ORIGAMI CONSTRUCTIBLE NUMBERS AND SOLVING THE PROBLEMS OF ANTIQUITY

The Problems of Antiquity, which have challenged and fascinated mathematicians for hundreds of years, include squaring the circle, trisecting the angle, and doubling the cube. Mathematicians of Ancient Greece attempted to solve these problems through the traditional construction methods involving a compass and straightedge. It was discovered in the nineteenth century, however, that these problems are impossible to solve using a compass and straightedge. Surprisingly, it is origami - the ancient art of Japanese paper folding - that holds the key to solving two of these classical problems. The development of the field of origami constructible numbers has led to modern axioms that, when coupled with traditional paper folding techniques, make trisecting the angle and doubling the cube possible. The applications of mathematical origami are seemingly endless, ranging from solving these ancient problems to designing folding space telescopes.