What Does Qualitative Spatial Knowledge Tell About Origami Geometric Folds?

Abstract

Origami geometry is based on a set of 7 fundamental folding operations. By applying a well-chosen sequence of the operations, we are able to solve a variety of geometric problems including those impossible by using Euclidean tools. In this paper, we examine these operations from spatial qualitative point of view, i.e. a common-sense knowledge of the space and the relations between its objects. The qualitative spatial representation of the origami folds is suitable for human cognition when practicing origami by hand. We analyze the spatial relations between the parameters of the folding operations using some existing spatial calculus. We attempt to divide the set of possible values of the parameters into disjoint spatial configurations that correspond to a specific number of fold lines. Our analyses and proofs use the power of a computer algebra system and in particular the Grobner basis algorithm.