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