Origami^5 Table of Contents

Preface

I Origami History, Art, and Design

History of Origami in the East and the West before Interfusion
Koshiro Hatori

Deictic Properties of Origami Technical Terms and Translatability
Koichi Tateishi

Betsy Ross Revisited: General Fold and One-Cut Regular and Star Polygons
Arnold Tubis and Crystal Elaine Mills

Reconstructing David Huffman’s Legacy in Curved-Crease Folding
Erik D. Demaine, Martin L. Demaine, and Duks Koschitz

Simulation of Nonzero Gaussian Curvature in Origami by Curved-Crease Couplets
Cheng Chit Leong

Compression and Rotational Limitations of Curved Corrugations
Christine E. Edison

Polygon Symmetry Systems
Andrew Hudson

New Collaboration on Modular Origami and LED
Miyuki Kawamura and Hiroyuki Moriwaki

Using the Snapology Technique to Teach Convex Polyhedra
Faye Goldman

A Systematic Approach to Twirl Design
Krystyna Burczyk and Wojciech Burczyk

Oribotics: The Future Unfolds
Matthew Gardiner

II Origami in Education

Origametria and the van Hiele Theory of Teaching Geometry
Miri Golan

Student-Teachers Introduce Origami in Kindergarten and Primary Schools
Maria Llu¨ısa Fiol, Neus Dasquens, and Montserrat Prat

Narratives of Success: Teaching Origami in Low-Income Urban Communities
Christine Edison

Origami and Spatial Thinking of College-Age Students
Norma Boakes

Close Observation and Reverse Engineering of Origami Models
James Morrow and Charlene Morrow

Origami and Learning Mathematics
Sue Pope and Tung Ken Lam

Hands-On Geometry with Origami
Michael J. Winckler, Kathrin D. Wolf, and Hans Georg Bock

My Favorite Origamics Lessons on the Volume of Solids
Shi-Pui Kwan

III Origami Science, Engineering, and Technology

Rigid-Foldable Thick Origami
Tomohiro Tachi

Folding a Patterned Cylinder by Rigid Origami
Kunfeng Wang and Yan Chen

The Origami Crash Box
Jiayao Ma and Zhong You

Origami Folding: A Structural Engineering Approach
Mark Schenk and Simon D. Guest

Designing Technical Tessellations
Yves Klett and Klaus Drechsler

A Simulator for Origami-Inspired Self-Reconfigurable Robots
Steven Gray, Nathan J. Zeichner, Mark Yim, and Vijay Kumar

A CAD System for Diagramming Origami with Prediction of Folding Processes
Naoya Tsuruta, Jun Mitani, Yoshihiro Kanamori, and Yukio Fukui

Development of an Intuitive Algorithm for Diagramming and 3D Animated Tutorial for Folding Crease Patterns
Hugo Akitaya, Matheus Ribeiro, Carla Koike, and Jose Ralha

Hands-Free Microscale Origami
Noy Bassik, George M. Stern, Alla Brafman, Nana Y. Atuobi, and David H. Gracias

Foldable Parylene Origami Sheets Covered with Cells: Toward Applications in Bio-Implantable Devices
Kaori Kuribayashi-Shigetomi and Shoji Takeuchi

IV Mathematics of Origami

Introduction to the Study of Tape Knots
Jun Maekawa

Universal Hinge Patterns for Folding Orthogonal Shapes
Nadia M. Benbernou, Erik D. Demaine, Martin L. Demaine, and Aviv Ovadya

A General Method of Drawing Biplanar Crease Patterns
Cheng Herng Yi

A Design Method for Axisymmetric Curved Origami with Triangular Prism Protrusions
Jun Mitani

Folding Any Orthogonal Maze
Erik D. Demaine, Martin L. Demaine, and Jason S. Ku

Every Spider Web Has a Simple Flat Twist Tessellation
Robert J. Lang and Alex Bateman

Flat-Unfoldability and Woven Origami Tessellations
Robert J. Lang

Degenerative Coordinates in 22.5o Grid System
Tomohiro Tachi and Erik D. Demaine

Two Folding Constructions
Robert Orndorff

Variations on a Theorem of Haga
Emma Frigerio

Precise Division of Rectangular Paper into an Odd Number of Equal Parts without Tools: An Origamics Exercise
Kazuo Haga

The Speed of Origami Constructions Versus Other Construction Tools
Eul`alia Tramuns

A Note on Operations of Spherical Origami Construction
Toshikazu Kawasaki

Origami Alignments and Constructions in the Hyperbolic Plane
Roger C. Alperin

A Combinatorial Definition of 1D Flat-Folding
Hidefumi Kawasaki

Stamp Foldings with a Given Mountain-Valley Assignment
Ryuhei Uehara

Flat Vertex Fold Sequences
Thomas C. Hull and Eric Chang

Circle Packing for Origami Design Is Hard
Erik D. Demaine, S´andor P. Fekete, and Robert J. Lang

Contributors