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My God, its full of stars!
December 26, 2012 4:59 PM   Subscribe

What do you get if you slice a Menger Sponge on a diagonal plane?
Watch this video to find out.
posted by thatwhichfalls (44 comments total) 50 users marked this as a favorite

 
Neat. I was picturing triangles, so I was sorta on the right track, but not close enough ...
posted by feckless at 5:05 PM on December 26, 2012 [1 favorite]


(And failed to read the post title. Obvsly.)
posted by feckless at 5:09 PM on December 26, 2012


I was looking for a holiday present for the math teacher wife...thanks!
posted by HuronBob at 5:10 PM on December 26, 2012


Cool. I was surprised.
posted by straight at 5:11 PM on December 26, 2012


I predicted the Mistubishi Logo so I guess I was kinda right, too.
posted by ShutterBun at 5:13 PM on December 26, 2012 [1 favorite]


Super cool!
posted by Pope Guilty at 5:19 PM on December 26, 2012


Not surprisingly, this video was released during Hanukkah.
posted by benito.strauss at 5:23 PM on December 26, 2012 [5 favorites]


(Man. I'm completely distracted by how he speaks with a similar cadence as Vi Hart. Or, you know, Vi Hart speaks with a similar cadence as him)
posted by ambilevous at 5:23 PM on December 26, 2012 [1 favorite]


Yep. The fractally self-similar apple didn't fall too far from the directed acyclic tree.
posted by benito.strauss at 5:26 PM on December 26, 2012 [3 favorites]


It also created Sierpinski gaskets on some slices. That interested me.
posted by Grimgrin at 5:34 PM on December 26, 2012 [1 favorite]


What do you get if you slice a Menger Sponge on a diagonal plane?

Trick question. You'd never be able to sneak a knife onboard.
posted by hal9k at 5:46 PM on December 26, 2012 [16 favorites]


I also guessed triangles. I imagine the practical value of such things is of an architectural nature, possibly even cryptography.
posted by Renoroc at 5:52 PM on December 26, 2012


I was expecting tesselating hexagons.
posted by dunkadunc at 5:55 PM on December 26, 2012 [3 favorites]


...Described in 1926.... first thought to slice diagonally in 2007...

That's one of the most amazing things about math, to me, that sometimes questions just never get asked for some weird reason.
posted by odinsdream at 6:02 PM on December 26, 2012 [1 favorite]


ambilevous: "(Man. I'm completely distracted by how he speaks with a similar cadence as Vi Hart. Or, you know, Vi Hart speaks with a similar cadence as him)"

Like father, like daughter.
posted by radwolf76 at 6:09 PM on December 26, 2012


I just could not love nerds more. I could not.
posted by prefpara at 6:18 PM on December 26, 2012 [2 favorites]


I also thought it'd be the hex equivalent of the Sierpinski gasket.
posted by BrotherCaine at 6:22 PM on December 26, 2012


If you create a bagel in the shape of a Menger Sponge and cut it along the edge, it oddly turns into a Bavarian Creme donut.
posted by xingcat at 6:26 PM on December 26, 2012 [11 favorites]


I guess I'll have to create the CAD file myself since he didn't supply one. Glad I have access to a 3D printer.
posted by Confess, Fletch at 6:29 PM on December 26, 2012


All I'm sayin' is I don't want a mohel who is looking to mathematics for new ways to see *cough* things.
posted by Smedleyman at 6:34 PM on December 26, 2012


Confess, Fletch: I'm betting 3 out of 10 randomly generated AutoCAD lisp programs generate a menger sponge.
posted by phrontist at 6:53 PM on December 26, 2012 [1 favorite]


I guessed a sort-of Sierpinski curve -- I had the Star of David right, but thought that each edge would have a little equilateral triangle of its own, and so on and so forth. Frustratingly, I don't know whether that's correct or not, because I think it would only show up if you started with at least an order-4 sponge. Now I have to write a program to find out. Damn you, MetaFilter!
posted by spacewrench at 6:54 PM on December 26, 2012 [1 favorite]


That was neat. I also had some thought of hexagons, although maybe that was primed by the first part of the video.
posted by carter at 7:25 PM on December 26, 2012


Phrontist: LOL....
posted by Confess, Fletch at 7:35 PM on December 26, 2012


The most amazing thing to me was when he said "I've made a Menger Sponge by 3d printing." Something lights up in me when I realize that I am now living in a world where that is possible.
posted by salishsea at 7:59 PM on December 26, 2012 [9 favorites]


ambilevous, radwolf76, thanks for clueing me into the existence of Vi Hart (and thanks to thatwhichfalls for this post, clueing me into the existence of George Hart). This video by Vi blew my mind with the amount of creative, exploratory thinking that she brings to exploring math, visually. It's joyful and beautiful and expresses so much of what I love about math, but what is so often lost in how it is taught to us as kids (and what I seem to have lost as I've gotten older, regrettably).

