Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (Paperback)

Origami History, Art, and DesignHistory of Origami in the East and the West before Interfusion, Koshiro HatoriIntroductionOrigin of Origami: Many Misunderstandings and Some SuppositionsThe East and the West: Different Styles, Different TraditionsConclusionBibliographyDeictic Properties of Origami Technical Terms and Translatability, Koichi Tateishi IntroductionPrevious Studies on Origami TermsTheoretical BackgroundsMaze of (Un)TranslatabilityReferentiality/Deictic versus Similarity: The Role of a Japanese Verbal Noun OriWhy Don’t the Japanese Use Verbs?Further ConsiderationsConclusionBibliographyBetsy Ross Revisited: General Fold and One-Cut Regular and Star Polygons, Arnold Tubis and Crystal Elaine MillsIntroductionHistorical Sources for the StoryFolding and One-Cut of the Pattern for Stars ArtifactGeneralizing the Betsy Ross Method to Fold and One-Cut Any Regular and Star PolygonsDiscussionBibliographyReconstructing David Huffman’s Legacy in Curved-Crease Folding, Erik D. Demaine, Martin L. Demaine, and Duks KoschitzIntroductionApproachReconstructionsConclusionBibliographySimulation of Nonzero Gaussian Curvature in Origami by Curved-Crease Couplets, Cheng Chit LeongIntroductionGeometry of a Curved SurfaceRepresentation of Curved Surfaces by Paper FoldingRuled SurfacesRadial Formed Rotational Symmetric ModelsCylindrical Formed Rotational Symmetric ModelsApplications of Couplets to Folding Animal ModelsConclusionBibliographyCompression and Rotational Limitations of Curved Corrugations, Christine E. EdisonIntroductionMethodDiscussion of ResultsConclusionsBibliographyPolygon Symmetry Systems, Andrew HudsonIntroductionPolygon ConstructionUnified Algorithm for Polygon ConstructionPolygonal Grids and Their PropertiesSymmetrical Twist-Fold ConstructionsGeneralizing Folding Algorithms to DifferentPolygonsConclusionBibliographyNew Collaboration on Modular Origami and LED, Miyuki Kawamura and Hiroyuki MoriwakiIntroductionAKARI-ORIGAMI: Some Modular WorksWorkshopFuture of AKARI-ORIGAMIBibliographyUsing the Snapology Technique to Teach Convex Polyhedra, Faye GoldmanIntroductionPolyhedra ReviewSnapology TechniqueBrief Introduction to General SnapologyObservationsConclusionsBibliographyA Systematic Approach to Twirl Design, Krystyna Burczyk and Wojciech BurczykIntroductionThe First Attempt: Small (Change) Is BeautifulA Square Is a Rectangle: MetamorphosisPlanar Decorative Area: From Octahedron to Cube, Mosaic TwirlsShapes and Lengths: Different SpiralsMinimal Folding: No Crease OrigamiConsensus Building: Spirals Work Together with Flaps-and-Pockets, Macro-modules ConclusionBibliographyOribotics: The Future Unfolds, Matthew GardinerIntroductionIndustrial Evolution of OriboticsCrease Pattern and Mechanical DesignPaper versus FabricInteraction DesignConclusion and Further WorkBibliographyOrigami in EducationOrigametria and the van Hiele Theory of Teaching Geometry, Miri GolanIntroductionThe van Hiele Theory of Geometric TeachingOrigami and the Van Hiele TheoryTime of LearningGradually Building Knowledge and ConceptsUsing Origametria to Eliminate MisconceptionsOrigametria and van Hiele: An Example from the ClassroomConclusion: The Benefits of Using Origametria in the van Hiele SystemBibliographyStudent-Teachers Introduce Origami in Kindergarten and Primary Schools, Maria Lluisa Fiol, Neus Dasquens, and Montserrat PratIntroductionObjectivesReview of the LiteratureProblem StatementsData Collection, Analysis, and DiscussionConclusion and Next StepsBibliographyNarratives of Success: