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M. Bern, Barry Hayes (1996)
The complexity of flat origami
J. Justin, G. Pirillo (1992)
Intracommutativity properties for groups and semigroupsJournal of Algebra, 153
R. Randow (2004)
Plaited PolyhedraThe Mathematical Intelligencer, 26
Tom Rodgers (2009)
Spin a Tale
J. Justin (2000)
On a paper by Castelli, Mignosi, RestivoRAIRO Theor. Informatics Appl., 34
A. Glen, J. Justin (2008)
Episturmian words: a surveyArXiv, abs/0801.1655
Consolato Pellegrino (1986)
Aspetti Matematici del Tangram
E. Demaine, M. Demaine (2002)
Recent Results in Computational Origami
David Lister (2009)
Martin Gardner and Paperfolding
J. Justin, Laurent Vuillon
Theoretical Informatics and Applications Return Words in Sturmian and Episturmian Words
Joachim Konig, D. Nedrenco (2015)
Septic equations are solvable by 2-fold origamiarXiv: Algebraic Geometry
G. Deleuze, F. Guattari, B. Massumi (1980)
A Thousand Plateaus: Capitalism and Schizophrenia
E. Demaine, M. Demaine, Joseph Mitchell (1999)
Folding flat silhouettes and wrapping polyhedral packages: new results in computational origamiComput. Geom., 16
Kenneth Manders (2008)
Diagram‐Based Geometric Practice
Roger Alperin (2000)
A Mathematical Theory of Origami Constructions and Numbers
Donovan Johnson (1958)
Paper Folding for the Mathematics Class.American Mathematical Monthly, 65
Kenneth Manders (2008)
The Euclidean Diagram (1995)
R. Harrison, R. Yates (1941)
Tools. A Mathematical Sketch and Model Book.American Mathematical Monthly, 49
E. Demaine, J. O'Rourke (2007)
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
P. Mancosu (2005)
Visualization in Logic and Mathematics
[The final chapter is, of course, not a final conclusion concerning the “fruition” of the mathematics of paper folding: this domain is in a process of continuous development, and its interweaving with computer sciences and computer modeling becomes more and more apparent and prominent. This, of course, raises the question as to how materiality, which earlier functioned partially as a hindering element, is considered; one may wonder, for example, as to the epistemological implications and differences between the twenty-first century mathematical computer models and the nineteenth century mathematical material folded models, but this discussion is beyond the scope of this chapter. What this chapter will attempt to describe is that which can be called the first step of this new, modern movement concerning mathematics and folding-based geometry: the complete axiomatization of this geometry. Though not the single modern point of view with which the mathematics of paper folding has been considered, the attempt to find axioms or basic operations for this geometry, started at the beginning of the twentieth century, bore fruit only towards the end of the 1980s. If Beloch’s interest lay in proving that folding-based geometry is at least as powerful as straightedge and compass geometry, from an algebraic point of view as well as construction-wise, during the mid-1980s, one was interested in finding the basic, fundamental operations from which a folded figure was composed, and by this means, giving this geometry a logical sound basis, the same that straightedge and compass geometry had for centuries.]
Published: May 26, 2018
Keywords: Beloch; Paper Folding; Straightedge; Huzita; Origami Geometry
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