DOCSLIB.ORG

El Pliegue En La Arquitectura

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
El Pliegue En La Arquitectura Universidad Politécnica de Madrid Escuela Técnica Superior de Arquitectura El pliegue en la arquitectura The Fold in Architecture Tesis Doctoral Pablo Miguel De Souza Sánchez Máster en teoría, historia y crítica de la arquitectura. Arquitecto. Licenciado en Bellas Artes. Madrid. Junio de 2017 Departamento de Composición Arquitectónica Escuela Técnica Superior de Arquitectura El pliegue en la arquitectura The Fold in Architecture Pablo Miguel De Souza Sánchez Máster en teoría, historia y crítica de la arquitectura. Arquitecto. Licenciado en Bellas Artes. DIRECTORES. D. Rafael García García. Doctor Arquitecto D. Juan Bordes Caballero. Doctor Arquitecto Madrid. Junio de 2017 Tribunal nombrado por el Magfco. y Excmo. Sr. Rector de la Universidad Politécnica de Madrid, el día de de 20 . Presidente: Vocal: Vocal: Vocal: Secretario: Suplente: Suplente: Realizado el acto de defensa y lectura de la Tesis el día de 20 , en la Escuela Técnica Superior de Arquitectura de Madrid. Calificación:………………………………. El PRESIDENTE LOS VOCALES EL SECRETARIO Agradecimientos. A mis directores Juan Bordes Caballero y Rafael García García, sus respectivas investigaciones me han abierto caminos y ayudado a dar respuesta a muchas de las incógnitas que quedaban sin resolver en mi investigación. La publicación de Juan Bordes “La infancia de las vanguardias” y los artículos de Rafael García “Estructuras laminares de hormigón en Holanda y Láminas plegadas de hormigón armado. Realizaciones en España” y el acceso al artículo “La structura come forma” de Luigi Moretti aportado por Rafael, han sido esenciales a la hora de completar el documento aquí presentado, sin esta información no habría sido posible concluir con éxito y enlazar los diferentes capítulos desarrollados en la investigación. A los tutores de las cuatro prácticas de investigación realizadas durante el periodo de formación en las que pude dar forma desde diferentes puntos de vista a esta investigación: José Manuel Barbeito y Manuel De Prada tutores de la asignatura “Sobre la separación de las artes”, Miguel Ángel Baldellou y Ana Estéban Maluenda: “Arquitectura y arquitectos españoles contemporáneos, historia y crítica”, Rafael García: “Documentación y análisis de la arquitectura” y Mª Teresa Valcárce y Roberto Osuna tutores de la asignatura “Las publicaciones periódicas de arquitectura desde 1930 como fuente documental”. A Sophia Vyzoviti, mi supervisora de la estancia de investigación y docencia en la Πανεπιστήμιο Θεσσαλίας (Universidad de Tesalia). Una experiencia inolvidable que me abrió las puertas a un mundo nuevo de posibilidades formales y práctica docente. A mis compañeros de doctorado y máster, en especial a Francisco Casas por aportar sus ideas y conocimientos y haber iniciado esta ruta conmigo. A Ricardo Antón, que sembraste la semilla de la arquitectura en mí. A José Luis Esteban Penelas, mi mentor, me diste el impulso suficiente para acabar mi etapa de formación y la inspiración necesaria para comenzar con esta investigación. A Beatriz, María, Román y Pedro, por su apoyo y ayuda. A mis padres Fernando y Sofía, vuestro amor es mi mejor tesoro. A mis hermanos, Javier, que siempre estará con nosotros e Inés que ha crecido conmigo, vió comenzar este camino compartiendo libros, juegos y música nocturna, y ahora lo acaba haciéndolo suyo. A mi querida esposa Elena, ejemplo de tesón, esfuerzo y comprensión, sin ti no hubiera sido posible completar esta tesis. A todos, Gracias. Resumen. En el último cuarto del siglo XX reconocidos arquitectos y teóricos de la arquitectura como Greg Lynn, José Morales, Manuel Gausa, Juan Carlos Sancho y Sol Madridejos, así como filósofos como Félix Guattari y Guilles Deleuze