Teaching Origami in Low-Income Urban Communities, Christine EdisonIntroductionOrigami in MathematicsOrigami in Art ClassOrigami in Elementary SchoolDiscussionBibliographyOrigami and Spatial Thinking of College-Age Students, Norma Boakes IntroductionDesign and PurposeResultsConclusionBibliographyClose Observation and Reverse Engineering of Origami Models, James Morrow and Charlene MorrowIntroductionRationale/GoalsOrigins and ContextAn Approach to Close Observation and Reverse EngineeringAn ExampleClose Observation and Reverse Engineering in Learning and Problem SolvingOur Observations of COREChallenges, a Question, and Next StepsConclusionBibliographyOrigami and Learning Mathematics, Sue Pope and Tung Ken LamIntroductionUsing Origami in Mathematics LessonsUsing Origami to Teach Conceptually Demanding MathematicsConclusionsBibliographyHands-On Geometry with Origami, Michael J. Winckler, Kathrin D. Wolf, and Hans-Georg BockIntroductionNew Trends in TeachingDesign of the CourseworkEvaluation and Lessons LearnedMy Favorite Origamics Lessons on the Volume of Solids, Shi-Pui KwanIntroductionExploration: Origami Masu Cubic BoxExploration: Origami CK-OctahedronExploration: The Building Block of CK and KCExploration: Origami KC-HeptahedronExploration: Tessellating SolidsOrigami, Science, Mathematics, and EducationConclusionBibliographyOrigami Science, Engineering, and TechnologyRigid-Foldable Thick Origami, Tomohiro TachiIntroductionProblem DescriptionProposed MethodApplication for DesignsConclusionBibliographyFolding a Patterned Cylinder by Rigid Origami, Kunfeng Wang and Yan ChenIntroductionKinematics of SphericalR Linkage and Its One DoF AssemblyRigid Origami Patterns to Form Cylindrical StructuresConclusions and DiscussionBibliographyThe Origami Crash Box, Jiayao Ma and Zhong YouIntroductionDescription of the Origami Pattern DesignFinite Element ModelingResults and DiscussionConclusionBibliographyOrigami Folding: A Structural Engineering Approach, Mark Schenk and Simon D. GuestIntroductionFolded Textured SheetsMechanical Modeling MethodConclusionBibliographyDesigning Technical Tessellations, Yves Klett and Klaus DrechslerIntroduction: Paper as Technical MaterialLightweight Construction with PaperModular Isometric OrigamiDesign StrategiesNot So Serious?Some FunConclusionBibliographyA Simulator for Origami-Inspired Self-Reconfigurable Robots, Steven Gray, Nathan J. Zeichner, Mark Yim, and Vijay KumarIntroductionFoldable Programmable MatterRepresenting Programmable MatterEditor Implementation and UsagePhysX Simulator and IntegrationConclusionBibliographyA CAD System for Diagramming Origami with Prediction of Folding Processes, Naoya Tsuruta, Jun Mitani, Yoshihiro Kanamori, and Yukio FukuiIntroductionRelated WorkOur Proposed SystemResults and DiscussionConclusion and Future WorkBibliographyDevelopment of an Intuitive Algorithm for Diagramming and 3D Animated…, Hugo Akitaya, Matheus Ribeiro, Carla Koike, and Jose RalhaIntroductionComputational OrigamiBasic Definitions on Technical OrigamiTurning a CP into a Folding SequenceApplicability ScopeExampleSoftware ImplementationConclusionBibliographyHands-Free Microscale Origami, Noy Bassik, George M. Stern, Alla Brafman, Nana Y. Atuobi, and David H. GraciasIntroductionStress-Based Microscale FoldingMiniaturized Microscale Origami Structures:Unidirectional FoldingBidirectional Microscale Folding UsingThin Metal FilmsConclusion and Future PossibilitiesBibliographyFoldable Parylene Origami Sheets Covered with Cells: Toward Applications…, Kaori Kuribayashi-Shigetomi and Shoji TakeuchiIntroductionMaterials