dimmddr1 Yes, of course. Besides the fact that you can look up the Wallis products to confirm, it's a matter of simple logic - a square divided into an even number of squares doesn't have a center square.
@Paul_Kielty8 жыл бұрын
+jesusthroughmary that was kinda condescending, they noticed the mistake, and pointed it out politely in case it was intended. For all you know they used that logic when the decided to make the comment.
@jsmunroe8 жыл бұрын
So does that mean we have successfully squared the circle? And well cubed the sphere?
@needarandomname43308 жыл бұрын
+Jordan Munroe lmao!
@PhilBagels8 жыл бұрын
+Jordan Munroe Yes! In an infinite number of steps.
@DustinRodriguez1_08 жыл бұрын
+Jordan Munroe Heh, that was my first immediate reaction as well, though I believe part of the rules of that kind of construction is that you have to be able to do it with only finitely many steps. I could be wrong about that, though.
@Shadow819898 жыл бұрын
+Jordan Munroe I think we didnt square the circle, we rather circled the square :D
@jasonbagley37128 жыл бұрын
+Jordan Munroe I think the fact that we've done an infinite number of steps means that we haven't truly squared the circle. As with anything involving the finding of Pi, it cannot be done in a finite number of steps when involving rationals. This is why Pi is called Transcendental.
@Punk4kids8 жыл бұрын
Since you didn't actually put toghether the actual lvl 4 Menger Sponge, can we say that you guys parker squared it ?
@HylianGirl568 жыл бұрын
They Parker *Cubed* it.
@ethangates58608 жыл бұрын
+T Alex LOL
@Fox_RZK8 жыл бұрын
It was a bit of a Parker sponge
@nathanliu20317 жыл бұрын
T Alex If Matt sees this, he will probably go insane
@Kebabrulle48697 жыл бұрын
PARKER SPONGE CONFIRMED
@irvanluhung33268 жыл бұрын
when Matt posts a Video, I press like even before I watch it
@standupmaths8 жыл бұрын
I hope you adjust that like if conflicting data later comes to light.
@XiphosCreates8 жыл бұрын
10:10 If you look at the square it makes sense it has the same surface area as a circle. If you moved all the holes to the corners from big to small, and do that infinitly many times, you'd end up with a circle.
@Michaelonyoutub8 жыл бұрын
+Lucas Mulder exactly what i was thinking
@xnick_uy8 жыл бұрын
+Lucas Mulder Does not look so clear to me: you could attempt the same with a part of the first "carpet" and you won't get a circle.
@alejandronq6458 жыл бұрын
I was just thinking the same! I got to try it on my computer
@alejandronq6458 жыл бұрын
+x nick since the area of the first "carpet" is 0 you'll end up with nothing
@XiphosCreates8 жыл бұрын
x nick Matt said the area of the first carpet is 0, it's a different square.
@BlobVanDam8 жыл бұрын
7:00 Make up your mind on the pronunciation, Matt! :P
@standupmaths8 жыл бұрын
+BlobVanDam I try to please everyone! Or annoy everyone. Depends how you look at it.
@BlobVanDam8 жыл бұрын
+standupmaths It's always the former for this viewer!
@foobar74718 жыл бұрын
+BlobVanDam It's definitely the former
@WyattJKR8 жыл бұрын
+standupmaths you should of showed what a menger sponge looks like when you cut it in half P.s. It looks awesome.
@Smartlylinked8 жыл бұрын
+standupmaths For completeness (second comment), here's a Level 4 Menger Sponge and a Level 5 Sierpinski Tetrahedron in Sketchup: drive.google.com/file/d/0B6HS5LXNwmKmZXc5b1ZPLWJNU2s/view?usp=sharing
@tggt008 жыл бұрын
Every week I discover another project you've been working on, a year ago I thought you were just a standup math lover who was featured on numberphile, now I can't even describe you besides being a math madman.
@BloodyHand298 жыл бұрын
I had goosebumps when you said 4/3 Pi.
@spicytaco24008 жыл бұрын
I like how you unintentionally poke fun at the location in more than one way.
@TheEvolNemesis8 жыл бұрын
Pi squeezed out of a Menger sponge? Doesn't sound very appetizing...
@jpdemer5Ай бұрын
The 2-D version would tend toward zero calories, so you could eat the whole thing without feeling guilty.
