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Origami${}^6$: I. Mathematics

Edited by: Koryo Miura University of Tokyo, Japan
Toshikazu Kawasaki Anan National College of Technology, Tokushima, Japan
Tomohiro Tachi University of Tokyo, Tokyo, Japan
Ryuhei Uehara Japan Advanced Institute of Science and Technology, Tokushima, Japan
Robert J. Lang Langorigami, Alamo, CA
Patsy Wang-Iverson Gabriella & Paul Rosenbaum Foundation, Bryn Mawr, PA
Available Formats:
Softcover ISBN: 978-1-4704-1875-5
Product Code: MBK/95.1
List Price: $84.00 MAA Member Price:$75.60
AMS Member Price: $58.80 Electronic ISBN: 978-1-4704-2789-4 Product Code: MBK/95.1.E List Price:$79.00
MAA Member Price: $71.10 AMS Member Price:$55.30
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $126.00 MAA Member Price:$113.40
AMS Member Price: $88.20 Click above image for expanded view Origami${}^6$: I. Mathematics Edited by: Koryo Miura University of Tokyo, Japan Toshikazu Kawasaki Anan National College of Technology, Tokushima, Japan Tomohiro Tachi University of Tokyo, Tokyo, Japan Ryuhei Uehara Japan Advanced Institute of Science and Technology, Tokushima, Japan Robert J. Lang Langorigami, Alamo, CA Patsy Wang-Iverson Gabriella & Paul Rosenbaum Foundation, Bryn Mawr, PA Available Formats:  Softcover ISBN: 978-1-4704-1875-5 Product Code: MBK/95.1  List Price:$84.00 MAA Member Price: $75.60 AMS Member Price:$58.80
 Electronic ISBN: 978-1-4704-2789-4 Product Code: MBK/95.1.E
 List Price: $79.00 MAA Member Price:$71.10 AMS Member Price: $55.30 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$126.00 MAA Member Price: $113.40 AMS Member Price:$88.20
• Book Details

2015; 368 pp
MSC: Primary 00; 01; 51; 52; 53; 68; 70; 74; 92; 97;

$Origami^6$ is a unique collection of papers illustrating the connections between origami and a wide range of fields. The papers compiled in this two-part set were presented at the 6th International Meeting on Origami Science, Mathematics and Education (10–13 August 2014, Tokyo, Japan). They display the creative melding of origami (or, more broadly, folding) with fields ranging from cell biology to space exploration, from education to kinematics, from abstract mathematical laws to the artistic and aesthetics of sculptural design.

This two-part book contains papers accessible to a wide audience, including those interested in art, design, history, and education and researchers interested in the connections between origami and science, technology, engineering, and mathematics. Part 1 contains papers on various aspects of mathematics of origami: coloring, constructibility, rigid foldability, and design algorithms.

Undergraduate and graduate students and research mathematicians interested in origami and applications in mathematics, technology, art, and education.

This item is also available as part of a set:

