The Fractal Menger Sponge and Pi

Рет қаралды 453,480

Күн бұрын

MegaMenger project:
megamenger.com/
Ed Pegg's article "Squeezing Pi from a Menger Sponge"
community.wolfram.com/groups/-...
Mega Menger: Building a Menger Sponge at MIT
• Mega Menger: Building ...
Watch Matt calculate pi with...
pies: • Calculating Pi with Re...
a pi-endulum: • Calculating pi with a ...
a lot of chalk: • Calculating π by hand
CORRECTIONS:
- A comment by Starkiller Base pointed out that at the end, I need eight of the Wallis Sponges stacked in a cube. As each one is a unit side, that gives the 'radius' of 1. A single sponge is one eighth of the volume of the unit sphere.
- Jon Mound (@ChthonicJon on Twitter) first spotted that 63/64 should not have been there. I accidentally animated a slip of the tongue. Product should be: 8/9 × 24/25 × 48/49 × 80/81 × 120/121 … (Also spotted in the comments by pjrkearsley87 & hweigel528.)
- Meta-correction: SithBowman noticed I had "132" instead of "121" in the above correction. The correction has since been correctly corrected.
Sorry everyone! Two mistakes and counting. I was really pushed for time this week, which is why some animations are a bit lazy and it's so late in the week (also, so many errors).
Music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
New book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/

Пікірлер: 1 200

@gery49 8 жыл бұрын

It's a very useful shape when you want to 3D print something but you don't have any filament :P

@Nusma 8 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)

@gery49 8 жыл бұрын

Nusm4 :'D

@ciarfah 8 жыл бұрын

+Nusm4 you, I like you.

@JNCressey 8 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.

@iqbaltrojan 8 жыл бұрын

+Gergely H 181 likes on your comment no reply's intill this one XD

@imacds 8 жыл бұрын

Time to build a level 5! Let's get other planets into this project...

@lavaande 6 жыл бұрын

and after a while it would be great to announce that all the multiverses are now united :D

@firefish111 5 жыл бұрын

@Whited Out Black holes

@vasudevraghav2109 3 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....

@ChrisLuigiTails 3 жыл бұрын

Level 5! = Level 120

@R1ckr011 3 жыл бұрын

@Whited Out they just make them out of unit square crystal materials and you can probably get do level 14 or something

@esyrim 6 жыл бұрын

The Menger Sponge is WITHOUT A DOUBT the scariest fractal in 3D and the friendliest fractal in 2D.

@TheNdoki 8 жыл бұрын

I feel cheated. I really wanted to see a level 4 actually assembled.

@YouTubist666 8 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 ..."

@azuritet3 6 жыл бұрын

if they keep up the tradition for 20 years in a row then we could have a level 5

@maxnullifidian 6 жыл бұрын

I'm trying to visualize in my head what it would look like...

@skydivingisfun 5 жыл бұрын

Lol let's see a level grahams number

@brcoutme 5 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.

@54m0h7 5 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.

@Box-of-hats 8 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!

@standupmaths 8 жыл бұрын

My pleasure. Thank you for watching the videos.

@jonahvanke5002 8 жыл бұрын

+standupmaths You probably won't see or answer this, but is there another fractal to get Tau?

@secularmonk5176 8 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.

@peter7718 8 жыл бұрын

+standupmaths You need to make some videos about τ. =P

@trobin 8 жыл бұрын

+Laurelindo he supports pi not tau

@BlightVonDrake 7 жыл бұрын

Someone had to say this. "Dojyaaa~~n!"

@Decimator69420 2 жыл бұрын

D4C’s favourite puzzle cube

@Periwinkleaccount 2 ай бұрын

What’s this a reference to?

@TheEvolNemesis 8 жыл бұрын

Pi squeezed out of a Menger sponge? Doesn't sound very appetizing...

@Punk4kids 8 жыл бұрын

Since you didn't actually put toghether the actual lvl 4 Menger Sponge, can we say that you guys parker squared it ?

@HylianGirl56 8 жыл бұрын

They Parker *Cubed* it.