@jeffirwin78628 жыл бұрын
You just created a set that is uncountably infinite yet dense nowhere, you damn magician.
@0xBADFECE58 жыл бұрын
Squeezing Pi out of the square also makes geometric sense because if each of the holes you punch gets moved to the closest corner, the shape actually approaches a circle quite fast. Same happens with the cube.
@kenhaley48 жыл бұрын
Well, not exactly. You will still end up with holes inside after level 2. It's not clear how to methodically shift the remaining bits to fill those gaps. But if you could...
@0xBADFECE58 жыл бұрын
you might be right; it was 1am when i wrote that lol
@watcherfox96988 жыл бұрын
One of the things I love about maths is how things are connected in such surprising ways.
@asp-uwu8 жыл бұрын
var val=4;for(var i = 3;i
@standupmaths8 жыл бұрын
That's my kinda π calculation!
@lawrencecalablaster5688 жыл бұрын
+standupmaths :D Matt, you've coupled together two of my favourite mathematical phenomena! I thank you profusely.
@Guil1188 жыл бұрын
+standupmaths I'm trying here to find a way to calculate the result of the product of an infinite series ( just like the sum ), but I can't seem to find any info on how to do this kind of calculations. Of course if you multiply it by yourself one by one, you will realise it goes to pi, but I need to test with a valid mathematical method.
@asp-uwu8 жыл бұрын
+ILYES brb *steps away to write a program to draw a graphic sponge*
@ELYESSS8 жыл бұрын
+Eric Pratt I'll be waiting
@cananamanda6 жыл бұрын
Great Flying Pi in the Sky, I'm in one of those photos (5:51)! I was a student from one of the high schools that the Perimeter Institute in Kitchener/Waterloo, Canada, outsourced to do the tedious segment construction. My partner and I were two of the hand-full of students representing our school at the final assembly, and we made one of the level 2 cubes. How have I not found this video sooner!? By the way, I still have a single cube made from the spare cards! I doubt Matt will see this almost two years later, but I had a blast! Thanks Matt & friends!
@huash91796 жыл бұрын
5:51 : Matt, youre insulting canada :'(
@johnny1410938 жыл бұрын
We did this at my university (Leeds)! We have desks made out of them all over the maths department now!
@standupmaths8 жыл бұрын
+John Pearmain Yes, I have put my coffee on one of the Leeds fractal coffee tables.
@you_just7 жыл бұрын
You can squeeze pie out of an infinite sponge Finally, math I can get behind
@TPRJones8 жыл бұрын
"Distributed" seems like cheating. I mean we could observe that almost 30 million business cards are printed every day, which could be considered roughly 2.5 "fully distributed" level 6 menger sponges. That's more than 2 "fully distributed" level 8 menger sponges every year.
@Paul_Kielty8 жыл бұрын
Yeah but only the 4th iteration is distributed, which to me is a whole lot better than the 1st.
@TPRJones8 жыл бұрын
+Paul Kielty That's fair.
@danjones44928 жыл бұрын
This channel is even better than Numberphile (which is also really good). Best channel on KZbin! Great stuff Matt!
@z-beeblebrox8 жыл бұрын
Someone needs to create a MegaMenger manga
@ourgloriousgodoursaviourbe27573 жыл бұрын
Yeah, about that...
@ourgloriousgodoursaviourbe27573 жыл бұрын
Also hello person from 5 yrs ago
@timetodowhatever8 жыл бұрын
i am blown away. in highschool my friend had shown my how to make an aragami puzzle piece witch is by far on of my favorite things to make. it started of with using 6 of them to make a simple box. after making a few of them i realized that i could make a 6 sided trangle and a bunch of other complex shapes, for a wile i was making a 24 sided cube, then i got board. i make over 1000 of the pieces and made this manger spounge without even knowing this is so cool
@superliro1008 жыл бұрын
10:42 why isnt it 80/81? Shouldn we remove the square of odd numbers?
@tomprogramming8 жыл бұрын
+superliro100 I was wondering that myself. The graphic a) doesn't show the center third (ninth?) being taken out. Then the outer squares have their third taken out, then a fifth, then a seventh, then an eighth? Such weirdness.
