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Space Graph: Properties of 2-D Space in Paper Folding

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Title: Space Graph: Properties of 2-D Space in Paper Folding
Authors: Niimoto, James
Advisor: Leineweber, Spencer
Issue Date: May 2012
Abstract: This doctorate project thesis explores space within the context of flat paper folding, spatial systems, and geometry in a 2‐Dimensional format. This thesis considers that space acts as an interdependent feature with the configurations of physical matter. The term “paper folding”, rather than origami, is used as the preferred term. Although both concepts are considered interchangeable by the paper folding community, origami has specific cultural associations which are outside the scope of this thesis. This thesis shows how the information of space is structurally contained in the layering process in 2‐Dimensions of paper folding. Space can be visualized into chunks or parts not by slicing space physically but by understanding it through folding. The properties of 2‐Dimensional space are explored in the flat paper folding process by visualizing the folding cycle through concyclic graphs and hyperplanes. The exploration is primarily conducted through a nominal size, single isometric square sheet of paper, which cannot be cut nor glued, and must be flat‐foldable into 2‐Dimensional form. The graphs are taken through the entire paper folding cycle. As the layering process is of primary importance, a translucent paper medium is used track changes during folding. The primary basis for this thesis is that space and physical form, or object, share an interdependent relationship. The experiment is based on three core ideas. First, space can be represented physically through geometry as a line, more specifically, a hyperplane. Second, space and the object represented in the folding process must remain isometric or continuous, and cannot be physically cut. And third, paper has two operative sides, one positive (front) and the other negative (reverse). The research for this thesis is based on contemporary literature and theory, and acknowledges the possibility that other relevant and valid knowledge of space may exist from other sources. There are no special facilities or equipment which is used for this work, nor does it require any human or biological subjects, or samples for study. One method proved particularly helpful in organizing many of the initial questions related to the research problem, TRIZ Analysis. TRIZ is a step‐by‐step methodology specifically developed to address ill‐defined topics. Genrich Altshuller the developed the method of TRIZ (Teoriya Resheniya Izobretatelskikh Zadatch) or the Theory of Inventive Problem Solving during the 1950s.2 Altshuller discovered that patterns of technological development exist in virtually known scientific and technical discovery. Altshuller discovered that the patterns of technical knowledge followed a time‐dependent process, where both the entire life‐cycle of technological development or scientific ideas could be taken into account and could also be used to predict its next stages. The generalized principles on which TRIZ is based can be applied to virtually any field of study. Although the methodology is currently used mainly in the science and engineering fields, there are several examples which TRIZ is used in architecture. Examples include those from Joe A. Miller3, Darrell Mann’s Computer Based TRIZ‐Systematic Innovation Methods for Architecture4 and 40 Inventive (Architecture) Principles with Examples.5 For a more detailed description of TRIZ the reader may consult the TRIZICZS reference. To determine where each area of study is plotted along the evolutionary graph their technological states are compared through the list of evolutionary steps listed below. As this may be a first application of TRIZ to paper folding and space, the conclusions are basically observations based on experience during the doctorate thesis project. The Evolutionary graph, Figure A is based on 5 time‐dependent stages where any subject can be graphed and compared with other related studies. The graph is created from a selection of 40 technological patterns, based on physical behavior, 21 of which were pre‐selected for this analysis. The closest area of study, at least in architectural terms, the context of which this thesis is written, isan area of spatial analysis called space syntax. The pink graph describes general spatial analyses, the green shaded area shows the space syntax plot, while the purple area show the graph of paper folding. The white areas indicate untapped potential of all respective fields. The Evolutionary Graph shows that the areas of highest potential of the paper folding model include object segmentation, mechanic substitution, and color changes.There are five areas of potential in terms of how the research problem might be approached, these include: 1) space segmentation, 2) object segmentation, 3) mechanics substitution, and 4) color changes. It was determined that a mirror line or hyperplane could be used in combination with the features identified in the Evolutionary graph to approach the thesis problem. 2 Gordon Cameron. TRIZICS, CreateSpace, 2010. 3 Joe. A Miller. TRIZ Solutions for Systems Dynamics Models of A Small Community Downtown Revitalization Project. TRIZCONN 2004, Seattle, 2004. 4 Darrell Mann and Connal O Cathain. Systematic Innovation Methods For Architects. University of Bath, Bath: 2001. 5 Darrell Mann and Connal O Cathain. 40 Inventive (Architecture) Principles with Examples. University of Bath, Bath: 2001.
Pages/Duration: 150 pages
URI/DOI: http://hdl.handle.net/10125/45694
Appears in Collections:2012



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