It also really pleases me to see that this father has obviously passed on his love for the beauty of math to his daughter, in the most vibrant way possible. And like her father she has a gift for exploring and sharing complex mathematical concepts with others in elegant, intuitive ways, without diminishing the concepts involved or insulting the intelligence of the viewer (on the contrary).

Just what I'm always looking for!
posted by dubitable at 8:25 PM on December 26, 2012 [8 favorites]


Wait till you learn we can make a nanoscale algorithmically self-assembled 2d sierpinski triangle out of DNA!
posted by lalochezia at 8:26 PM on December 26, 2012


Neat!!

Relatedly, making a Menger sponge out of business cards.
posted by rmd1023 at 8:37 PM on December 26, 2012


The universe is a p-brane propagating through a Menger Sponge-shaped spacetime, and stars as we know them exist for only an infinitesimal moment that seems like billions of years to us.

Before this cosmological period, the stars were shaped like rectangles and triangles. It was really weird.
posted by dephlogisticated at 9:00 PM on December 26, 2012 [1 favorite]


What do you get if you slice a Menger Sponge on a diagonal plane?

Two Menger Sponges. Thank you, I'll be here all week.
posted by Greg_Ace at 9:09 PM on December 26, 2012 [6 favorites]


My God, its full of stars overlapping rhomboids!
posted by mazola at 9:51 PM on December 26, 2012


I HEARD THE WORDS MENGER SPONGE AND CAME AS SOON AS I COULD WHAT IS GOING ON GUYS

Actually, this is a really neat result. I was guessing hexagons but I laughed out loud once I saw where there stars were coming from; it makes total sense once you get your head around it.
posted by cortex at 10:28 PM on December 26, 2012 [4 favorites]


Thanks for posting, that was just the kind of thing I needed over breakfast.
(Bonus points for a spoiler that wasn't a spoiler but was a 2001 reference.)
posted by Drew Glass at 12:57 AM on December 27, 2012


This is why I keep coming back to Metafilter. Thanks for this.
posted by Blazecock Pileon at 1:19 AM on December 27, 2012


Love these sort of posts. Please keep them coming as I am too lazy to look for them myself.
posted by greenhornet at 1:41 AM on December 27, 2012


I was expecting Yog Sothoth
posted by fearfulsymmetry at 2:42 AM on December 27, 2012 [3 favorites]


I wanted it to be circles. That would have really impressed me.
posted by scrowdid at 3:24 AM on December 27, 2012 [1 favorite]


Since I am spatially-challenged it was going to be a surprise regardless of the result, but this was really unexpected (even with the title of the post.) Definitely sponge-worthy.
posted by Room 641-A at 5:39 AM on December 27, 2012 [1 favorite]


I ruined all of the potatoes. Thanks a lot, pal.
posted by orme at 7:47 AM on December 27, 2012 [1 favorite]


him: see, these are really intersecting rhombi...

me: no. It's just a line. and don't you mean rhomba?

him: (goddam flatlanders)

me: I'm going to cut some cheese. want some?
posted by mule98J at 7:53 AM on December 27, 2012 [1 favorite]


His rapid prototyping page has lots of cool stuff.
posted by Rhomboid at 10:00 PM on December 27, 2012


True dat Rhomboid. And he has a replicator. I'd like to take tea with this man.
posted by salishsea at 12:33 PM on December 28, 2012


I'm not a math geek and had never heard of this fractal, but by the time we saw the slice my face lit up. What a delightful surprise.
posted by kostia at 4:51 PM on December 28, 2012


Yeah, I echo kostia's response. Have sent this link - with attribution - to one online community and to friends, including my tweenage niecephew.
posted by goofyfoot at 1:34 AM on December 29, 2012


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