han encontrado múltiples vínculos entre el concepto de pliegue, su exploración formal y definición topológica y la creación arquitectónica. El término pliegue abarca una gran variedad de definiciones y aplicaciones en la arquitectura, desde la descripción y utilización estructural de Fred Angerer y Heino Engel y la exploración formal de Farshid Moussavi, hasta la lectura más conceptual y teórica de Peter Eisenman, Greg Lynn y Deleuze. En palabras de Manuel Gausa “hablamos de pliegues, despliegues y repliegues como posibles trayectorias dinámicas. Trayectorias a- escalares entre estructuras y organizaciones, entre dispositivos y ciudades, entre escenarios y proyectos, referidas a geometrías evolutivas (formaciones rizomáticas -en forma de raíz-, despuntes y estirones, arracimamientos -en forma de racimo-, entramados y enrroscamientos, fluctuaciones, reversas y quiebros)”. La finalización en el año 2002 de las obras de la terminal internacional del puerto de Yokohama en Japón, dirigidas por Alejandro Zaera y Farshid Moussavi -FOA-, y la construcción de la Capilla de Valleacerón de los arquitectos Sol Madridejos y Juan Carlos Sancho Osinaga realizada en el año 2000 en Almadenejos, Castilla-La Mancha, trajeron a escena una práctica común entre los arquitectos y estudiantes durante el siglo XX, la utilización arquitectónica de pliegues de elementos superficiales planos inspirados en los patrones desarrollables del origami, el arte japonés de la papiroflexia. ¿Qué obras de arquitectura se han visto inspiradas en sus composiciones formales por el arte del origami japonés? ¿Cómo y cuándo la arquitectura integró los patrones geométricos de la papiroflexia? ¿Cuáles son los diferentes mensajes que evoca el pliegue arquitectónico? El presente trabajo trata de entender y explorar el origen de los recursos y mecanismos de formalización arquitectónica inspirados en el origami. Busca recapitular el conocimiento adquirido en las diferentes experiencias arquitectónicas para analizar y sintetizar tanto sus configuraciones morfológicas como su contenido semántico, destacando las relaciones conceptuales y formales entre el origami y la arquitectura. En conclusión, este documento se constituye como un estudio de metodología histórica, de caso y experimental, de las variables semánticas, sintácticas y morfológicas, derivadas del uso de patrones de superficies plegadas en la arquitectura contemporánea, desde estructuras estáticas de superficies plegadas hasta arquitecturas cinéticas e interactivas de diseño paramétrico. Palabras clave: origami, papiroflexia, pliegue, origami y arquitectura, pliegue arquitectónico, papiroflexia abstracta, arquitecturas plegadas, la levedad del pliegue, estructuras laminares plegadas, láminas plegadas de hormigón armado, morfologías estereométricas facetadas, configuraciones morfológicas plegadas, arquitecturas paramétricas, geometrías dinámicas, estructura como forma. Abstract. In the last quarter of the 20th century, renowned architects and architecture theorists such as Greg Lynn, José Morales, Manuel Gausa, Juan Carlos Sancho and Sol Madridejos, as well as philosophers like Felix Guattari and Guilles Deleuze have found multiple links between the concept of folding, its formal exploration and the topological definition and architectural creation. The term "fold" covers a wide variety of definitions and applications in architecture, from the structural description and use of Fred Angerer and Heino Engel and the formal exploration of Farshid Moussavi, to the more conceptual and theoretical reading of Peter Eisenman, Greg Lynn and Deleuze. In the words of Manuel Gausa "we speak of crease, deployments and folds as possible dynamic trajectories. A-scalar trajectories between structures and organizations, between devices and cities, between scenarios and