@kristianhaverasmussen85583 жыл бұрын
Matt is the kind of person who is haunted by an idea of doing something until he’s done it. And he end up making all sorts of wierd math things
8 жыл бұрын
63/64? Or 80/81? How can you remove the center square of an 8x8 square?
@jesusthroughmary8 жыл бұрын
+Víktor Bautista i Roca Beat me to it.
@andrewolesen87738 жыл бұрын
+Víktor Bautista i Roca That threw me off as well, the denominator of each fraction should be the square of an odd number.
@PJoriginal8 жыл бұрын
was thinking the same
@carsonwood15138 жыл бұрын
I think he screwed up on it.
@nicholaswallingford36138 жыл бұрын
+Víktor Bautista i Roca you are correct www.wolframalpha.com/input/?i=4*product(((2k%2B1)%5E2-1)%2F(2k%2B1)%5E2),1..inf)
@lawrencecalablaster5688 жыл бұрын
:D Matt, this is amazing! You've married together my favourite fractal & one of my favourite numbers in an awesome way. I salute you.
@doggonemess18 жыл бұрын
When I drop my pi, I always use a Menger Sponge to clean it up.
@branthebrave8 жыл бұрын
I like Mandelbrot, Julia set, and the dragon curve.
@GuiltyGearRockYou8 жыл бұрын
LET's GO FOR A LEVEL 4 MENGER! =)))
@eekee60343 жыл бұрын
Speaking as a lifelong sci-fi nut, "scalesick" is the best new word I've learned this century. :D
@philosofickle8 жыл бұрын
Try to bring all these lvl 3 sponges together and build that level four member sponge. Please try
@glmathgrant8 жыл бұрын
A while back, inspired by your love of the Menger sponge, I actually assembled my own level 2 Menger sponge out of playing card-sized cards rather than business cards (including many actual playing cards, some Magic: the Gathering cards, and some Pokémon cards). Because of all that hard work I did, I can't help but also love the Menger sponge. :)
@DiCasaFilm8 жыл бұрын
Is there any feasible way that this level 4 can actually made?? We have to unite the clans!
@vlogdemon8 жыл бұрын
Cargo ships?
@YouTubist6668 жыл бұрын
I think the resulting structure would just collapse under its own weight.
@rossthebesiegebuilder35638 жыл бұрын
+YouTubist666 Only one way to find out...
@chrismofer6 жыл бұрын
no, they're quite strong with all those stacked edgewise cards in box form not to mention adhesive. If they were only assembled up to level 3 then they could be shipped in less volume to the combination site, where they would be assembled into level 4 form. If a smaller standard for level 0 cubes was determined (like half business cards) then universities could build small level 4s, making a merged level 5 even more impressive.
@nikkirennardo51006 жыл бұрын
I’d suggest private flights to make sure it doesn’t get crushed in shipping
@code_explorations8 жыл бұрын
At 11:38 you mention the equality of area with a unit circle. I think there could be a nice animation there. The biggest black squares could move to the corners. Then the next- biggest, then the next-biggest, etc. It should end up looking like a square with enough bits removed from the corners to make it look like a circle. This could be an actual geometric demonstration of Wallis's product.
@hweigel5288 жыл бұрын
Shouldn't it be 80/81 at 9:53? Looks like you're supposed to take the product of (n^2 - 1)/n^2 for all ODD n.
@standupmaths8 жыл бұрын
Absolutely correct! I've added you to the corrections.
@Coldo38958 жыл бұрын
+standupmaths Oh I was so happy to have found a mistake !! But I am not the first.... ;)
@Ganpan14O4 жыл бұрын
Neat thing: Minecraft actually added a menger sponge in the April fool's update.
@kordellcurl75598 жыл бұрын
What about a hyper cube factual of the same geometric series what is the "volume" of it. I have in quotations because I don't know what a hyper cube would be volume in the 4 dimension.
@teaser60893 жыл бұрын
I feel that Matt tries to escape the Pi, but the Pi always catches up with Matt.
@SebastianLopez-nh1rr8 жыл бұрын
Doesn't this counts as squaring the circle?
@joshhyyym8 жыл бұрын
No. Squaring the circles is a Greek construction, ie it must be completed with a pair of loose compasses and a straight edge, in a finite number of steps. This takes an infinite number of steps.
