Kawasaki's theorem, also called the Kawasaki-Justin theorem, is a result in the mathematics of paper folding that characterizes when a single-vertex crease pattern can be folded flat. It states that such a pattern is flat-foldable if and only if alternately adding and subtracting the angles between consecutive creases around the vertex produces a sum of zero. Crease patterns with more than one vertex do not follow this simple rule, and deciding whether they fold flat is an NP-hard problem.
Facts
StatementA single-vertex crease pattern is flat-foldable if and only if the alternating sum of the angles of consecutive folds around the vertex is zero. 2 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Kawasaki's theorem (Wikipedia)
Sources
1. Wikipedia: Kawasaki's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
It states that the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero.
2. Kawasaki's theorem (Wikipedia)
Statement
the pattern is flat-foldable if and only if alternatingly adding and subtracting the angles of consecutive folds around the vertex gives an alternating sum of zero.
In Branch: Discrete Geometry, Lead section
Kawasaki-Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single
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