@ethangates5860 8 жыл бұрын

+T Alex LOL

@Fox_RZK 7 жыл бұрын

It was a bit of a Parker sponge

@nathanliu2031 7 жыл бұрын

T Alex If Matt sees this, he will probably go insane

@Kebabrulle4869 6 жыл бұрын

PARKER SPONGE CONFIRMED

@GeekyAsItGets 8 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.

@ValanceJ 7 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?

@anthonycourte1384 5 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.

@rewrose2838 5 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)

@grassy556 4 жыл бұрын

Good idea for a video game

@jsmunroe 8 жыл бұрын

So does that mean we have successfully squared the circle? And well cubed the sphere?

@needarandomname4330 8 жыл бұрын

+Jordan Munroe lmao!

@PhilBagels 8 жыл бұрын

+Jordan Munroe Yes! In an infinite number of steps.

@DustinRodriguez1_0 8 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.

@Shadow81989 8 жыл бұрын

+Jordan Munroe I think we didnt square the circle, we rather circled the square :D

@jasonbagley3712 8 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.

@BlobVanDam 8 жыл бұрын

7:00 Make up your mind on the pronunciation, Matt! :P

@standupmaths 8 жыл бұрын

+BlobVanDam I try to please everyone! Or annoy everyone. Depends how you look at it.

@BlobVanDam 8 жыл бұрын

+standupmaths It's always the former for this viewer!

@foobar7471 8 жыл бұрын

+BlobVanDam It's definitely the former

@wyattrichard9399 8 жыл бұрын

+standupmaths you should of showed what a menger sponge looks like when you cut it in half P.s. It looks awesome.

@Smartlylinked 8 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

@KryssAA 8 жыл бұрын

"Send money for researches, please, we need more, for project GigaMenger !"

@SaHaRaSquad 8 жыл бұрын

+Christophe Abi Akle But why stop there? TeraMenger is just a bit larger!

@lawrencecalablaster568 8 жыл бұрын

+SaHaRaSquad I prefer the great new dawn of human-fractal understanding, YoctoMenger.

@DomenBremecXCVI 8 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.

@XiphosCreates 8 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.

@Michaelonyoutub 8 жыл бұрын

+Lucas Mulder exactly what i was thinking

@xnick_uy 8 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.

@alejandronq645 8 жыл бұрын

I was just thinking the same! I got to try it on my computer

@alejandronq645 8 жыл бұрын

+x nick since the area of the first "carpet" is 0 you'll end up with nothing

@XiphosCreates 8 жыл бұрын

x nick Matt said the area of the first carpet is 0, it's a different square.

@denascite2029 8 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.

@BloodyHand29 8 жыл бұрын

I had goosebumps when you said 4/3 Pi.

@Crlarl 8 жыл бұрын

9:53 Shouldn't it be "80/81" not "63/64"?

@Henrix1998 8 жыл бұрын

Probably

@DaveScottAggie 8 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

@juggernaut93 8 жыл бұрын

+dimmddr1 Yeah, I thought the same thing and checking on Wikipedia it seems so.

@jesusthroughmary 8 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_Kielty 8 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.

@tacobor 5 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.

@MasterC2012 8 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.

@0xBADFECE5 8 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.

@kenhaley4 8 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...

@0xBADFECE5 8 жыл бұрын

you might be right; it was 1am when i wrote that lol

@irvanluhung3326 8 жыл бұрын

when Matt posts a Video, I press like even before I watch it

@standupmaths 8 жыл бұрын

I hope you adjust that like if conflicting data later comes to light.

@lawrencecalablaster568 8 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.

@TheMikkelOLaursen 8 жыл бұрын

Great video as always, love your content. Awesome graphics, the video doesn't feel rushed to me!

@asp-uwu 8 жыл бұрын

var val=4;for(var i = 3;i

@standupmaths 8 жыл бұрын

That's my kinda π calculation!

@lawrencecalablaster568 8 жыл бұрын

+standupmaths :D Matt, you've coupled together two of my favourite mathematical phenomena! I thank you profusely.

@Guil118 8 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-uwu 8 жыл бұрын

+ILYES brb *steps away to write a program to draw a graphic sponge*

@ELYESSS 8 жыл бұрын

+Eric Pratt I'll be waiting

@TPRJones 8 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_Kielty 8 жыл бұрын

Yeah but only the 4th iteration is distributed, which to me is a whole lot better than the 1st.