projects, referring to evolutionary geometries (rhizomatic formations, shoots and spurs, clusters, trusses and twists, fluctuations, revesas and squares). The completion in 2002 of the building of the Yokohama international port terminal in Japan, led by Alejandro Zaera and Farshid Moussavi -FOA-, and the construction of the Chapel of Valleacerón by the architects Sol Madridejos and Juan Carlos Sancho Osinaga in the year 2000 in Almadenejos, Castilla-La Mancha, brought to the scene a common practice between architects and students during the twentieth century, the architectural use of folds of flat surface elements inspired by the crease patterns of origami, the Japanese art of paperfolding. What works of architecture have been inspired in their formal compositions by the art of origami? How and when did architecture integrate the geometric patterns of origami? What are the different messages that evokes the architectural fold? The present work tries to understand and to explore the origin of the resources and mechanisms of architectonic morphogenesis inspired by origami. It seeks to recapitulate the knowledge acquired in the different architectural experiences to analyze and synthesize both its morphological configurations and its semantic content, highlighting the conceptual and formal relations between origami and architecture. In conclusion, this document constituted an historical, case study and experimental research methodology of the semantic, syntactic and morphological variables of the use of folded patterns derived from origami in contemporary architecture, from folded plate static structures, to kinetic and interactive architectures of parametric design. Keywords: Origami, origami and folding, origami and architecture, architectural folding, abstract origami, folded architectures, the lightness of fold, folded laminated structures, reinforced concrete folded sheets, faceted stereometric morphologies, folded morphological configurations, dynamic geometries, Shape ÍNDICE ÍNDICE INTRODUCCIÓN 6 APROXIMACIÓN CONCEPTUAL 7 METODOLOGÍA
Load more

Recommended publications
  • Pleat Folding, 6.849 Fall 2010
    Demaine, Demaine, Lubiw Courtesy of Erik D. Demaine, Martin L. Demaine, and Anna Lubiw. Used with permission. 1999 1 Hyperbolic Paraboloid Courtesy of Jenna Fizel. Used with permission. [Albers at Bauhaus, 1927–1928] 2 Circular Variation from Bauhaus [Albers at Bauhaus, 1927–1928] 3 Courtesy of Erik Demaine, Martin Demaine, Jenna Fizel, and John Ochsendorf. Used with permission. Virtual Origami Demaine, Demaine, Fizel, Ochsendorf 2006 4 Virtual Origami Demaine, Demaine, Fizel, Ochsendorf 2006 Courtesy of Erik Demaine, Martin Demaine, Jenna Fizel, and John Ochsendorf. Used with permission. 5 “Black Hexagon” Demaine, Demaine, Fizel 2006 Courtesy of Erik Demaine, Martin Demaine, and Jenna Fizel. Used with permission. 6 Hyparhedra: Platonic Solids [Demaine, Demaine, Lubiw 1999] 7 Courtesy of Erik Demaine, Martin Demaine, Jenna Fizel, and John Ochsendorf. Used with permission. Virtual Origami Demaine, Demaine, Fizel, Ochsendorf 2006 8 “Computational Origami” Erik & Martin Demaine MoMA, 2008– Elephant hide paper ~9”x15”x7” Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/Computational/. 9 Peel Gallery, Houston Nov. 2009 Demaine & Demaine 2009 Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/Limit/. 10 “Natural Cycles” Erik & Martin Demaine JMM Exhibition of Mathematical Art, San Francisco, 2010 Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/NaturalCycles/. 11 Courtesy of Erik Demaine and Martin Demaine. Used with permission. See also http://erikdemaine.org/curved/BlindGlass/. Demaine & Demaine 2010 12 Hyperbolic Paraboloid Courtesy of Jenna Fizel. Used with permission. [Demaine, Demaine, Hart, Price, Tachi 2009/2010] 13 θ = 30° n = 16 Courtesy of Erik D.
