Origami and Math

TheBoostedBrain writes "I found a nice site that explains a little bit about the math in Origami. Origami is one of my favorite hobbies, but I never thought about it being related to science."

Nifty

And everything old is new again. Fascinating art

Re:Nifty

Math and origami aren't that new..

About 10 years ago, a friend of mine named Joseph Wu [origami.as] tried to do his MSc in computing science on computer origami. After a couple of years of trying, his thesis adviser pointed out that some of the mathematical/algorithmic problems he had uncovered were beyond what would be appropriate to a PhD. He's now a professional origami artist [vancouver.bc.ca].

To give you an idea as to his ability, He used to fold $2 bills into mules and leave them as tips for waitresses. Now that the smallest Canadian bill is $5, I'm not sure if he's still doing it. According to an online article, one of his dreams is to produce origami smoke [vancourier.com].

Everything can be related to math.

Sometimes you just have to be creative. Math is everywhere.

Re:Everything can be related to math.

Math is everywhere.

Well, not everywhere.

Math doesn't exist in our President's budget proposal, for example...

Re:Everything can be related to math.

Imaginary numbers are part of math.

Re: Pi

"As it turns out, Pi can be found everywhere, from astronomy to probability to the physics of sound and light. To date it has been calculated to over 51 billion digits, so far with no discernible pattern emerging from its numbers. In fact, the first time that the sequence 123456789 appears, it is over 500 million digits into the ratio. Calculating the digits to millions of decimal places is now used to test computers for bugs in hardware and software (which is how Intel's Pentium found a chip bug a few years ago)." -- from the web site for the movie Pi. [pithemovie.com]

Re: Pi

http://www.lacim.uqam.ca/~plouffe/articles/Miracul ous.pdf

It's a PDF (obviously), but that's the only good way I've found to express the formula.

Re: Pi

Pi is irrational. Pi has been proved irrational long ago. That means there is no repeating pattern. A formula to calculate a digit (in any base) is not a pattern, just a formula. There is still no pattern.

Honestly, some people...

/.'d after 0 posts

Apparently the math goes like this: Origami Website + (/. crowd) = 0

Huh?

How does math relate to the Origami Boulder? [origamiboulder.com] :)

The two are *definitely* related

I've always found that my stress level is directly proportional to the number of times I've tried to fold a goddam pterodactyl or swan or whatever the hell it's supposed to be. I think this guy [origamiboulder.com] has the right idea. =)

Not what I read

Man am I sad. When I saw the headline I wasn't thinking about folding paper, and I couldn't figure out what it had to do with math.

This would make learning a little more fun...

I wish I would have seen something like this when I was going through school. Geometry was my weakest subject, which made visualizing things in Calc and absolute pain. That in turn hurt me in physics when trying to derive motion calculations.

And all of that together eventually turned me into a Information Systems/Business major, because it didn't require math.

Orgasms and Math?

Orgasms and Math?

[/me reads article header again]

Wow! Too much studying. I'm studying for a big compiler exam and was reading this section talking about how to approach things mathematically to help prove a compiler implementation is correct.

When I first saw the title, I thought someone set out how to make an orgasm mathematically correct. I know women do complain about these things and I would be the first to congratulate the geek who could break this magical barrier by using something I can understand better than most things: Math.

Sigh... unfortunately orgasms are an NP-complete task. Something about reachability and satisfiabilty.

Another Link

A math professor [ohio-state.edu] at the school I go to (OSU) also has a page about math and origami. I think she gave a talk over this subject not too long ago at our math club. Anyway, the page has some pictures, notes, and a bunch of relevant links at the bottom.

This whole business turns out to be trivial

Once Wiles proves the Goldbach Conjecture (Journal of the American Mathematical Society, Spring 2019), the entire art of origami ends up reducible to polynomial-time modelling.

Interestingly, Wiles publishes the proof at the age of 68, while residing at the Shady Acres Convalescent Center in Far Rockaway, New Jersey. Perhaps the most important aspect of his discovery is that no, as a matter of fact, mathematicians are not all washed up by age 40. At the time I came back (no pun intended), there was talk of a third Fields Medal for him.

Origami pick-up lines

Origami is one of my favorite hobbies, but I never thought about it being related to science.

I think we've just found a new entry for the "World's Least Effective Pick-Up Lines Competition" held anually in Reno, Nevada.