@TPRJones 8 жыл бұрын

+Paul Kielty That's fair.

@spicytaco2400 8 жыл бұрын

I like how you unintentionally poke fun at the location in more than one way.

@tggt00 8 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.

@johnny141093 8 жыл бұрын

We did this at my university (Leeds)! We have desks made out of them all over the maths department now!

@standupmaths 8 жыл бұрын

+John Pearmain Yes, I have put my coffee on one of the Leeds fractal coffee tables.

@doggonemess1 8 жыл бұрын

When I drop my pi, I always use a Menger Sponge to clean it up.

@jeffirwin7862 8 жыл бұрын

You just created a set that is uncountably infinite yet dense nowhere, you damn magician.

@MrGallagher 8 жыл бұрын

Fascinating! And also that seems to be about as close to naturally squaring a circle as one can get!

@nikosaarinen3258 4 жыл бұрын

0:15 You could call that a Parker square

@z-beeblebrox 8 жыл бұрын

Someone needs to create a MegaMenger manga

@ourgloriousgodoursaviourbe2757 2 жыл бұрын

Yeah, about that...

@ourgloriousgodoursaviourbe2757 2 жыл бұрын

Also hello person from 5 yrs ago

@danjones4492 8 жыл бұрын

This channel is even better than Numberphile (which is also really good). Best channel on KZfaq! Great stuff Matt!

@glmathgrant 8 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. :)

@GuiltyGearRockYou 8 жыл бұрын

LET's GO FOR A LEVEL 4 MENGER! =)))

@DiCasaFilm 8 жыл бұрын

Is there any feasible way that this level 4 can actually made?? We have to unite the clans!

@vlogdemon 8 жыл бұрын

Cargo ships?

@YouTubist666 8 жыл бұрын

I think the resulting structure would just collapse under its own weight.

@rossthebesiegebuilder3563 8 жыл бұрын

+YouTubist666 Only one way to find out...

@chrismofer 6 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.

@nikkirennardo5100 5 жыл бұрын

I’d suggest private flights to make sure it doesn’t get crushed in shipping

@thesemoves 8 жыл бұрын

Brilliant video as usual!

@pravinshingadia7337 3 жыл бұрын

Your videos are brilliant! Very funny and very interesting and make maths fun. Keep it up please!

@philosofickle 8 жыл бұрын

Try to bring all these lvl 3 sponges together and build that level four member sponge. Please try

@elzearcontelly2651 8 жыл бұрын

"for completeness" talking about 3D fractals...

@code_explorations 8 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.

@watcherfox9698 8 жыл бұрын

One of the things I love about maths is how things are connected in such surprising ways.

@Ollervo100 8 жыл бұрын

Classic pi.

@trudyneo 8 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.

@andycohen3365 8 жыл бұрын

This was the most awesome thing I've ever seen

@chraffx8217 8 жыл бұрын

I liked the way you presented the sierpinski carpets. Nice video!

@standupmaths 8 жыл бұрын

Thanks! I was very pleased with that.

@GroovingPict 8 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?

@UCreations 8 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 ;)

@you_just 7 жыл бұрын

You can squeeze pie out of an infinite sponge Finally, math I can get behind

@Scy 8 жыл бұрын

That is so wicked sick. I think they just levelled up fractals.

@ViktorLox 8 жыл бұрын

I want them to actually assemble a level 4, then burn it!

@prawtism 8 жыл бұрын

#lifegoals: Make a Menger sponge with your friends :>

@nBasedAce 8 жыл бұрын

Great video Dr. Mengerla! That's a sponge Elaine Bennis would think worthy of using!

@ifyoubelieveanythingmatter8924 7 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.

@SebastianLopez-nh1rr 8 жыл бұрын

Doesn't this counts as squaring the circle?

@joshhyyym 8 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.

@roberteospeedwagon3708 8 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.

@DanDart 8 жыл бұрын

Then this must be circling the square!! XD

@engineer_cat 8 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.

@MisterHunterWolf 5 жыл бұрын

Cubing the sphere

8 жыл бұрын

63/64? Or 80/81? How can you remove the center square of an 8x8 square?

@jesusthroughmary 8 жыл бұрын

+Víktor Bautista i Roca Beat me to it.