@roberteospeedwagon37088 жыл бұрын
+Joshua Mcateer Yeah, Numberphile did a video on it, they did say getting a square to be the area of a circle is possible, but the nature of pi means the squares length will be off because we can't know 100% of pi, and they said doing it the old fashion way like the Greeks with rulers and compasses only, would as this guy says, take an infinite number of steps.
@DanDart8 жыл бұрын
Then this must be circling the square!! XD
@engineer_cat8 жыл бұрын
+Sebastián López squaring the circle would be constructing a square with the same area. The Wallis sieve isn't a square, although each step is (I think) constructible.
@MisterHunterWolf5 жыл бұрын
Cubing the sphere
@jingalls91424 жыл бұрын
Its quite strange that Pi seems to show up at seemingly random point in all of mathematics. Its persistence is beyond interesting.
@revenevan113 жыл бұрын
Transcendental numbers always doing that seriously freaks me out lol.
@trudyneo8 жыл бұрын
it would make more sense if you took a third of the cube out from the center rather than from each side. Although you wouldn't be able to see it, it would still be the correct higher dimension up. if you were in the forth dimension, you would be able to see it.
@chraffx82178 жыл бұрын
I liked the way you presented the sierpinski carpets. Nice video!
@standupmaths8 жыл бұрын
Thanks! I was very pleased with that.
@ViktorLox8 жыл бұрын
I want them to actually assemble a level 4, then burn it!
@ebrahimalfardan88238 жыл бұрын
That's amazing. You know Matt what would be more amazing that this, that is to repeatedly take the corner cube of the fractal and fill the holes in the middle and transform the square/cube into a circle/sphere. The animation would be neat.
@UCreations8 жыл бұрын
Correction on the correction: "8/9 × 24/25 × 48/49 × 80/81 × 120/132" should have 120/121 as 5th fraction, if I'm correct ;)
@ifyoubelieveanythingmatter89247 жыл бұрын
A friend directed me here ... beautiful ... this helps explain so much about the MacDonald Codex ... a work in progress for all who like an adventure.
@nikosaarinen32585 жыл бұрын
0:15 You could call that a Parker square
@gabor62598 жыл бұрын
The beauty of maths never ceases to impress me.
@infrabread8 жыл бұрын
What would a 4D Menger Sponge look like?
@pokestep8 жыл бұрын
+infrabread You'd be taking out a tesseract out of a tesseract, I assume. It's a really interesting thought though and I'm intrigued now.
@Wombat20208 жыл бұрын
when looking at the menger sponge in 2 dimensions it makes sense that it becomes a circle as you could move the larger pieces to the corners and slowly tile toward the circle with the smaller ones progressively
@GroovingPict8 жыл бұрын
Doesnt this really highlight an inherent problem with the way we work with limits and infinity? It very obviously has a surface area, otherwise it would all be just one big black box: we can still see some white. And yet the maths tells us it has no surface area. So which is more likely to be broken and in need of fixing here: reality, or the maths used to describe reality?
@Victor-sw4ne7 жыл бұрын
the cantor's conjunt in 2D, and an actual proof that it has zero meazure... loved it!
@gojoubabee8 жыл бұрын
Hey Matt, today is 4/8/16 (written the American way) aka 2^2/2^3/2^4. happy powers of 2 day!
@CASTCorp8 жыл бұрын
Cool! It's my birthday tomorrow
@gojoubabee8 жыл бұрын
+CAST Corp Happy birthday!
@gojoubabee8 жыл бұрын
+CAST Corp Wow, your birthday will be on 4/9/16 which is 2^2/3^2/4^2
@branthebrave8 жыл бұрын
4/4/16 was square day 4^2=16 4*4=16
@VittorioMass8 жыл бұрын
Today it's 2day
@ToastyRoland8 жыл бұрын
I'm feeling a level 1 sponge in my desks future. Cheers Matt.
@frikkthoen8 жыл бұрын
Drop some LSD, and you'll see plenty of fractals, they're beautiful.
@hanniffydinn60198 жыл бұрын
Unfortunately mathematicians into fractals are too fucking dumb to do so. I mentioned this on a fractal forum and got banned. If you want proof reality and God is just an infinite fractal, take psychedelics. Totally fucking amazing! I knew God and reality were a fractal, lsd will prove it to you!
@Scy8 жыл бұрын
That is so wicked sick. I think they just levelled up fractals.
