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Origami 6: I: Mathematics

Koryo Miura, et al., editors
American Mathematical Society
Publication Date: 
Number of Pages: 
[Reviewed by
Peter T. Olszewski
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Origiami6 is a two-volume book edited by the committees that planned and raised funds for the 6th International Meeting on Origami Science, Mathematics, and Education (6OSME), which took place on August 11–13, 2014 in Tokyo, Japan. Both volumes point out that Origami (the Japanese art of paper-folding) has many important and beautiful connections to mathematics, science, technology, design, and education. These connections were formally presented in 1989 with the First International Conference on Origami Science and Technology, organized by Humiaki Huzita held in Ferrara, Italy. As a result of this conference, five more conferences have followed: Otus, Japan (1994), Asilomor, California (2001), Pasadena, California (2006), and Singapore (2010). Each meeting led to a proceedings volume.

Over the years, the conferences have grown in the number of attendees and the diversity of fields represented, such as scientists, artists, engineers, teachers, and various structures to represent the origami. As pointed out in the introduction: “As the power of folding came to the attention of scientists, mathematicians, and technologists they, in turn, brought powerful tools — abstraction, analysis, optimization, computation — to the world of folding, giving rise not just to new artworks but to new engineering applications that better the human condition. With the combination of geometric precision and physical tangibility that folding provides, it continues to serve as an educational tool, with ripple effects that extend far beyond the narrow province of paper alone.”

These books present many papers on the most recent relationships between the art of origami and scientific and technical fields. Volume 1: Mathematics focuses on the connections between origami and the mathematics, with modern interpretations of definitions, computations, rigorous proofs, coloring, constructability, rigid foldability, and design algorithms. Volume 2: Technology, Art, Education presents papers on the connections between origami and the applied areas of science, engineering, physics, architecture, and industrial design. Different media used in the construction of the origami are also presented, such as polymers, metals, and textiles. Manufacturing techniques, computational tools, and process development based in traditional and historical folding techniques in design and art are also treated. In short, volume 1 is for the pure mathematician reader and volume 2 is for the applied mathematician, physicists, and engineer.

In addition, there are several papers offering a pedagogical ideas that can be used in classrooms starting at the elementary level. For collaboration purposes, after each paper is presented, contact information is given for each author.

Some of the most interesting creations found in volume 2 are the White Bison, Flight of Folds (a Pegasus), and Hero’s Horse presented in the paper Master Peace: An Evolution of Monumental Origami by Kevin Box and Robert J. Lang. The “Master Peace” is a piece inspired by the legend of 1000 cranes. It took nine years to create involving all 1000 cranes cast in stainless steel, 500 of the cranes are gathered together in a 25’ tall monument while 500 of the cranes are scattered throughout the piece. The monument stands on a 20’x20’ black granite base that reflects all 1000 cranes.

In the paper Wearable Metal Origami, Tine De Ruysser makes the connection between origami and fashion and textiles. Ruysser talks about electroforming, an electrochemical process in which a layer of metal is deposited on an object. The object is made electrically conductive and is suspended in a solution containing metal particles. An electric current is run through the solution and the object, so that the metal particles in the solution move towards the object and adhere to the surface. A metal layer forms, and the process continues until the desired thickness is achieved. This process is used to mold, which is then covered and later removed so only the metal piece remains. On page 617, the Shoulder Cape is presented, which takes the shape of shoulders on a woman. Other examples of jewelry are presented on page 623 with the Silver Bracelet, design for a dress, and a bracelet that can be converted into a carrier bag for women.

From our elementary school days, we have seen and known origami as a fragile art form making cute creations from paper. However, in the last half of the 20th century, origami has grown in many ways across various fields, both scientifically and artistically. In these two volumes, the reader is presented with a vast array of applications with endless possibilities.

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Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He can be reached at Webpage: Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes.