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Origami Science
mpark6288 writes: "Alright, so we all remember elementary school, and the endless paper cuts that we got from trying to learn some origami. Some how my crane was always a boat. But, as News Factor: Sci Tech states: 'The theorem is, you can make any shape, and there is an algorithm for folding the piece of paper,' stated MIT Associate Professor of Electrical Engineering Erik Demaine said. Referencing applications of origami in robotic arm manipulation, bioinformatics, protein folding and molecular biology, Demaine said there is a multitude of possibilities from origami principles as simple as folding a square piece of paper in half and making one calculated cut. So who knows, those annoying little shuriken (throwing stars) that you made to throw at girls (eww cooties) could have been a major scientific breakthrough!"
What a disappointing article
I can make a sphere without any trouble at all.
Hypercubes are a little bit more troublesome, but become obvious when I throw my little origami box at the wall and you watch it in 4 spatial dimensions.
"They thought we might be able to adapt (origami-based) algorithms to solve their problem," Lang recalled. "Sure enough, it worked; now it's used to simulate airbags."
What wasn't mentioned was all the failed attempts to bring origami to airbags, including the infamous "1000-paper-cranes-exploding-in-your-face" airbag.
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And I though origami was just for making fleets of boats when you're bored during lectures :-)
I have directions for folding an F-14 Tomcat from a square of paper. It flies great, and even has airfoils on the wings and control surfaces on the tail. You can see a picture of it here - it's the blue one in the middle.
/.'s, and when else will it be even close to on topic. ;)
The model is by Micheal LaFosse (you can find books by him with instructions for the "Aero-gami" F-14), and he has some other amazing models on this
site.
I know this is not completely on topic, but I thought it would be interesting to fellow
_sig_ is away
Origami math is cool... (check out the galleries!) ;).
hyperbolic paraboloids are actually pretty easy and fun to make (and they drive the ladies wild
The Five Intersecting Tetrahedra are neat too but can get really hard when you're putting in the last couple.
And there's plently of theoretical stuff; for example, you can axiomitize origami, and trisect angles and double cubes and stuff.
Some people have even made origami/combinatorial geometry courses.
Directions for making those cool paper shurikens can be found here.
When making origami ninja stars, use two pieces of origami paper. Do not cut one sheet in half as directed in these instructions.
The two-sheet shurikens are heavier and more accurate than their single-sheet brethren. They make larger dents in drywall as well.
I corresponded for a while with Robert Lang in the mid-90s about this. I provided him with a handwaving proof of one of his conjectures (referred to obliquely in the 'Art of Origami' paragraph). This is only of historical interest now, but its still out there on the net:
( incidentally all the origamis produced by the method in this paper do actually fold flat, and look like little mountain ranges with a long open pocket at their base)
http://origami.kvi.nl/articles/circles.ps
As it turns out, a more concrete, and practical proof had been published in Japanese (tiling the plane with both triangles and quadrilaterals, not just triangles as in my paper). Some mathematicians in the states were sufficiently intrigued by my description of this on sci.math to have a closer look into paper folding, and came up with a proof that deciding if a given pattern of folds is flat-foldable is actually NP-complete.
All kudos to Robert. He has really put a lot of hard science into his origami programs and he is a truly impressive folder. I would recommend his book 'Origami Sea Animals' to anyone who wants their jaw to drop.
-Baz
Is there? Or is it rather that there is plenty of science in art. Generally, research shows that art itself, if generally accepted to be "good", harks back to some scientific principle. Like most portraits having part of the eye along the central vertical axis, etc. It's all about geometry and natural forms, which all come down to science of molecule binding, the way atoms arrange themselves, etc.
For more on portraits and face perception, see this link on Amazon, to the book of the study by 3 Scottish postgrads. I saw an exhibition of this at the Scottish National Portrait gallery and it was cool. Lot of science in portrait "art", for sure.
But then... if you're an artist you'd say there was plenty of science in art, and as a scientist the inverse.
What is cool with this origami stuff is that really folding in the natural world (protein folding, etc) predates everything by several million years. Now they're playing catchup, and it's getting really interesting.
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Well, as far as I know, "true" origami is made with no cuts at all on the paper. If cuts were to be used on the paper for creating an origami, it would be so far easier to create shapes.
And as far as I can remember, some 30 years ago, a computer was used to create feasible origamis. Just crunching numbers, generating origamis, and all that could not be made were discarded. Sorry, no links on that, it was taken from a book.
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