@Ollervo1008 жыл бұрын
Classic pi.
@smoorecrux8 жыл бұрын
Matt Parker is the master of doing things that he says are insane to do and then later it's revealed he's already done it.
@thytom85348 жыл бұрын
Would you call the Pi sponge a method of squaring the circle?
@treufuss-yt8 жыл бұрын
+Thyt0m No. For that you have to construct it in a finite number of steps.
@thytom85348 жыл бұрын
Ahh.
@g.seangourlay25938 жыл бұрын
absolutely. except it's not. you can't repeat the process infinitely on paper. but you can get close.
@Nicegeist8 жыл бұрын
Well you would be actively squaring the circle... but the circle would never be squared.
@moraigna668 жыл бұрын
+Thyt0m Circling the square?
@dhruvbhat38665 жыл бұрын
"No one will be ridiculous enough to put together- okay I may have done it" hahahahaha wow matt parker you're amazing
@unvergebeneid8 жыл бұрын
2:20 More like a 1.8928D shape, amirite?
@standupmaths8 жыл бұрын
I think Hausdorff dimensions deserve their own video!
@chrisdrew17688 жыл бұрын
but how do fractals exist if that dont have whole dimesions arrrrgggghhhhh
@unvergebeneid8 жыл бұрын
Chris Drew Well, sure it's mind-bending but on the other hand, it does make some kind of intuitive sense. How could it be a 2D object if it has no area? 1D objects have no area. Same for the 3D sponge without a volume. Sounds more like a 2D shape then, doesn't it? So those fractals really are somewhere between two dimensions.
@unvergebeneid8 жыл бұрын
standupmaths I'm looking forward to it!
@chrisdrew17688 жыл бұрын
Penny Lane this is why I do physics, things are simpler here.
@hpesoj008 жыл бұрын
You should start a crowdfunding campaign to have all the Menger fractals shipped to the same place.
@dolantremp8 жыл бұрын
+hpesoj00 i concur...the level 4 needs to happen
@prawtism8 жыл бұрын
#lifegoals: Make a Menger sponge with your friends :>
@MrGallagher8 жыл бұрын
Fascinating! And also that seems to be about as close to naturally squaring a circle as one can get!
@PlasmaHH8 жыл бұрын
I wonder what would happen if you get your hands on a high speed high resolution 3d printer...
@cosmicjenny45088 жыл бұрын
+Dennis Lubert L E V E L F I V E M E N G E R S P O N G E S
@IndigoGollum4 жыл бұрын
Wouldn't even need to be high speed.
@zakuraayame50914 жыл бұрын
0:39 now that is what I call a Parker square.
@SergeofBIBEK8 жыл бұрын
Awww, you were here in Atlanta and I didn't know. :(
@standupmaths8 жыл бұрын
+SergeofBIBEK Sorry, it was a flying visit! I barely left the conference hotel.
@SergeofBIBEK8 жыл бұрын
standupmaths That's too bad. Oh well, I'm sure I'll get over it eventually. ;)
@chrismofer6 жыл бұрын
what you gotta do is ship 20 to one location and glue them together: then the kicker. every year the same crew makes another 20, along with additional universities the world round till you have 20 mega mengers: the sheer beauty of a GigaMenger is something i hope to see in my lifetime.
@StudioArrayMusic8 жыл бұрын
did you say 'recreational math'?!
@Gold1618038 жыл бұрын
Uncle Jesse Look up a guy named Martin Gardner.
@MinusPi-p9c8 жыл бұрын
Yup. Math is extremely fun if you're doing it for yourself.
@howardg20105 жыл бұрын
He meant 'recreational meth'.
@IndigoGollum4 жыл бұрын
I know, it sounds like recreational spreadsheets.
@RafidW98 жыл бұрын
what you did with megamenger, I have no words to describe how I feel about it *nerdtears*
@elzearcontelly26518 жыл бұрын
"for completeness" talking about 3D fractals...
@luukderuijter13322 жыл бұрын
Ladies and gentlemen, we have squared the circle
@IoEstasCedonta8 жыл бұрын
"It was 1916 when Sierpinski came up with this." Written out of history is its discovery a century earlier by Queen Elsa.
@TheMikkelOLaursen8 жыл бұрын
Great video as always, love your content. Awesome graphics, the video doesn't feel rushed to me!