@andrewolesen8773 8 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.

@PJoriginal 8 жыл бұрын

was thinking the same

@carsonwood1513 8 жыл бұрын

I think he screwed up on it.

@nicholaswallingford3613 8 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)

@ebrahimalfardan8823 8 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.

@branthebrave 8 жыл бұрын

I like Mandelbrot, Julia set, and the dragon curve.

@frikkthoen 8 жыл бұрын

Drop some LSD, and you'll see plenty of fractals, they're beautiful.

@hanniffydinn6019 8 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!

@kordellcurl7559 8 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.

@cananamanda 6 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!

@huash9179 6 жыл бұрын

5:51 : Matt, youre insulting canada :'(

@Ganpan14O 4 жыл бұрын

Neat thing: Minecraft actually added a menger sponge in the April fool's update.

@maxbuskirk5302 8 жыл бұрын

Hello everyone

@smokeweed9901 8 жыл бұрын

@Bella_Stend 8 жыл бұрын

+Max Buskirk What's up?

@GeneralKronosRocks 8 жыл бұрын

+michael ruoff he has a fractal as his profile picture, i believe thats why he commented

@Bella_Stend 8 жыл бұрын

+Amir Allidina I know. Looks like the mandelbrot set. I was just greeting him back

@Ottmar555 8 жыл бұрын

+Max Buskirk hOI

@PlasmaHH 7 жыл бұрын

I wonder what would happen if you get your hands on a high speed high resolution 3d printer...

@cosmicjenny4508 7 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

@IndigoGollum 3 жыл бұрын

Wouldn't even need to be high speed.

@mercatorpsi 8 жыл бұрын

The Menger Sponge is my fave fractal too, and I'm very impressed with all the people who helped out on the project! See (I tell my cynical self), humans CAN do cool things! And that teasing pi out of the modified carpet was the icing on the cake. Super groovy!

@Victor-sw4ne 7 жыл бұрын

the cantor's conjunt in 2D, and an actual proof that it has zero meazure... loved it!

@donfolstar 8 жыл бұрын

No pic of a level 2 menger sponge? Stop slackin'.

@infrabread 8 жыл бұрын

What would a 4D Menger Sponge look like?

@pokestep 8 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.

@BennoRob95 8 жыл бұрын

You rock dude this is awesome

@timetodowhatever 7 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

@superliro100 8 жыл бұрын

10:42 why isnt it 80/81? Shouldn we remove the square of odd numbers?

@tomprogramming 8 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.

@gojoubabee 8 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!

@CASTCorp 8 жыл бұрын

Cool! It's my birthday tomorrow

@gojoubabee 8 жыл бұрын

+CAST Corp Happy birthday!

@gojoubabee 8 жыл бұрын

+CAST Corp Wow, your birthday will be on 4/9/16 which is 2^2/3^2/4^2

@branthebrave 8 жыл бұрын

4/4/16 was square day 4^2=16 4*4=16

@VittorioMass 8 жыл бұрын

Today it's 2day

@teaser6089 3 жыл бұрын

I feel that Matt tries to escape the Pi, but the Pi always catches up with Matt.

@jensdevries6532 8 жыл бұрын

Incredible... Currently studying infinite sums, but this infinite product just blows my mind! I really want to take a look at the proof of this convergence to pi and 4/3pi.

@StudioArrayMusic 7 жыл бұрын

did you say 'recreational math'?!

@Gold161803 7 жыл бұрын

Uncle Jesse Look up a guy named Martin Gardner.

@user-kh5tv9rb6y 7 жыл бұрын

Yup. Math is extremely fun if you're doing it for yourself.

@howardg2010 5 жыл бұрын

He meant 'recreational meth'.

@IndigoGollum 3 жыл бұрын

I know, it sounds like recreational spreadsheets.

@hweigel528 8 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.

@standupmaths 8 жыл бұрын

Absolutely correct! I've added you to the corrections.

@Coldo3895 8 жыл бұрын

+standupmaths Oh I was so happy to have found a mistake !! But I am not the first.... ;)

@ToastyRoland 8 жыл бұрын

I'm feeling a level 1 sponge in my desks future. Cheers Matt.

