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Origami Science & ORIGAMI SCIENCE & ART 1994 Otsu Shiga Japan Proceedings of the Second International Meeting of Origami Science and Scientific Origami TECHNISCHE INFORMATIONSBIBLIOTHEK UNIVERSITATSBIBLIOTHEK HAMNOVER November 29-December 2, 1994 Seian University of Art and Design Otsu, Shiga, Japan TIB/UB Hannover 89 128 083 670 Editors: Koryo Miura Tomoko Fuse Toshikazu Kawasaki Jun Maekawa Contents Preface Koryo Miura, Tomoko Fuse, Toshikazu Kawasaki, and Jun Maekawa I Welcome to Otsu Yoheilzutsu IE For the Second International Meeting of Origami Science and Scientific Origami Kodi Husimi IV Papers Fujimoto Successive Method to Obtain Odd-Number Section of a Segment or an Angle by Folding Operations Humiaki Huzita and Shuzo Fujimoto 1 Towards a Mathematical Theory of Origami Jacques Justin 15 Toshikazu Kawasaki 31 Fold - its Physical and Mathematical Principles Koryo Miura 41 Four-dimensional Origami Koji Miyazaki 51 The Technique to Fold Free Flaps of Formative Art "ORIGAMI" Fumiaki Kawahata 63 The Tree Method of Origami Design Robert J. Lang 73 Folding of Uniform Plane Tessellations Tibor Tarnai 83 Folded and Unfolded Nature Biruta Kresling 93 Similarity in Origami Jun Maekawa 109 Breaking Symmetry: Origami, Architecture, and the Forms of Nature Peter Engel 119 Discrete Symmetric Origami Structures : Dissigami Misha Litvinov 147 Planar Graphs and Modular Origami Thomas Hull 151 Origami-Model of Crystal Structure, II. Spinel and Corundum Structures Shozo Ishihara 161 The Platonic Solids and its Interrelated Solids Shuzo Fujimoto 171 Molecular Modeling of Fullerenes with Modular Origami Louis A. Cuccia , R. Bruce Lennox and Francis M.Y.Ow 181 Envelope-Folding Useful for Chemical Education Shukichi Yamana 189 Finding Convex Deltahedra through Origami Youko Horii 201 Polyhedron Origami: A Possible Formulation by "Simple Units" Miyuki Kawamura 209 Modular Origami Polyhedra Rona Gurkewitz 221 Symmetry in Two-and Three-dimensional Origami with Knotted Tape Heinz Strobl 225 A Study on the Twist in Quadrangular Origami Tubes Noriko Nagata 233 Proposal of a Term Origamics for Plastic Origami - Workless Scientific Origami Kazuo Haga 239 ORIGAMI as an Aid to Understanding Symmetry Groups Junko Nitta 249 HyperGami : A Computational System for Creating Decorated Paper Constructions Michael Eisenberg and Ann Nishioka 259 Using Origami as a Teaching Tool Toshinori Tanaka 269 Teaching Origami to Develop Visual/Spatial Perception Judy Hall 279 Physically Handicapped and Origami Saburo Kase 295 Origamic Architecture Masahiro Chatani 303 Tridimensional Transformations of Paper by Cutting and Folding Ramin Razani 311 Artistic Tiling Problem by Origami Peterpaul Forcher 313 Extruding and Tessellating Polygons from a Plane Chris K. Palmer 323 Hikari-ori Reflective Folding James Minoru Sakoda 333 lines Meeting on a Surface the "MARS" Paperfolding Paulo Taborda Barreto 343 Creative Origami 'Snow Crystals' : Some New Approaches to Geometric Origami Kunio Suzuki 361 Art, Origami and Education John S. Smith 379 Form of Origami Yoshihide Momotani 389 Origami Fractal Kenzo Takei 395 Block Origami System Yoshio Sato 401 Traditional and Technical ( David Brill • 413 Thoughts on the Future of Origami Design : Something Old, Something New Herman Van Goubergen 425 One Crease Origami : Less is More Paul Jackson 431 Image Game Kunihiko Kasahara 441 The Cube Story Told in Modular-Origami Language Tomoko Fuse 451 Movement of Nature and Folding line Structures and Others Akira Yoshizawa 463 Origami and Motivation Thoki Yenn 469 How the Origami Model Explains the Theory of Kikujutsu Toshiyuki Iwasaki 481 The Origins of Origami or the Other Side to Origami Makio Araki 495 The Roots of Origami and its Cultural Background Koya Ohashi 503 Some Observations on the History of Paperfolding in Japan and the West - a Development in Parallel David Lister 511 Another View of the Word "ORIGAMI" Masao Okamura 525 Right Angle Billiard Games and their Solutions by Folding Paper Humiaki Huzita 541 Program A— I Meeting Organization A— V Participating Organizations A— VI About the picture on the cover page Orizuru (Paper crane) is one of representative models in origami. The motif of the picture on the cover page is orizuru too. Square parts in the picture show main structures of orizurus. Straight lines show creases, and arcs and circles lengths of projections..
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