Of course, in the rare event that the line actually works, you've found every geek's dream: a soul-mate who will never, ever grow bored of you. ;-)

Computational Origami and protein folding

Don't dismiss origami immediately - it could have implications for things like protein folding. As it stands, computing and examining the number of ways a protein can fold is an NP-complete problem. Imagine the insights into molecular biology we might get with further research into the computational complexity of origami.

There's a 21 year old professor at MIT, Erik Demaine [mit.edu] who is interested in computational origami. Check out his page for some interesting papers and a story of some very untraditional education.

Chick magnet, dude...

Dude, don't dismiss origami at all. Chicks love a guy who can work with his hands.

Geeks worldwide, trust me on this one: Learn to massage, do origami, and sketch semi-decent drawings of girls, and you could pick up WHOEVER YOU WANT!!!

::Rests arm on blow-up doll::

Trust me.

Origami for geometrical constructions and a plug.

There's a page here [merrimack.edu] that descsribes Origami folds as an alternative to straight edge and compass contructions. You can trisect the angle using folds, interesting stuff

I should also plug hexaflexagon.sourceforge.net [sourceforge.net] a little app that puts six pictures onto a foldable template

Inorganic chemistry

I remeber many homework assignments/problem sets in my inorganic chemistry class (Cornell '96) that ask ones to find and name all the symmetry in Escher drawings. (It's harder than you think.)

With crossed-eyes, I soon learned to both admire and curse Escher's briiliance.

"for my next trick...."

Origami is one of my favorite hobbies

Impress the slashdot crowd by:

1. Making a Beowulf origami cluster
2. Making a goatse model
3. Profit!

Poincare Conjecture

The Poincare Conjecture [wolfram.com] was proven [wolfram.com] last month. (Maybe.)
If the proof turns out to be correct, all your Origami is mathematically equivalent to a ball (3-sphere).
Conclusion: Nerds (who play with Origami) are now mathematically equivalent to professional sports players (who play games involving a ball). Amazing, isn't it?

(Don't try to explain this to a sports player.)

Never thought of science!?!?!

When i think of Origami, I think of paper cuts, flapping swans, and science.

I usally end up making complex Origami abstract scupltures, which is just another way of saying that I suck at it.

Modern origami artists familiar with math

As it turns out, a lot of the best modern origami artists (in my opinion) are somehow technical: John Montroll and Peter Engel are mathematicians, and Robert Lang is an engineer. Even Dr. David Huffman [sgi.com] (of Huffman compression fame) was into origami.

Lang has a pretty cool program called TreeMaker [origami.kvi.nl] which lets him specify a model's "base" characteristics (like a stick figure) and algorithmically produces a fold pattern! [siam.org] Lang also has some of the most fiendishly complex origami [origami.kvi.nl] I've ever attempted. (And yes, I have to say "attempted" on most of his insect models, not "completed".)

ok

who else read that as Orgasm and math ? i need some sleep..

Is Origami just for paper?

Or could there be and real benafits from folding thin sheet metal using origami techniques, to create an attractive and unually strong structure??

An example would be say a fence with gates.

Imagine how attractive it would be and how resistant to things like strong winds it would be.. you could design it to flex and even bend but to never break, tear or snap..

Its just an "out of box" thought..

Mind you it would be terribly wastefull of materials..

business card cubes

Boy am I glad I hadn't taken out the recycling and gotten rid of more than 1000 old business cards yet.

I have a new-found idle-time project thanks to finding out how to build business card cubes [std.com] via this story :)

Paper folding

This is all cool to know but it doesn't help me with my basic problem of not being able to fold paper in a straight line. Prehaps I'm using the wrong type of paper

Rus

This is funny

I like Origami. Cranes are cool, but what I really like are boulders [origamiboulder.com] and rocks [origamirock.com].

origami mathematics

while it's impossible to solve cube duplication or trisection of an arbitrary angle using just a straightedge (not a marked ruler) and a compass, it can be accomplished utilizing origami. there are a number of recent very powerful results in origami mathematics. i wonder if you could take a sheet of paper and fold together the quadrature of the circle.

Oktaeder out of simply parts

Once on a scout trip a guy was trying to show us how to make this oktaeder [origamiseiten.de] out of this simple parts [12testing.net] - his only problem was to put the 12 pieces together in the right order. Anyhow we had fun and later on I build more complex models out of larger numbers of parts. Try this at home ;-)

Origami Effect?

I bet his server is folding right now!

Thank you, I'll be here all week, try the fish!