and MethodsResults and DiscussionConclusionsBibliographyMathematics of OrigamiIntroduction to the Study of Tape Knots, Jun MaekawaIntroductionWhy a Knot in a Tape Forms a Regular PentagonRegular Odd-Sided Polygonal KnotsRegular Even-Sided Polygonal KnotsRegular Decagonal KnotsStability of KnotsNonregular Polygonal KnotsConclusion and Further ResearchBibliographyUniversal Hinge Patterns for Folding Orthogonal Shapes, Nadia M. Benbernou, Erik D. Demaine, Martin L. Demaine, and Aviv OvadyaIntroductionDefinitionsCube GadgetsFolding PolycubesImplementationRigid Foldability and Self-Folding SheetsBibliographyA General Method of Drawing Biplanar Crease Patterns, Cheng Herng YiIntroductionMathematical ConventionsDefining the BiplanarDrawing the NetDrawing the Crease PatternConclusionBibliographyA Design Method for Axisymmetric Curved Origami with Triangular Prism Protrusions, Jun MitaniIntroductionShape of the TargetD OrigamiDesigning the Crease PatternExamples and DiscussionsConclusionBibliographyFolding Any Orthogonal Maze, Erik D. Demaine, Martin L. Demaine, and Jason KuIntroductionAlgorithmBibliographyEvery Spider Web Has a Simple Flat Twist Tessellation, Robert J. Lang and Alex BatemanIntroductionShrink and RotateNonregular PolygonsMaxwell’s Reciprocal FiguresBibliographyFlat-Unfoldability and Woven Origami Tessellations, Robert J. LangIntroductionWoven TessellationsSimple Woven PatternsFlat-UnfoldabilityParameterizing the Woven TessellationConclusionBibliographyDegenerative Coordinates in 22.5° Grid System, Tomohiro Tachi and Erik D. DemaineIntroductionModelConstructionDegeneracyConclusionBibliographyTwo Folding Constructions, Robert OrndorffIntroductionMethod A: Descartes’ ConstructionMethod B: My ConstructionConclusionBibliographyVariations on a Theorem of Haga, Emma FrigerioIntroductionHaga’s TheoremVariationVariationA ComparisonVariations on the VariationsConclusionBibliographyPrecise Division of Rectangular Paper into an Odd Number of Equal Parts. . ., Kazuo HagaIntroductionPreparationTrisectionFive-SectionSeven-SectionPendulum SymmetryNine-sectionIndividual Line for Higher-Number SectionsConclusionsBibliographyThe Speed of Origami Constructions Versus Other Construction Tools, Eulalia TramunsIntroductionGeometric ToolsConstructions and MeasuresOptimal ConstructionsConclusionsBibliographyA Note on Operations of Spherical Origami Construction, Toshikazu KawasakiIntroductionThe Eight Operations of Planar OrigamiConstructionNotationSpherical OrigamiOperations of Spherical Origami ConstructionConclusionBibliographyOrigami Alignments and Constructions in the Hyperbolic Plane, Roger C. AlperinIntroductionBasic Alignments and FoldsRelations between the Alignment AxiomsTrigonometry and More Folding in H2The Non-Euclidean ParabolaH6BibliographyA Combinatorial Definition of 1D Flat-Folding, Hidefumi KawasakiIntroductionFlat-Foldable 3D OrigamiMinglingProof of the Flat-Foldability TheoremBibliography85Stamp Foldings with a Given Mountain-Valley Assignment, Ryuhei UeharaIntroductionPreliminariesUniversality of the Simple Folding ModelThe Number of Folded StatesConcluding RemarksBibliographyFlat Vertex Fold Sequences, Thomas C. Hull and Eric ChangIntroductionThe Basics of Flat Vertex FoldsFlat Vertex Fold SequencesConclusionBibliographyCircle Packing for Origami Design Is Hard, Erik D. Demaine, Sandor P. Fekete, and Robert J. LangIntroductionCircle-River DesignPacking and ComplexitySymmetric-PocketsTriangular PaperRectangular PaperSquare PaperFilling GapsEncoding the InputA Positive ResultConclusionsBibliographyContributors