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The Japanese art of paper folding to make 3-dimensional objects. Cube Duplication and Trisection of an Angle can be solved using origami, although they cannot be solved using the traditional rules for Geometric Constructions.
See also Folding, Geometric Construction, Stomachion, Tangram
References
Andersen, E. ``Origami on the Web.''
http://www.netspace.org/users/ema/oriweb.html.
Eppstein, D. ``Origami.''
http://www.ics.uci.edu/~eppstein/junkyard/origami.html.
Geretschläger, R. ``Euclidean Constructions and the Geometry of Origami.'' Math. Mag. 68, 357-371, 1995.
Gurkewitz, R. and Arnstein, B. 3-D Geometric Origami. New York: Dover, 1996.
Kasahara, K. Origami Omnibus. Tokyo: Japan Publications, 1988.
Kasahara, K. and Takahara, T. Origami for the Connoisseur. Tokyo: Japan Publications, 1987.
Palacios, V. Fascinating Origami: 101 Models by Alfredo Cerceda. New York: Dover, 1997.
Pappas, T. ``Mathematics & Paperfolding.'' The Joy of Mathematics.
San Carlos, CA: Wide World Publ./Tetra, pp. 48-50, 1989.
Row, T. S. Geometric Exercises in Paper Folding. New York: Dover, 1966.
Tomoko, F. Unit Origami. Tokyo: Japan Publications, 1990.
Wu, J. ``Joseph Wu's Origami Page.'' http://www.origami.vancouver.bc.ca/.