• I. Mathematics of origami: Coloring
• Thomas C. Hull - Coloring connections with counting mountain-valley assignments
• Ma. Louise Antonette N. De las Peñas, Eduard C. Taganap and Teofina A. Rapanut - Color symmetry approach to the construction of crystallographic flat origami
• Sarah-Marie Belcastro and Thomas C. Hull - Symmetric colorings of polypolyhedra
• II. Mathematics of origami: constructibility
• Jordi Guardia and Eulalia Tramuns - Geometric and arithmetic relations concerning origami
• Jose Ignacio Royo Prieto and Eulalia Tramuns - Abelian and non-abelian numbers via 3D origami
• Fadoua Ghourabi, Tetsuo Ida and Kazuko Takahashi - Interactive construction and automated proof in Eos system with application to knot fold of regular polygons
• Sy Chen - Equal division on any polygon side by folding
• Ryuhei Uehara - A survey and recent results about commmon developments of two or more boxes
• Hugo A. Akitaya, Jun Mitani, Yoshihiro Kanamori and Yukio Fukui - Unfolding simple folds from crease patterns
• III. Mathematics of origami: Rigid foldability
• Tomohiro Tachi - Rigid folding of periodic origami tessellations
• Zachary Abel, Robert Connelly, Erik D. Demaine, Martin L. Demaine, Thomas C. Hull, Anna Lubiw and Tomohiro Tachi - Rigid flattening of polyhedra with slits
• Thomas A. Evans, Robert J. Lang, Spencer P. Magleby and Larry L. Howell - Rigidly foldable origami twists
• Zachary Abel, Thomas C. Hull and Tomohiro Ta - Locked rigid origami with multiple degrees of freedom
• Ketao Zhang, Chen Qiu and Jian S. Dai - Screw-algebra-based kinematic and static modeling of origami-inspired mechanisms
• Bryce J. Edmondson, Robert J. Lang, Michael R. Morgan, Spencer P. Magleby and Larry L. Howell - Thick rigidly foldable structures realized by an offset panel technique
• Jian S. Dai - Configuration transformation and manipulation of origami cartons
• IV. Mathematics of origami: design algorithms
• Erik D. Demaine and Jason S. Ku - Filling a hole in a crease pattern: Isometric mapping from prescribed boundary folding
• Robert J. Lang - Spiderwebs, tilings, and flagstone tessellations
• Erik D. Demaine, Martin L. Demaine and Kayhan F. Qaiser - Scaling any surface down to any fraction
• Erik D. Demaine, Martin L. Demaine, David A. Huffman, Duks Koschitz and Tomohiro Tachi - Characterization of curved creases and rulings: Design and analysis of lens tessellations
• Suryansh Chandra, Shajay Bhooshan and Mustafa El-Sayed - Curve-folding polyhedra skeletons through smoothing
• Takamichi Sushida, Akio Hizume and Yoshikazu Yamagishi - Design methods of origami tessellations for triangular spiral multiple tilings
• Thomas R. Crain - A new scheme to describe twist-fold tessellations
• Eli Davis, Erik D. Demaine, Martin L. Demaine and Jennifer Ramseyer - Weaving a uniformly thick sheet from rectangles
• Herng Yi Cheng - Extruding towers by serially grafting prismoids
• Goran Konjevod - On pleat rearrangements in pureland tessellations
• Robert J. Lang and Roger C. Alperin - Graph paper for polygon-packed origami design
• Toshikazu Kawasaki - A method to fold generalized bird bases from a given quadrilateral containing an inscribed circle
• Robert J. Lang and Barry Hayes - Pentasia: An aperiodic origami surface
• Ushio Ikegami - Base design of a snowflake curve model and its difficulties
• Miyuki Kawamura - Two calculations for geodesic modular works

• Reviews

• [A]s a high school mathematics teacher, my favorite part of the book is the applications of origami that align with many of the pedagogical ideas implemented in my class. Flow between chapters was smooth and I could sense the comprehensiveness of each key aspect of the book. I highly recommended this book to the secondary and higher education STEM teachers in my building and the local college; I am hopeful that many interdisciplinary projects can come out of it.

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2015; 368 pp
MSC: Primary 00; 01; 51; 52; 53; 68; 70; 74; 92; 97;

$Origami^6$ is a unique collection of papers illustrating the connections between origami and a wide range of fields. The papers compiled in this two-part set were presented at the 6th International Meeting on Origami Science, Mathematics and Education (10–13 August 2014, Tokyo, Japan). They display the creative melding of origami (or, more broadly, folding) with fields ranging from cell biology to space exploration, from education to kinematics, from abstract mathematical laws to the artistic and aesthetics of sculptural design.

This two-part book contains papers accessible to a wide audience, including those interested in art, design, history, and education and researchers interested in the connections between origami and science, technology, engineering, and mathematics. Part 1 contains papers on various aspects of mathematics of origami: coloring, constructibility, rigid foldability, and design algorithms.

Undergraduate and graduate students and research mathematicians interested in origami and applications in mathematics, technology, art, and education.