@maxbuskirk53028 жыл бұрын
Hello everyone
@smokeweed99018 жыл бұрын
hi
@Bella_Stend8 жыл бұрын
+Max Buskirk What's up?
@GeneralKronosRocks8 жыл бұрын
+michael ruoff he has a fractal as his profile picture, i believe thats why he commented
@Bella_Stend8 жыл бұрын
+Amir Allidina I know. Looks like the mandelbrot set. I was just greeting him back
@Ottmar5558 жыл бұрын
+Max Buskirk hOI
@frankharr94668 жыл бұрын
Happy Birthday fractals! Hey, he pronounced Oregon properly!
@colinjava84478 жыл бұрын
Very interesting, but he can't count, it should be: 4 * 8/9 * 24/25 * 48/49 * 80/81 * ... * ((2k+1)^2 - 1)/(2k+1)^2 * ... And also, its no longer a fractal since as your removing a smaller and smaller fraction each step, the shape is not self-similar at all scales. You would techinically be able to determine how far zoomed in to the shape you were by just looking at the shape in front of you, which is impossible to do in the menger sponge or carpet.
@YounesLayachi8 жыл бұрын
thank you
@justinlasker62698 жыл бұрын
+Colin Java I guess we could call it a Parker Fractal
@ferdiaobrien15008 жыл бұрын
Fractal =/= self-similar. All it means is fractional dimension. Some fractals are self-similar, some aren't.
@colinjava84478 жыл бұрын
Yes, you're right, I'm used to infinite sums, so just put a + out of habit. Thanks, I have edited it now.
@colinjava84478 жыл бұрын
Well there's not really a strict definition, some say a true fractal must be self-similar, which makes the Mandelbrot set not a true fractal, and also the fractal in the video. If one wants to call it a fractal, I guess that's legal.
@otakuribo7 жыл бұрын
This reminds me of that classic "π=4" false proof wherein the perimeter of a unit square appears to approach that of a unit circle through a recursive process but still remains 4, when, in fact, the same process actually does approach the area of a circle and thus would yield π
@themeeman8 жыл бұрын
MUSIC. SOUNDCLOUD. PLEASE. I LOVE YOU MATT.
@quaglemy8 жыл бұрын
+Clingfilm Productions Seconded, we beg you Matt the music is amazing!!!
@lochies54078 жыл бұрын
It does make sense if you think about it. If you take all those squares that were removed from the total area of the Menger Carpet and move them to the four corners of the biggest square, the remaining space in the middle will be a unit circle as the number of squares approaches infinity.
@David-uc4hc8 жыл бұрын
What's with pi anyway? Always showing up uninvited and acts like it's the life of the party. It's just rude.
@nBasedAce8 жыл бұрын
Great video Dr. Mengerla! That's a sponge Elaine Bennis would think worthy of using!
@donfolstar8 жыл бұрын
No pic of a level 2 menger sponge? Stop slackin'.
@Kasimeran8 жыл бұрын
makes total sense it even seems simple if you break down what you are doing when you are reducing a square to a circle (Imagine having all the cutting away done at one corner, so that it gets rounder and rounder, so you end up with a quarter of a circle)
@jrt99b8 жыл бұрын
The natural out working of this? A menger sponge big enough to encapsulate the solar system. Whenever some future generation does achieve this I hope they will call it a Menger-Dyson cage.
@SpaghettiToaster7 жыл бұрын
It's not a cage, it has no volume
@dlevi677 жыл бұрын
But it encloses one.
@BrackenDawson8 жыл бұрын
Its like drawing a sphere in progressively higher resolution. except rater than chipping ever smaller bits of marble off the corners, you're taking them evenly through the thing.
@jaakkohintsala25978 жыл бұрын
5:49 SUOMI MAINITTU TORILLA TAVATAAN!!!
@ukko19988 жыл бұрын
+Jaakko Hintsala Tampere mainittu!
@fakedeltatime8 жыл бұрын
If I may ask, why are you people always like this?
@ukko19988 жыл бұрын
Neko Haxor since this is fun :D
@KingArthurDent7 жыл бұрын
Suomi Manitu Tortilla Leviathan?
@lucca77165 жыл бұрын
A square with area 0 and infinite perimeter. I’m gonna call that a Parker Square.