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Mathematical Lego Sculptures
Daedalus_ writes "Some guy has created mathematical surfaces (mobius strips, klein bottles, etc) out of Legos. He also has some other interesting creations (such as Dilbert figurines and a Hoberman Sphere)."
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One of those snakey thingeys that have all those sections you twist go back into the container?
I could NEVER figure that out.
WWJD? JWRTFA!
Reading between the lines, of course.
I have been pwned because my
Does this mean that the lego representation of a surface integral is not far behind?
"Oh no, 3 horny women and only 2 condoms...Thank god I read slashdot"
Here's the un-hrefed link.
t m
http://www.lipsons.pwp.blueyonder.co.uk/index.h
I have been pwned because my
Lego people can walk sideways on buildings?? We must make them our leaders!
This message was brought to you by the death of 30 brain cells.
Creating legos out of mathematical surfaces... (Use POVRay to render this :D).
// example of object unions
,
.5
#include "colors.inc"
#include "textures.inc"
#include "metals.inc"
camera {
location
look_at
}
plane { , -1
pigment {
checker color Red, color Blue
}
}
light_source { color White}
#declare lego=union {
box {
}
#declare cyl1=cylinder {
,
}
object { cyl1 }
object { cyl1 translate }
object { cyl1 translate }
object { cyl1 translate }
object { cyl1 translate }
object { cyl1 translate }
texture { Glossy
pigment { Red }
}
}
object { lego }
object { lego
translate
rotate 20*y
}
That is totally amazing. And for what it's worth, I think it's a worthwhile use of his time (not that my opinion on how someone uses their time matters, but whatever). I don't know, to me for some reason non-trivial acts of creation like this seem to touch whatever it is to be human -- our creative endowment is one of our signature traits, I think. What impulse would drive this sort of creative urge, to create beautiful mathematical shapes out of Lego, of all things? Whatever it is, it's mysterious, and it wasn't a waste of time. That figure eight knot is incredible.
Very, very cool.
Now show me a hypercube and I'll be really impressed.
"Moderate drinking can help prevent amputated limbs" -- Abigail Zuger, NYTimes, 12/31/02
I love Andrew Lipson's Math site, thought it was on slashdot for a while. If you like to see other such sites check out Eric Harshbarge's Lego page (cool stuff like wedding cakes and skyscrapers), Henry Lim's totally awsome lego sculptures, he's even got Natalie Portman (Not naked, and next to the petrified beethovan). BTW, Eric's got a very interesting page on on San Mononoke (more on those).
Much like fish or sheep.
Wait a second, isn't this idea very very close to the Oop! idea in Douglas Coupland's "Microserfs"?
Actually, he mentions building something to amuse his 5 year old son,
so I imagine that he IS married...
He must have a very patient wife : )
Im not here now... Im out KILLING pepperoni
I would be impressed with a Dyson Sphere out of legos. That would be cool.
And you could have a little Scotty Lego charachter next to a crashed shuttle craft on the surface.
I'm not the only person that realizes that a klein bottle can't be made with lego? Or with anything that we know of...
klein bottles can't really be represented in three dimensions...
This is left as an exercise for the reader.
On his other page I particularly liked the machine for switching itself off. Mind you, he'd need to be careful, he might be breaching Microsoft's patent on Windows.
You call me a pedant? I prefer the term "correct"
I can make a near-perfect rectangular parallelepiped out of single Lego brick. Top THAT!
Mirror site up.
www.netmar.com/~will/lego
Disclaimers:
1.) Not my work, I don't claim any of it.
2.) I didn't get the
3.) I know it's not slashdotted yet, just preparing/ karma whoring.
4.) If it does get slashdotted, and everyone starts testing my load balancing, why not sign up for hosting at the same time? We're running a no setup fee promotion at the moment.
~Will
P.S. became friends with the
sig?
I think slashdot has discovered a mozilla bug. ...Or maybe there is a new weapon against the /. effect!
Everytime i click on the "out of legos" link, my
Mozilla(1.0) crashes!
lots of legos
Comment removed based on user account deletion
Looks an awful lot like a 2D projection of a hypercube to me.
Impressed yet?
Man, one time we were so desperate we put ourselves together a lego bong! More like a pipe, but it was wild man!
(for tobacco use only, of course)
I would like to see this guy get together with the creater of this site:
http://drew.corrupt.net/lp/series2.html
The Kline Bottle would then never be looked at in the same light.
(Warning: not for minors)
Table-ized A.I.
http://mrl.nyu.edu/~perlin/demox/Hyper.html
Tim
Omnia vestra castrorum habetur nobis.
- Jon Katz
- Trollaxor
- PhysicsGenius
- dipfan
- 56ker
- Cack-cack-cack-cack-cack!
Mark your guesses in the reply. Remember, you are allowed to "write-in" other answers...keep those number twos sharp and...go!Cack-cack-cack-cack-cack!
CACK
Thanks for the warning. I wonder why this wasn't publicized. It seems quite contrary to the spirit of Open Source.
I wonder if Klein's bottle emerged waterproof. It will be a great vase for flowers if put to stand.
I would like to have one, made of glass. Will look gorgeous, especially if made of colored glass.
This might be a good way to start kids on geometry. Being able to actually build something like a mobius strip makes it much easier to understand it. And to think that the only things I built with legos were space ships.
Don't give me none of this "nature theme" business.
i wish i had that much time, cause if i did, i'd do something worthwhile like cleaning the 328 ramen cups stacked in a sphere out of my room
Righteousness postpones the inevitable
http://burningaureole.caveism.net
This is a test.
Where does this guy get all of these lego blocks? It looks like he has all weird sizes too.
;-)
Maybe he cheats and makes his own lego blocks...
I'm a firm believer in Legos * and am thoroughly convinced that they helped strongly in developing my inquisitive intellect. I still have my Legos from when I was 10.
... well, here's hoping that the world's first Lego Julia or Mandelbrot set will be made within our lifetimes. Lipson's surface models are just beautiful, so just imagine the beauty of a more sophisticated set.
... that's the strength and appeal of Legos. However, I admit that the addition of gears makes the entire matter more challenging, perhaps for the 14+ age group.
Look at 'em: they teach you to design, build, modify, and to have the patience for all of that. Legos are the best thing for the price that I can think of that can spur a young intellect. (Erector Sets were great for that too.) And if you get older and still play with them
BTW, I am down on all this Lego model crap I see in the stores. Give kids a bucket of basic blocks and let them create
* Legos {tm} is the registered trademark of some silly corporation or something like that.
[also misbehaves on Kuro5hin as Peahippo]
You try to make a little joke, but there is always some Poindexter out there who takes you literally and points out your "mistake" in mind-numbing detail...
...doesn't his Klein bottle have multiple surfaces? Damn legos!
proton != antielectron
C'mon. Mod him up. That's a great song. I was wiping tears from my eyes.
Comment removed based on user account deletion
Sorry, but technically a klein bottle is a four-dimensional figure (impossible to A) comprehend and B) create). Still looks cool!
Why do people insist on saying Legos? The plural and singular of the word is: LEGO.
;-)
I think it's the "sheeps" syndrome
-psyconaut
Come on now. There is NO Plural of LEGO® there is ONLY ONE LEGO® and that is the 'Group of companies' that makes the bricks.
As for the usual argument as to the correct LEGO® terminology check out what LEGO® has to say about it (about 13 parragraphs down 'Proper Use of the LEGO Trademark')
LEGO® is a trademark of the LEGO Group of companies
Me lost me cookie at the disco.
Oh, I'm sorry. I forgot that this post obeys the laws of thermodynamics!
/^[A-Z0-9._%+-]+@[A-Z0-9.-]+\.[A-Z]{2,4}$/i
But, for those interested, here are some other cool Lego sites:
Stegosaurus
Lego Town
Lego City
Beethoven
Queen Amidala
Audrey Hepburn Wall
Big Clock
Alice in Wonderland
Click here or here.
This isn't WIDE!
I had no computer, not even a graphical calculator, so I had to calculate separately for each dot the distance to the center using and ordinary calculator and the pytogoras formula. The radius was 10 "units". Unfortunately, the unit brick in lego is not a cube. I think to ratio of base to height of these pieces is 5:6. So the sphere now looks more like an ellipsoid. Maybe I should photograph it and put it on the web.
-- 1.e4 c6 2.d4 d5 3.Sc3 de4: 4.Se4: Sd7 5.Sg5 Sgf6 6.Ld3 e6 7.S1f3 h6 8.Se6:
I still have not figured out the correct plural of Elvis and Lexus (the car). Elvi and Lexi?
Table-ized A.I.
Look you lot.
While we are having a discussion in English, the plural of Lego is not Legos
We don't make stuff from Legos
We make stuff from Lego
or We make stuff from Lego bricks
I hope that this will help some of you comments look less ignorant
GrumpyBastard
Wow. Maybe it's the beer I just drank, but this is truly TRULY the coolest thing /. has shown in some time. Okay, maybe it's not strictly _news_, but WOW.
...can he build a lego page counter than can keep up with the hits from /. ? :)
Never, ever lose a file again. Ever.
For inspiration, check http://ben.com/LEGO/ out
I'm sure I'm not the first to say it, but that's what it is.
It always has been, it always will be, you can confirm this on their web site.
It's like Sheep and Sheep - ok, NEVER call them "LEGOS" it grates people (whiners) like myself intensely.
Not interested. Unless the guy can make an image of Natalie Portman buck naked, otherwise... don't bother. Oh and if he can do that, I think that would certainly call for a new /. topic "Naked lego images".