This item is also available as part of a set:
• I. Mathematics of origami: Coloring
• Thomas C. Hull - Coloring connections with counting mountain-valley assignments
• Ma. Louise Antonette N. De las Peñas, Eduard C. Taganap and Teofina A. Rapanut - Color symmetry approach to the construction of crystallographic flat origami
• Sarah-Marie Belcastro and Thomas C. Hull - Symmetric colorings of polypolyhedra
• II. Mathematics of origami: constructibility
• Jordi Guardia and Eulalia Tramuns - Geometric and arithmetic relations concerning origami
• Jose Ignacio Royo Prieto and Eulalia Tramuns - Abelian and non-abelian numbers via 3D origami
• Fadoua Ghourabi, Tetsuo Ida and Kazuko Takahashi - Interactive construction and automated proof in Eos system with application to knot fold of regular polygons
• Sy Chen - Equal division on any polygon side by folding
• Ryuhei Uehara - A survey and recent results about commmon developments of two or more boxes
• Hugo A. Akitaya, Jun Mitani, Yoshihiro Kanamori and Yukio Fukui - Unfolding simple folds from crease patterns
• III. Mathematics of origami: Rigid foldability
• Tomohiro Tachi - Rigid folding of periodic origami tessellations
• Zachary Abel, Robert Connelly, Erik D. Demaine, Martin L. Demaine, Thomas C. Hull, Anna Lubiw and Tomohiro Tachi - Rigid flattening of polyhedra with slits
• Thomas A. Evans, Robert J. Lang, Spencer P. Magleby and Larry L. Howell - Rigidly foldable origami twists
• Zachary Abel, Thomas C. Hull and Tomohiro Ta - Locked rigid origami with multiple degrees of freedom
• Ketao Zhang, Chen Qiu and Jian S. Dai - Screw-algebra-based kinematic and static modeling of origami-inspired mechanisms
• Bryce J. Edmondson, Robert J. Lang, Michael R. Morgan, Spencer P. Magleby and Larry L. Howell - Thick rigidly foldable structures realized by an offset panel technique
• Jian S. Dai - Configuration transformation and manipulation of origami cartons
• IV. Mathematics of origami: design algorithms
• Erik D. Demaine and Jason S. Ku - Filling a hole in a crease pattern: Isometric mapping from prescribed boundary folding
• Robert J. Lang - Spiderwebs, tilings, and flagstone tessellations
• Erik D. Demaine, Martin L. Demaine and Kayhan F. Qaiser - Scaling any surface down to any fraction
• Erik D. Demaine, Martin L. Demaine, David A. Huffman, Duks Koschitz and Tomohiro Tachi - Characterization of curved creases and rulings: Design and analysis of lens tessellations
• Suryansh Chandra, Shajay Bhooshan and Mustafa El-Sayed - Curve-folding polyhedra skeletons through smoothing
• Takamichi Sushida, Akio Hizume and Yoshikazu Yamagishi - Design methods of origami tessellations for triangular spiral multiple tilings
• Thomas R. Crain - A new scheme to describe twist-fold tessellations
• Eli Davis, Erik D. Demaine, Martin L. Demaine and Jennifer Ramseyer - Weaving a uniformly thick sheet from rectangles
• Herng Yi Cheng - Extruding towers by serially grafting prismoids
• Goran Konjevod - On pleat rearrangements in pureland tessellations
• Robert J. Lang and Roger C. Alperin - Graph paper for polygon-packed origami design
• Toshikazu Kawasaki - A method to fold generalized bird bases from a given quadrilateral containing an inscribed circle
• Robert J. Lang and Barry Hayes - Pentasia: An aperiodic origami surface
• Ushio Ikegami - Base design of a snowflake curve model and its difficulties
• Miyuki Kawamura - Two calculations for geodesic modular works
• [A]s a high school mathematics teacher, my favorite part of the book is the applications of origami that align with many of the pedagogical ideas implemented in my class. Flow between chapters was smooth and I could sense the comprehensiveness of each key aspect of the book. I highly recommended this book to the secondary and higher education STEM teachers in my building and the local college; I am hopeful that many interdisciplinary projects can come out of it.