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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."
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In the end... you can reduce everything to 0's and 1's.... and logic operators...
-- When did Ignorance Become a Point of View?
There's a page here 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 a little app that puts six pictures onto a foldable template
With crossed-eyes, I soon learned to both admire and curse Escher's briiliance.
The Poincare Conjecture was proven 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.)
void*x=(*((void*(*)())&(x=(void*)0xfdeb58)))();
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 (of Huffman compression fame) was into origami.
Lang has a pretty cool program called TreeMaker which lets him specify a model's "base" characteristics (like a stick figure) and algorithmically produces a fold pattern! Lang also has some of the most fiendishly complex origami I've ever attempted. (And yes, I have to say "attempted" on most of his insect models, not "completed".)
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..
"Consider how lucky you are that life has been good to you so far. Alternatively, if life hasn't been good to you so far
"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.
Palaces, barricades, threats, meet promises
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.
but what do i know, i'm just a model.
Once on a scout trip a guy was trying to show us how to make this oktaeder out of this simple parts - 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 ;-)
I had a hands on expirience when me and my girlfriend should assemble our 16-pieces IQ-light. It did seem like she liked my lecture about graph theory and geometric algebra and was more focus on the new lamp.
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:h tml
http://web.merrimack.edu/hullt/OrigamiMath.
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.
Fun Stuff
Never have I seen math and paper folding get more freakishly kewl than this:
Flexagons. For a real challanager, make a hexaflexagon.
M@
Krispy Cream is people
A finite, repeating pattern, yes.
Try this for a pattern:
0.10203040506070809010011012013...etc.
I don't *think* this is rational, but you'd have to admit there is a pattern and that it won't repeat. Further, because of the pattern in this number, it can be calculated what digit is at any position of the number without examining all the previous digits. This will be left as an exercise for the reader.
t
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.
Bill - aka taniwha
--
Leave others their otherness. -- Aratak
About 10 years ago, a friend of mine named Joseph Wu 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.
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.
OS Software is like love: The best way to make it grow is to give it away.