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."

Everything can be related to math.

[localghost (659616)]

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

Re:Everything can be related to math.

[TheBoostedBrain (622439)]

In the end... you can reduce everything to 0's and 1's.... and logic operators...

Re:Everything can be related to math.

[stefanlasiewski (63134)]

Yes, but you can break the logic operators into even smaller 1's and 0's...

The plus sign is simply two 1's criss-crossing each other.

The multiplication sign is the same thing as the plus sign, but at a 45-degree angle.

The division sign is a sideways '1' with very small 0's above and below it...

Re:Everything can be related to math.

[localghost (659616)]

Those aren't logic operators, those are arithmetic operators. Logic operators are AND (&), OR (|), NOT (!), and XOR (^). There are a few other less common ones too, but they don't have any symbols I'm familiar with.

Even the c0ffee you like

[bstadil (7110)]

110000001111111111101110

Re:Everything can be related to math.

[by Anonymous Coward]

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.

[by Anonymous Coward]

Imaginary numbers are part of math.

Re: Pi

[Kargan (250092)]

"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

[Dylan Zimmerman (607218)]

Well, they are wrong. There IS a pattern to it. Just not in decimal. There is a formula that you can use to get any digit of the hexidecimal expansion of Pi without calculating the previous digits. This has been known for years.

Re: Pi

[Omkar (618823)]

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...

Re: Pi

[Bill Currie (487)]

what about this fun pattern?

1 1 2 3 5 8 13 21 ...

ie, the fibanocci series. Definitly non repeating but most definitly a pattern. Also happens to be easilly computable.

f(x) = (g**x - (g**-x)*e**-(j*pi*x))/sqrt(5)

where g is the golden mean (1.618... or (sqrt(5)+1)/2). And yes, that formula allows you to compute the points in between fibanocci numbers. You get a neat 3d logarithmic spiral that follows an exponential curve.

Re: Pi

[Dylan Zimmerman (607218)]

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.

the pattern of pi

[js7a (579872)]

This is a good page on the pattern of pi:
http://fabrice.bellard.free.fr/pi [bellard.free.fr]

And try this one if you can view raw postscript [cecm.sfu.ca].

Re: Pi

[Ed Avis (5917)]

No repeating pattern does not mean no formula. Take the number .010110111011110111110... where you have groups of 1 digits getting one digit longer each time. This is an irrational number in that it can't be represented as M/N where M and N are integer. But clearly it's possible to write a formula to calculate the digit at a given position.

Although what matters is not finding *a formula* but an 'efficient' formula in some sense. The digits of pi are certainly computable and you can write a program to g

/.'d after 0 posts

[Madsci (616781)]

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

Re:/.'d after 0 posts

[localghost (659616)]

That would imply that either both the website and slashdot are zero, or that they are opposites. Perhaps this:

lim responsiveness = 0
hits->slashdot_users

Huh?

[MrP- (45616)]

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

The two are *definitely* related

[Spazholio (314843)]

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. =)

Re:The two are *definitely* related

[stefanlasiewski (63134)]

Fuck, and I've been recycling all of my wadded up paper.

Hell, instead of wadding up those "Thank you for submitting your resume. You will be contacted if your skills match the job requirements." type of letters in anger and frustration, I could be selling them for $10!!!

And I'll offer more then just wadded oragami like that cheapo. I mean the real stuff: paper wads, shredded paper, paper that I ripped into a million pieces, dipped in whiskey, set on fire and spit on the dead, charred remains.

Real emotio

Not what I read

[Beowulfto (169354)]

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.

Re:Not what I read

[prockcore (543967)]

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.

I dunno, maybe graph the projectile of a fluid?

This would make learning a little more fun...

[dWhisper (318846)]

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?

[by Anonymous Coward]

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.

Re:Orgasms and Math?

[napir (20855)]

Orgasms are only NP-complete in a threesome (3-CNF-SAT). It has been shown that the task can be completed in polynomial time when the conjunction is only between 2 entities (2-CNF-SAT). [see Kama Sutra (translated title: Algorithms) as interpreted by CLRS, exercise 34.4-7]

Another Link

[feed_me_cereal (452042)]

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.

Re:Another Link

[Wingie (554272)]

Ahh, her origami models for her undergrad math thesis still floats gloriously in the Amherst College math building. Here's another link: http://web.merrimack.edu/hullt/OrigamiMath.html Tom's a graph theorist who's been studying this subject basically for as long as mathematics and origami were linked. There are some very interesting stuff there, like curricula to courses involving origami that he's taught.

Origami pick-up lines

[sssmashy (612587)]

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. ;-)

Of Course It's in NV

[neurostar (578917)]

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 it's held in Nevada. If the line fails, you hit up the whore-house down the road.

Repeat to yourself: "Location, location, location."

Re:Origami pick-up lines

[Zirnike (640152)]

I picked up some decent quality stuff from AC Moore. Don't know if there are any in your area...

If you have access to a decent paper cutter, some wrapping paper makes good folding paper, as well.

And be really careful... I thought that was handy, too, until I started doing complex models. My first try on a rhino tore about 1/2 way through because of too-strong creasing. Not that I've gotten it right yet, but still.

Computational Origami and protein folding

[megazoid81 (573094)]

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...

[bazmonkey (555276)]

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.

[Flat Feet Pete (87786)]

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

[mrklin (608689)]

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...."

[Tablizer (95088)]

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

[xYoni69x (652510)]

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!?!?!

[heldlikesound (132717)]

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

[IvyMike (178408)]

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".)

Re:Modern origami artists familiar with math

[Our Man In Redmond (63094)]

Interesting that you should mention Engel. The introduction to his book Origami From Angelfish To Zen [bestwebbuys.com] deals with the mathematical aspects of origami, including its fractal aspects.

ok

[ramzak2k (596734)]

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

origami mathematics

[n3k5 (606163)]

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

[dh5fbr (209173)]

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?

[by Anonymous Coward]

I bet his server is folding right now!

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

IQ Light

[KrunZ (247479)]

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.

Origami + Math = Tom Hull

[Parthenogeny (577801)]

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 ?

[dorfsmay (566262)]

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...

Flexagon

[msheppard (150231)]

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

[pongo000 (97357)]

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.

Re:come on, michael...

[billstr78 (535271)]

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

[FatalTourist (633757)]

It's math dammit! We're the US, we know these things! If you don't agree we might have to come over there and liberate the English language from the evil plural maths.

And we might possibly liberate your oil too.

Re:Nifty

[Black Copter Control (464012)]

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].