    [Show full text]
  • Constructing Points Through Folding and Intersection
    CONSTRUCTING POINTS THROUGH FOLDING AND INTERSECTION The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Butler, Steve, Erik Demaine, Ron Graham and Tomohiro Tachi. "Constructing points through folding and intersection." International Journal of Computational Geometry & Applications, Vol. 23 (01) 2016: 49-64. As Published 10.1142/S0218195913500039 Publisher World Scientific Pub Co Pte Lt Version Author's final manuscript Citable link https://hdl.handle.net/1721.1/121356 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ Constructing points through folding and intersection Steve Butler∗ Erik Demaine† Ron Graham‡ Tomohiro Tachi§ Abstract Fix an n 3. Consider the following two operations: given a line with a specified point on the line we≥ can construct a new line through the point which forms an angle with the new line which is a multiple of π/n (folding); and given two lines we can construct the point where they cross (intersection). Starting with the line y = 0 and the points (0, 0) and (1, 0) we determine which points in the plane can be constructed using only these two operations for n =3, 4, 5, 6, 8, 10, 12, 24 and also consider the problem of the minimum number of steps it takes to construct such a point. 1 Introduction If an origami model is laid flat the piece of paper will retain a memory of the folds that went into the construction of the model as creases (or lines) in the paper.
    [Show full text]
  • Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi
    HEXAFLEXAGONS, PROBABILITY PARADOXES, AND THE TOWER OF HANOI For 25 of his 90 years, Martin Gard- ner wrote “Mathematical Games and Recreations,” a monthly column for Scientific American magazine. These columns have inspired hundreds of thousands of readers to delve more deeply into the large world of math- ematics. He has also made signifi- cant contributions to magic, philos- ophy, debunking pseudoscience, and children’s literature. He has produced more than 60 books, including many best sellers, most of which are still in print. His Annotated Alice has sold more than a million copies. He continues to write a regular column for the Skeptical Inquirer magazine. (The photograph is of the author at the time of the first edition.) THE NEW MARTIN GARDNER MATHEMATICAL LIBRARY Editorial Board Donald J. Albers, Menlo College Gerald L. Alexanderson, Santa Clara University John H. Conway, F.R. S., Princeton University Richard K. Guy, University of Calgary Harold R. Jacobs Donald E. Knuth, Stanford University Peter L. Renz From 1957 through 1986 Martin Gardner wrote the “Mathematical Games” columns for Scientific American that are the basis for these books. Scientific American editor Dennis Flanagan noted that this column contributed substantially to the success of the magazine. The exchanges between Martin Gardner and his readers gave life to these columns and books. These exchanges have continued and the impact of the columns and books has grown. These new editions give Martin Gardner the chance to bring readers up to date on newer twists on old puzzles and games, on new explanations and proofs, and on links to recent developments and discoveries.
    [Show full text]
  • The Miura-Ori Opened out Like a Fan INTERNATIONAL SOCIETY for the INTERDISCIPLINARY STUDY of SYMMETRY (ISIS-SYMMETRY)
    The Quarterly of the Editors: International Society for the GyiSrgy Darvas and D~nes Nag¥ interdisciplinary Study of Symmetry (ISIS-Symmetry) Volume 5, Number 2, 1994 The Miura-ori opened out like a fan INTERNATIONAL SOCIETY FOR THE INTERDISCIPLINARY STUDY OF SYMMETRY (ISIS-SYMMETRY) President ASIA D~nes Nagy, lnslltute of Apphed Physics, University of China. t~R. Da-Fu Ding, Shangha~ Institute of Biochemistry. Tsukuba, Tsukuba Soence C~ty 305, Japan Academia Stoma, 320 Yue-Yang Road, (on leave from Eotvos Lot’find Umve~ty, Budapest, Hungary) Shanghai 200031, PR China IGeometry and Crystallography, H~story of Science and [Theoreucal B~ology] Tecbnology, Lmgmsucs] Le~Xiao Yu, Department of Fine Arts. Nanjmg Normal Umvers~ty, Nanjmg 210024, P.R China Honorary Presidents }Free Art, Folk Art, Calhgraphy] Konstantin V. Frolov (Moscow) and lndta. Kirti Trivedi, Industrial Design Cenlre, lndmn Maval Ne’eman (TeI-Avw) Institute of Technology, Powa~, Bombay 400076, India lDes~gn, lndmn Art] Vice-President Israel. Hanan Bruen, School of Education, Arthur L. Loeb, Carpenter