Origami as a Tool for Mathematical Investigation and Error Modelling in Origami Construction

Origami is the ancient Japanese art of paper folding. It has inspired applications in industries ranging from Bio-Medical Engineering to Architecture. This thesis reviews ways in which Origami is used in a number of fields and investigates unexplored areas providing insight and new results which may lead to better understanding and new uses. The OSME conference series arguably covers most of the research activities in the field of Origami and its links to Science and Mathematics. The thesis provides a comprehensive review of the work that has been presented at these conferences and published in their proceedings. The mathematics of Origami has been explored before and much of the fundamental work in this field is presented in chapter 3. Here an attempt is made to push the bounds of this field by suggesting ways in which Origami can be used as a mathematical tool for in-depth exploration of non trivial problems. A particular problem we consider is the 4-colour theorem and its proof. Looking at some well known methods for producing angles and lengths mathematically the thesis also explores how accurate these might be. This leads to the surprisingly unstudied field of error modelling in Origami. Errors in folding processes have not previously been looked at from a mathematical point of view. The thesis develops a model for error estimation in crease patterns and a framework for error modelling in Origami applications. By introducing a standardised error into alignments, uniform error bounds for each of the one-fold constructions are generated. This defines a region in which a crease could lie in order to satisfy the alignments of a given fold within a specified tolerance. Analysis of this method on some examples provides insight into how this might be used in multi-fold constructions. An algorithm to that effect is introduced.