IQ Light

I had a hands on expirience when me and my girlfriend should assemble our 16-pieces IQ-light [iqlight.com]. It did seem like she liked my lecture about graph theory and geometric algebra and was more focus on the new lamp.

Maths

Yes, very interesting article. But to quote the post:

"I found a nice site that explains a little bit about the math in Origami. Origami is one of my favorite hobbies, but I never thought about it being related to science."

This is like saying, "I found a site explaining the engineering in cars. I love cars, but I never thought about it it being related to haute cuisine."

-Tez

Origami + Math = Tom Hull

When it comes to Origami and Math I think of Tom Hull right off the bat. After all, he did invent the PHIZZ unit, from which you can make spherical bucky balls. Here, check it out:
http://web.merrimack.edu/hullt/OrigamiMath.h tml

No Klein bottle ?

Hmmmm.... I remember doing mobius [umn.edu] out of paper in topology classes, but somehow we never made a klein bottle [umn.edu].

I read the whole article, they do talk about geometry, they do talk about topology, but nowhere do they show you how to make a klein bottle out of paper...

Knots are great fun too

Knots have been a hobby of mine for years. I was on vacation recently and saw a book (in my all-time favorite bookstore) about the mathmatics of knots [tatteredcover.com].

Fun Stuff

Flexagon

Never have I seen math and paper folding get more freakishly kewl than this:
Flexagons [cinvestav.mx]. For a real challanager, make a hexaflexagon.

M@

Polygons from circles

I teach high school geometry, and believe the only way to learn geometry is by doing. There's an excellent book I use that is also used in many Chicago-area schools called "Wholemovement Geometry," which involves constructing various 3-D polyhedra using only paper plates (the cheaper the better) and tape. No cutting necessary, as the unused parts of the circles are simply extra information that are folded away. Here's a link [depaul.edu] to some of the things you never thought were possible to create from paper plates.

Kawasaki's Theorem

as stated in the article is wrong. Try it - just fold a paper twice in random angles so that the creases meet. The angles will not add up to 180. The author forgot to indicate that n must be odd.

hellbound origami scientists

Origami is one of my favorite hobbies, but I never thought about it being related to science.

The Good Book clearly states in II Meshugginahs 3:16 that paper cannot be creased, heathen. As with Galileo we must threaten these idolatrous reprobates with excommunication unless they recant their immoral paper-fondling! Glory!

Is Math a Science?

Reminds me of something Richard Feynman said about the term 'computer science' being a misnomer. Science is the study of nature through observation, whereas computers and math are human creations and therefore not natural. They were created by us to do useful things and are quite helpful for placing the natural world in terms that are explict and understandable. However, the laws that these disciplines are built from are, in the end, created by us for their utility. Mathematics is changed and altered by our scientific research, but it is morphed to fit by our doing. The new rules were not 'discovered', but created by necessity. It is like a bridge we design to span a particular space. We cannot 'discover' the bridge because it did not exist before we saw a need for it. Math has no carte blanche. When it does not help us illustrate the natural world it is useless, though pretty, mumbo-jumbo- like numerology.

The difference seems subtle, but it is profound. We cannot blindly take math to be the 'language of god'. It is our language and nothing more or less.

Anyone with me?

Another Paper Folding Article

I enjoyed this article [strangehorizons.com]. Not so much math, but some great paper-folding puzzles.

Feynman invented Flexagons...

that were a form of folded triangles on which one could perform flexing operations he found non-trivial to think about. When he was at MIT, I think...before we were born. Martin Gardner of SciAm made them into a fad...

we have this class at my university

We offer a math & origami class at the university where I teach: Origami of Math [elon.edu] It's writing-intensive too, if you can believe that! :) -megan

Re:come on, michael...

I agree, this sum total of the interesting bits of this "Math in Oragami" page is a single proof regarding coloring that is not any more profound that what you would find in a u-grad course on graph theory.

There might be a lot of math in Oragami that impresses 4th graders, but this indeed is not "News for Teacher's Stuff to Assign for Homework".

Re:its maths damn it

This discussion is getting a little off topic, however you are incorrect in saying "maths" is not a word. In Australia "maths" is used without exception to represent mathematics (or even mathamatics, if that's how you're comfortable spelling it), not "math". I guess by your definition, our country is full of anal instructors in a misguided attempt at regularization. Or is that regularisation? So maths looks funny to you; well math looks strange to me. The English language is a work in progress - just look at the annual additions to the OED as an example. Just because a huge chunk of the English-speaking world (North America) says math, doesn't make it an absolute.