Center for the V~sual Arts, Umvers~ty of Hallo, Mount Carmel, Haffa 31999, Israel Harvard Umverslty. Cambridge, MA 02138, [Educanon] U S A. [Crystallography, Chemical Physics, Visual Art~, Jim Rosen, School of Physics and Astronomy, Choreography, Music} TeI-Av~v Umvers~ty, Ramat-Avtv, Tel-Av~v 69978. Israel and [Theoretical Physms] Sergei V Petukhov, Instnut mashmovedemya RAN (Mechamcal Engineering Research Institute, Russian, Japan. Yasushi Kajfl~awa, Synergel~cs Institute. Academy of Scmnces 101830 Moskva, ul Griboedova 4, Russia (also Head of the Russian Branch Office of the Society) 206 Nakammurahara, Odawara 256, Japan }Design, Geometry] }B~omechanlcs, B~ontcs, Informauon Mechamcs] Koichtro Mat~uno, Department of BioEngineering.
    [Show full text]
  • Origamizing Polyhedral Surfaces Tomohiro Tachi
    1 Origamizing Polyhedral Surfaces Tomohiro Tachi Abstract—This paper presents the first practical method for “origamizing” or obtaining the folding pattern that folds a single sheet of material into a given polyhedral surface without any cut. The basic idea is to tuck fold a planar paper to form a three-dimensional shape. The main contribution is to solve the inverse problem; the input is an arbitrary polyhedral surface and the output is the folding pattern. Our approach is to convert this problem into a problem of laying out the polygons of the surface on a planar paper by introducing the concept of tucking molecules. We investigate the equality and inequality conditions required for constructing a valid crease pattern. We propose an algorithm based on two-step mapping and edge splitting to solve these conditions. The two-step mapping precalculates linear equalities and separates them from other conditions. This allows an interactive manipulation of the crease pattern in the system implementation. We present the first system for designing three-dimensional origami, enabling a user can interactively design complex spatial origami models that have not been realizable thus far. Index Terms—Origami, origami design, developable surface, folding, computer-aided design. ✦ 1 INTRODUCTION proposed to obtain nearly developable patches represented as RIGAMI is an art of folding a single piece of paper triangle meshes, either by segmenting the surface through O into a variety of shapes without cutting or stretching the fitting of the patches to cones, as proposed by Julius it. Creating an origami with desired properties, particularly a [4], or by minimizing the Gauss area, as studied by Wang desired shape, is known as origami design.
    [Show full text]
  • Synthesis of Fast and Collision-Free Folding of Polyhedral Nets
    Synthesis of Fast and Collision-free Folding of Polyhedral Nets Yue Hao Yun-hyeong Kim Jyh-Ming Lien George Mason University Seoul National University George Mason University Fairfax, VA Seoul, South Korea Fairfax, VA [email protected] [email protected] [email protected] Figure 1: An optimized unfolding (top) created using our method and an arbitrary unfolding (bottom) for the fish mesh with 150 triangles (left). Each row shows the folding sequence by linearly interpolating the initial and target configurations. Self- intersecting faces, shown in red at bottom, result in failed folding. Additional results, foldable nets produced by the proposed method and an accompanied video are available on http://masc.cs.gmu.edu/wiki/LinearlyFoldableNets. ABSTRACT paper will provide a powerful tool to enable designers, materi- A predominant issue in the design and fabrication of highly non- als engineers, roboticists, to name just a few, to make physically convex polyhedral structures through self-folding, has been the conceivable structures through self-assembly by eliminating the collision of surfaces due to inadequate controls and the computa- common self-collision issue. It also simplifies the design of the tional complexity of folding-path planning. We propose a method control mechanisms when making deployable shape morphing de- that creates linearly foldable polyhedral nets, a kind of unfoldings vices. Additionally, our approach makes foldable papercraft more with linear collision-free folding paths. We combine the topolog- accessible to younger children and provides chances to enrich their ical and geometric features of polyhedral nets into a hypothesis education experiences. fitness function for a genetic-based unfolder and use it to mapthe polyhedral nets into a low dimensional space.
