Origami - is there anything they can't do?

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''Paper folds itself into a natural equilibrium form depending on its creases.'' [source] More info here.

How can I fold paper along a curve?
Examples:
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''Curved Folding'' [source]

And if you can download it, check out this one: "Curvature and Creases: A Primer on Paper" [source]
And here are some examples.


Free software to create origami: tree maker.

Origami are connected to interesting and complex problems in math and also chemistry.
''Computational Origami
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Lang had already developed algorithms to flatten a set of polygons, and he applied them to a computer simulation of how to flatten the 3-D polyhedron shape of an inflated air bag.
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The air-bag design was based on an algorithm Lang calls the "universal molecule," which flattens a set of polygons so their edges remain aligned to one another.
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Erik Demaine, a 22-year-old professor of electrical engineering and computer science at MIT, started folding paper at age 6 and developed that hobby into the study of the mathematics of folded forms.
Demaine now studies folds in proteins, the basic building blocks of life. He believes that computational origami could fight diseases that are currently incurable, such as mad cow disease, which are caused by proteins that have what he calls "bad folds."
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