AN APPLICATION OF A THEOREM OF ALTERNATIVES TO ORIGAMI

Abstract

Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in \mathbb{R}². So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale's theorem of alternatives is useful for the study of twist fold.