    [Show full text]
  • Mathematical Theory of Big Game Hunting
    DOCUMEWT RESUME ED 121 522 SE 020 770 AUTHOR Schaaf, Willie' L. TITLE A Bibliography of Recreational Mathematics, Volume 1. Fourth, Edition. INSTITUTION National Council of Teachers of Mathematics, Inc., Reston, Va. PUB DATE 70 NOTE 160p.; For related documents see Ed 040 874 and ED 087 631 AVAILABLE FROMNational Council of Teachers of Mathematics, Inc., 1906 Association Drive, Reston, Virginia 22091 EDRS PRICE MP-$0.83 Plus Postage. HC Not Available from EDRS. DESCRIPTORS *Annotated Bibliographies; *Games; Geometric Concepts; History; *Literature Guides; *Mathematical Enrichment; Mathematics; *Mathematics Education; Number Concepts; Reference Books ABSTRACT This book is a partially annotated bibliography of books, articles, and periodicals concerned with mathematical games, puzzles, and amusements. It is a reprinting of Volume 1 of a three-volume series. This volume, originally published in 1955, treats problems and recreations which have been important in the history of mathematics as well as some of more modern invention. The book is intended for use by both professional and amateur mathematicians. Works on recreational mathematics are listed in eight broad categories: general works, arithmetic and algebraic recreations, geometric recreations, assorted recreations, magic squares, the Pythagorean relationship, famous problems of antiquity, and aathematical 'miscellanies. (SD) *********************************************************************** Documents acquired by ERIC include many informal unpublished * materials not available from other sources. ERIC sakes every effort * * to obtain the best copy available. Nevertheless, items of marginal * * reproducibility are often encountered and this affects the quality* * of the microfiche and hardcopy reproductions ERIC aakes available * * via the ERIC Document Reproduction Service (EDRS). EDRS is not * responsible for the quality of the original document.
    [Show full text]
  • Exploring Mathematics
    ii A Teacher’s Guide to Exploring Mathematics Ames Bryant Kit Pavlekovsky Emily Turner Tessa Whalen-Wagner Adviser: Deanna Haunsperger ii Contents Contents I Introduction V I Number Sense 1 Counting Basics 3 Grocery Shopping 4 Units 5 Modular Arithmetic 6 Logarithms and Exponents 8 Changing Bases 11 II Geometry 15 Construction I 17 Construction II 21 Möbius Strips 22 Pythagorean Theorem 23 How Far Can a Robot Reach? 25 Spherical Geometry 27 I II CONTENTS III Sets 29 De Morgan’s Law 31 Building Sets 32 Subsets 34 Investigating Infinity 36 IV Probability 39 Probability vs. Reality 41 Game Theory 43 Continuous Probability 45 Bayes’ Theorem 45 V Patterns 51 Math in Nature 53 Fibonacci in Nature 53 Counting Patterns 55 Tiling 57 VI Data 61 Bad Graphs 63 Graphs 64 Introduction to Statistics 66 CONTENTS III VII Logic 71 Pigeonhole Principle 73 Formal Logic 74 Logical Paradoxes 76 Logic Puzzles 77 VIII Miscellaneous 85 Map Coloring 87 Shortest Path Problem 88 Flexagons 90 Math in Literature 92 IV CONTENTS Introduction V VI Part I Number Sense 1 Number Sense Counting Basics Goals Learn basic skills for counting possible choices, estimating number of possible outcomes Supplies N/A Prior Knowledge N/A 9. How many ways are there for the word "light?" How many ways can you rearrange the word "happy" and end up with "happy"? 10. Think about using the shepherd’s principle. The sheep are the number of circular arrange- ments, and their legs seem to be linear arrangements of the same number of people. How many legs on each sheep? 11.
