Mathematics of paper folding
|
|
The art of paper folding or origami has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it) and the use of paper folds to solve mathematical equations.
Some classical construction problems of geometry--trisecting an arbitrary angle, or doubling the volume of an arbitrary cube--are proven to be unsolvable using straightedge and compass, but can be solved using only a few paper folds. Paper folds can be constructed to solve square roots and cube roots; fourth-degree polynomial equations can also be solved by paper folds. The full scope of paper-folding-constructible algebraic numbers (e.g. whether it encompasses fifth or higher degree polynomial roots) remains unknown.
The problem of rigid origami, treating the folds as hinges joining two flat, rigid surfaces such as sheet metal, 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.
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.
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/)
- Origami & Math (http://www.paperfolding.com/math/) by Eric M. Andersen (http://www.paperfolding.com/email/)