An Axiomatic Approach to Error Modelling in Origami Constructions

Origami is the ancient art of paper folding. In the last century it has become popular around the world. As well as creating beautiful artistic models, many have looked into the mathematical and physical properties underpinning Origami and how it can be used in real world applications. These include collapsible tents and folding air-bags, folding solar panels of satellites and other artifacts of the space industry to name a few. Indeed, it is increasingly becoming a ubiquitous tool in engineering, architecture, bioscience, teaching, computing and many more fields.

Accuracy in Origami is very important, not just when an artist is making a model for an exhibition or display, but also, when a machine is producing a folded product. For example, if a machine is producing a folded box then its stacking ability might be affected by inaccuracies in folding. In real world applications of folding we have that every fold will be erroneous as, although this error might be tiny there is always an error. The concept of error modelling in Origami has not been looked at from a mathematical perspective.

Although many Origami artists will be able to demonstrate methods to reduce errors these tricks are mainly created through experience rather than using a mathematical basis. By looking at this problem from the ground up we aim to prove or disprove some of these using mathematical principles and also to be able to find others which are not yet known. We base our model on 'one-fold axiomatic construction', which is a model of folding based on generating one fold at a time without measuring.