Anybody seen White Stripe's "Fell in Love With a Girl" video? Made entierly out of Lego's, using real Lego set, not CGI, as I thought first.
You can see it here, along with some info of how it was done.
Not interested. Unless the guy can make a sculpture of Natalie Portman buck naked then let me know, otherwise don't bother. Oh, and if he can do that, I think that would deserve a new /. column "Naked Lego Chicks"
Later
Let's use time as our 4th dimension. Imagine a cube that appears and then disappears in an instant. That's a 3D cube. Now stare at a cube for a few seconds.
That's a hypercube.
A 4D being would see the difference instantly. The 3D cube would seem kind of "flat" next to the other one.
Donate background CPU time to fight cancer.
For people new to building and need a resources to buy their goodies, here is a pretty good site. They have just about everything you would need (all different kinds of gears, axles, motor boxes, etc.). Everything you wish the main Lego site sold.
This site has nice rotatable images:
http://mathworld.wolfram.com/topics/MinimalSurface s.html
Nice job indeed!
The machine that turns itself off is so cool!! During math-colleges I was completely facinated by this idea and drew cartoon-like scenario pictures of it again and again, dreaming of building it. it probably appeals only to the more math-minded people.
FLT, not just any theorem.
FLT, not just any theorem.
It is not really Natalie Portman it is Queen Amidala. I feel cheated, Queen Amidal looks more like a bad set of curtains than Natlie Portman.
h tm
On his web page he even titles the sculpture.
Queen Amidala
"My apologies to Ms. Portman"
Now this page is more like it (no lego though)
http://www.natalie-portman.net/pictures.
--
"This isn't a Troll"
Of course a troll would say that
Let me know when he has made a model of Gabriel's Trumpet! Now, that would be something!
-516
I work with this guy, he doesn't actually build the things out of lego's at all, they're just ray-traced :)
-snarkosm
...you'd hate for me to start my comment in the subject line, 'eh?
Imagine a 2 dimensional person seeing a 3 dimensional cube pass through his space. If the flat surface of the 3d cube is parallel with the 2d universe, the 2d person will simply see a square miraculously appear before him, hover for awhile, and then disappear. If the surface of the 3d cube is not completely uniform the 2d person might see the surface of the square "morph" a little. Similarly, if a 4d cube passed through our 3d universe, we would see a cube miraculously appear and then, after a few moments, disappear.
Things become interesting if you pass the corner of the 3d cube through the 2d universe first. The 2d person would see tiny triangle appear before him that grows larger and larger, until you hit the next corners and things become complex, especially if the cube entered at an angle. Eventually you'll get back to a floating triangle that shrinks down to nothingness. Similarly, a 4d cube going through our universe will appear as a 3 sided growing pyramid at first.
Another way to imagine a 4d cube is to think about what its shadow would look like in our universe. The way to do that is to take a 3d cube and project its shadow on a wall. Straight on from the light source it looks like a square. Move it around and see how it morphs. Now image a 4d person was projecting the shadow of a 4d cube onto our universe. Straight on we would have a 3d cube. If he moved the cube around, various corners of the 4th dimension would "morph" out of the flat sides.
When we talk about seeing a hypercube we usually talk about the shadow of a transparent cube, where you just see the connecting lines. This would give you a cube inside of a cube with the corners of the inner cube connected to the corners of the outer cube.
The Moore-Murphy Law: The number of things that will go wrong will double every 2 years.
Have any of you ever been to a Legoland amusement park? All I can say about that is holy cow. I went to the park near Munich and there are some incredible Lego sculptures, like Venice, Frankfurt skyscapers, Berlin, etc... How do they do that?
I figured I'd build the sphere first, and ignite the star inside it.
As it turns out, I could never get the damn fusion reaction going. Stupid Zippo.
The only surefire protection against Microsoft infections is abstinence. - The Onion
Wanna come over to my place and see my 14' lego stegosaurus?
Yeah, there's a reason why my dining table is on the front lawn.
--
E_NOSIG
mmmmm yeah that's what I'm talkin bout.
To quote Isaac Asimov:
A mathemtician confided,
That the mobius strip is one sided
And you'll get quite a laugh
When you cut it in half
For it stays in one piece when divided
...when I can get a Lego model of a singularity
ID-10-T is a way of life
Actually, according to the fairplay page on the LEGO website, "LEGO" is an adjective, not a noun, so it has no plural.
"Those who would sacrifice essential liberty for temporary safety deserve neither liberty nor safety."
Oddly enough, I wrote a tesseract viewer that uses OpenGL a few years ago. Source is in C++ and GLUT. The program, source and readme file are all on my OpenGL/GLUT demos page. Specific URL:
s s/ index.html
;-)
http://personal.nbnet.nb.ca/daveg/opengl/viewte
Enjoy.
.f00Dave