@Wombat2020 7 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

@SergeofBIBEK 8 жыл бұрын

Awww, you were here in Atlanta and I didn't know. :(

@standupmaths 8 жыл бұрын

+SergeofBIBEK Sorry, it was a flying visit! I barely left the conference hotel.

@SergeofBIBEK 8 жыл бұрын

standupmaths That's too bad. Oh well, I'm sure I'll get over it eventually. ;)

@jonnivuorinen8374 8 жыл бұрын

Suomi mainittu

@mikkoholopainen5112 8 жыл бұрын

Torilla tavataan!

@tube71000 8 жыл бұрын

Mikko Holopainen Tortillat avataan!

@mestiarcanus 8 жыл бұрын

I actually built a level 2 Menger sponge out of Magic: the Gathering cards years ago (though using Magic cards instead of the Menger pattern for the cladding). It was a nice way to keep my hands busy while I watched KZfaq videos. Took up a fair bit of space too. Sadly I ended up recycling it when I moved out of the apartment I was in at the time.

@Kasimeran 8 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)

@IoEstasCedonta 8 жыл бұрын

"It was 1916 when Sierpinski came up with this." Written out of history is its discovery a century earlier by Queen Elsa.

@colinjava8447 8 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.

@YounesLayachi 8 жыл бұрын

thank you

@justinlasker6269 8 жыл бұрын

+Colin Java I guess we could call it a Parker Fractal

@ferdiaobrien1500 7 жыл бұрын

Fractal =/= self-similar. All it means is fractional dimension. Some fractals are self-similar, some aren't.

@colinjava8447 7 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.

@colinjava8447 7 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.

@bobnash79 8 жыл бұрын

This is really great! Well done! Cheers from france

@kristianhaverasmussen8558 3 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

@FLOABName 8 жыл бұрын

well, guess what i'm building in minecraft now

@Ganpan14O 4 жыл бұрын

They added a menger sponge dimension in the April fool's update, so if you give up on making one just boot that up!

@jaakkohintsala2597 8 жыл бұрын

5:49 SUOMI MAINITTU TORILLA TAVATAAN!!!

@ukko1998 8 жыл бұрын

+Jaakko Hintsala Tampere mainittu!

@fakedeltatime 8 жыл бұрын

If I may ask, why are you people always like this?

@ukko1998 8 жыл бұрын

Neko Haxor since this is fun :D

@KingArthurDent 6 жыл бұрын

Suomi Manitu Tortilla Leviathan?

@origamikatakana 8 жыл бұрын

I heard about this a while back! I'm glad a youtube math(s) channel has picked up the topic!

@intrepidca80 8 жыл бұрын

2:29 - I hadn't realized that fractals were people at all, let alone amazing people!

@thytom8534 8 жыл бұрын

Would you call the Pi sponge a method of squaring the circle?

@pfeifenheini 8 жыл бұрын

+Thyt0m No. For that you have to construct it in a finite number of steps.

@thytom8534 8 жыл бұрын

Ahh.

@g.seangourlay2593 8 жыл бұрын

absolutely. except it's not. you can't repeat the process infinitely on paper. but you can get close.

@Nicegeist 8 жыл бұрын

Well you would be actively squaring the circle... but the circle would never be squared.

@moraigna66 8 жыл бұрын

+Thyt0m Circling the square?

@thomaskraus7077 8 жыл бұрын

Math, go home, you're drunk.

@alibengali1150 7 жыл бұрын

Alcohol, go home, you're on math

@thomaskraus7077 7 жыл бұрын

Math Not even once

@gabor6259 7 жыл бұрын

The beauty of maths never ceases to impress me.

@BrackenDawson 8 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.

@David-uc4hc 7 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.

@unvergebeneid 8 жыл бұрын

2:20 More like a 1.8928D shape, amirite?

@standupmaths 8 жыл бұрын

I think Hausdorff dimensions deserve their own video!

@chrisdrew1768 8 жыл бұрын

but how do fractals exist if that dont have whole dimesions arrrrgggghhhhh

@unvergebeneid 8 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.

@unvergebeneid 8 жыл бұрын

standupmaths I'm looking forward to it!

@chrisdrew1768 8 жыл бұрын

Penny Lane this is why I do physics, things are simpler here.