The art of origami has received a considerable amount of mathematical study. Questions regarding an origami model's flat-foldability (whether the model can be flattened without damaging it) are considered.

The capability of origami to solve mathematical equations is of interest as well. E.g. the classical construction problems of geometry - to trisect an arbitrary angle or to construct a cube of double volume, given an arbitrary cube - are proven to be unsolvable using straightedge and compass but can be constructed using (very few even) Origami folds. To put this in more algebraic terms, not only square roots but also cube roots can be constructed, hence also all nested terms using them. As one consequence, polynomial equations of degree up to four can be solved by Origami folds. The full scope of Origami-constructible algebraic numbers is as of yet unknown, e.g. whether it even encompasses fifth or still higher degree polynomial roots.

Folding a flat model from a crease pattern has been proven by Marshall Bern and Barry Hayes to be NP complete. [1] (http://citeseer.ist.psu.edu/bern96complexity.html)

Huzita's axioms are one important contribution to this field of study.

The problem of rigid origami ("if we replaced the paper with sheet metal and had hinges in place of the crease lines, could we could still fold the model?") has great practical importance. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.

External links

• Origami Mathematics Page (http://merrimack.edu/~thull/OrigamiMath.html) by Dr. Tom Hull (http://merrimack.edu/~thull/)
• Rigid Origami (http://merrimack.edu/~thull/rigid/rigid.html) by Dr. Tom Hull (http://merrimack.edu/~thull/)