    [Show full text]
  • Artistic Origami Design, 6.849 Fall 2012
    F-16 Fighting Falcon 1.2 Jason Ku, 2012 Courtesy of Jason Ku. Used with permission. 1 Lobster 1.8b Jason Ku, 2012 Courtesy of Jason Ku. Used with permission. 2 Crab 1.7 Jason Ku, 2012 Courtesy of Jason Ku. Used with permission. 3 Rabbit 1.3 Courtesy of Jason Ku. Used with permission. Jason Ku, 2011 4 Convertible 3.3 Courtesy of Jason Ku. Used with permission. Jason Ku, 2010 5 Bicycle 1.8 Jason Ku, 2009 Courtesy of Jason Ku. Used with permission. 6 Origami Mathematics & Algorithms • Explosion in technical origami thanks in part to growing mathematical and computational understanding of origami “Butterfly 2.2” Jason Ku 2008 Courtesy of Jason Ku. Used with permission. 7 Evie 2.4 Jason Ku, 2006 Courtesy of Jason Ku. Used with permission. 8 Ice Skate 1.1 Jason Ku, 2004 Courtesy of Jason Ku. Used with permission. 9 Are there examples of origami folding made from other materials (not paper)? 10 Puppy 2 Lizard 2 Buddha Penguin 2 Swan Velociraptor Alien Facehugger Courtesy of Marc Sky. Used with permission. Mark Sky 11 “Toilet Paper Roll Masks” Junior Fritz Jacquet Courtesy of Junior Fritz Jacquet. Used with permission. 12 To view video: http://vimeo.com/40307249. “Hydro-Fold” Christophe Guberan 13 stainless steel cast “White Bison” Robert Lang “Flight of Folds” & Kevin Box Robert Lang 2010 & Kevin Box Courtesy of Robert J. Lang and silicon bronze cast 2010 Kevin Box. Used with permission. 14 “Flight of Folds” Robert Lang 2010 Courtesy of Robert J. Lang. Used with permission. 15 To view video: http://www.youtube.com/watch?v=XEv8OFOr6Do.
    [Show full text]
  • On the Design of Physical Folded Structures by Jason S
    On the Design of Physical Folded Structures by Jason S. Ku B.S., Massachusetts Institute of Technology (2009) S.M., Massachusetts Institute of Technology (2011) Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2016 c Massachusetts Institute of Technology 2016. All rights reserved. ○ Author................................................................ Department of Mechanical Engineering May 18, 2016 Certified by. Sanjay E. Sarma Professor Thesis Supervisor Accepted by . Rohan Abeyaratne Chairman, Department Committee on Graduate Theses On the Design of Physical Folded Structures by Jason S. Ku Submitted to the Department of Mechanical Engineering on May 18, 2016, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Abstract Folding as a subject of mathematical, computational, and engineering study is rel- atively young. Most results in this field are hard to apply in engineering practice because the use of physical materials to construct folded structures has not been fully considered nor adequately addressed. I propose a three-fold approach to the design of folded structures with physical consideration, separating for independent investigation (1) the computational complexity of basic folding paradigms, (2) the automated accommodation of facet material volume, and (3) the design of folded ge- ometry under boundary constraints. These three topics are each necessary to create folded structures from physical materials and are closely related. Thesis Supervisor: Sanjay E. Sarma Title: Professor 2 Acknowledgments This thesis is dedicated to my wife and parents who have supported me so much throughout my time as a doctoral candidate.
