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# Kawasaki's theorem: Wikis

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# Encyclopedia

Updated live from Wikipedia, last check: May 19, 2013 18:08 UTC (50 seconds ago)

Kawasaki's theorem is a theorem in the mathematics of paper folding that gives a criterion for whether a given crease pattern is locally flat-foldable.

## Statement of the theorem

Let v be a vertex of degree 2n in a single vertex fold and let α1, α2, ⋯, α2n be the consecutive angles between the creases. Then v is a flat vertex fold if and only if

$\alpha _1 - \alpha _2 + \alpha _3 - \alpha _4 + \cdots - \alpha _{2n} = 0.\,$

That is basically saying, if you take the angle measurement of every other angle around a point and add them up, the sum will be 180 degrees.

## References

• Hull, T. "MA 323A Combinatorial Geometry!: Notes on Flat Folding." [1]