    [Show full text]
  • Contents More Information
    Cambridge University Press 0521819709 - Flexagons Inside Out Les Pook Table of Contents More information Contents Preface page ix List of notation xi Introduction 1 1 Making and flexing flexagons 5 1.1 The trihexaflexagon 5 1.2 The pinch flex 6 1.3 A simple square flexagon 7 1.4 General assembly instructions 8 1.5 Decoration of faces 13 2 Early history of flexagons 14 2.1 The discovery of flexagons 14 2.2 The Flexagon Committee 15 2.3 Revival of interest 16 3 Geometry of flexagons 18 3.1 Flexagon characteristics 19 3.2 Appearance of main positions 20 3.3 Flexagons as linkages 21 3.4 Mapping flexagons 24 3.5 Flexagon figures and symbols 29 4 Hexaflexagons 31 4.1 Degrees of freedom of hexaflexagons 32 4.2 The trihexaflexagon revisited 33 4.3 Multicycle hexaflexagons 36 4.4 Hexaflexagon design 40 4.5 Hexaflexagon face arrangements 42 5 Hexaflexagon variations 47 5.1 Triangle flexagons 47 5.2 The V-flex 49 v © Cambridge University Press www.cambridge.org Cambridge University Press 0521819709 - Flexagons Inside Out Les Pook Table of Contents More information vi Contents 5.3 Origami with hexaflexagons 52 6 Square flexagons 53 6.1 Single cycle square flexagons 54 6.2 Reconstruction from a flexagon figure 58 6.3 Square flexagons with main position links 59 6.4 Distinct types of square flexagon with main position links 69 6.5 Square flexagons with box position links 70 6.6 Square flexagon face arrangements 76 6.7 The interleaf flex 78 7 Introduction to convex polygon flexagons 82 7.1 The convex polygon family 83 7.2 Degrees of freedom of intermediate positions 84 7.3
    [Show full text]
  • Tta -Oral Roue
    DOCUM7NTPFSUM7 SE 007 731 03", C90 rtri Vf +h a?patics. 'T,TmT77, ',,=kna4" ior711 t-, N MathPmaics,:, Tnc., -r 1T C IT Tr'"r, TTa-oral roueit cff mPach,Prs 79,71,ina+nn, r 7) ri r 7), 1) "I 771 1r7n. ouncil oc mPacher of mathematics,1221 T,VA-TT,A.,v7-rT)()%1 r QtrPot, 7.W.rWashington, 7).C.2223'5 * from 71r)q. T7 r CZ 71T) 77 C T7 ur "of kvailab1=-?. T) *A,nri-a+r,r1 *LitPraturP c7(' 11)r 'DT() (7 T,it:sratu/-P royiews,*;6ithematicalPnrichmeilt, *mathe,matics 77-ancation,rPfPrPnce nooks rT litoraturn auiTh is ahil-liograrooy o' books, concccrneya withmathPmatical recreations. arfirlPc;, an-3 n0ro'rat than 2,n20 ml-is is tl-n +hirl itior of a hookwhich, con+ainPd mar,. Snpnlr,mPnts have henad1P1 to bring onfriPg it inal Plition. snide is intondndfor VIP, the }-11-,linaranT,y u interested in nronssional mat},Pmatician and tiqe amateurwho ma,thPmafics as a1-ohhv. 'or thiF: reasonboth popular articles ,.4ions are, irclud0'1. Tn many cases,entries are' tPchnical discus auth6',- poin-ls out as anail to t'lP user ofthis hook. Trhe annotaf to look for sourceratPrials and fl-at this guie can serve PF-.a place loolrig for nrojPctmaterial advanced will ImP hPinf,fl to (741-nPnts technical articlPs aPri in research.41so, -,c, many non- stulPrts enqa fn 7-1thematics, as a will proyia0PnlovmPnt for +.hPlayman intereste(7, recrPation.(T) 1 PHOCESSwailMICROFICHE AND PUBLISHER'S PRICES. MICROFICHE, REPRODUCTION ONLY. William L. Schaaf U -S.
    [Show full text]