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Origami Design Secrets: Mathematical Methods for an Ancient Art, Second Edition Paperback – Oct 5 2011

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Product Details

  • Paperback: 770 pages
  • Publisher: A K Peters/CRC Press; 2 edition (Oct. 5 2011)
  • Language: English
  • ISBN-10: 1568814364
  • ISBN-13: 978-1568814360
  • Product Dimensions: 3.2 x 21.6 x 27.3 cm
  • Shipping Weight: 2.2 Kg
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Bestsellers Rank: #20,516 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description


I am in complete agreement with the questions and thoughts expressed in his book. … This book is perfect for math geeks who aim to apply their math in a very creative way.
—, January 2012

Robert Lang made some substantial changes — much to the joy of many origami enthusiasts. The first edition impressed with 594 pages full of high-quality content going into techniques, mathematics, and folding instructions. The second edition tops that by an extra 176 pages, an extra 30% of content! … Altogether, this wealth of new content definitely makes it worth buying the second edition — even if you already have the first edition. As to if you don’t have either edition: I’d recommend going for the second one.
—Sara Adams,, December 2011

The good news is that a second edition of Robert Lang’s Origami Design Secrets is available. The bad news is you’re going to want to buy it, even if you have the first edition. … It’s a tribute to both the author and the publisher (CRC Press) that such major updates have been allowed. This book is without doubt the best guide to creating origami that has ever been published and I suspect it will retain the crown forever. … Quite simply, all creative folders should own this book if they have any interest in developing their skills. Even if they have no such interest, they should buy it — it’s that good.
—Nick Robinson, origami artist and author, on his blog, September 2011

Praise for the First Edition:
The first part of his plan was to write the book he’d been contemplating while still at JDS Uniphase — Origami Design Secrets, which was published in 2003 and lays out the underlying principles of origami and design techniques.
—Susan Orlean, The New Yorker, February 2007

When Robert J. Lang, a laser physicist, talks with passion about origami — the Japanese art of paper folding — the line between play and discovery also completely dissolves. Mr. Lang is what might be called an origamist (see He wrote the book Origami Design Secrets: Mathematical Methods for an Ancient Art and has created tarantulas, delicate herons, 12-spined shells and big-horned elk out of single, uncut, folded sheets of paper.
—Edward Rothstein, The New York Times, April 2006

This book is a synthesis of origami technique, history, and instructions, with very thoughtful and clear explanations for almost every aspect of the art of folding and designing origami.
—Sarah Gourlie, Math Horizons, January 2006

Lang chose to strike a balance between a book that describes origami design algorithmically and one that appeals to the origami community … . For mathematicians and origamists alike, Lang’s expository approach introduces the reader to technical aspects of folding and the mathematical models with clarity and good humor … Origami Design Secrets … is highly recommended for mathematicians and students alike who want to view, explore, wrestle with open problems in, or even try their own hand at the complexity of origami model design.
—Thomas C. Hull, The Mathematical Intelligencer, March 2005

This magisterial work, splendidly produced, covers all aspects of the art and science.
SIAM Book Review, November 2004

For most origami enthusiasts, the ancient Japanese art of folding and making creases is a mere hobby, and a grand pursuit for those giddily obsessed with the mathematics (or aesthetics) of how mere paper can be contorted into objects of beauty and interest. For Robert J. Lang, however, origami has become a life’s pursuit …
—Chad Berndtson, The Patriot Ledger, November 2004

… finally, the secrets of an origami master are revealed! It feels like Lang has taken you on as an apprentice as he teaches you his techniques, stepping you through examples of real origami designs and their development.
—Erik Demaine, October 2003

There is something for everyone here, whether beginner or expert, left-brained or right, specialist or dilettante.
—Gail Anderson, Engineering & Science, April 2003

About the Author

Robert J. Lang has been an avid student of origami for over forty years and is now recognized as one of the world’s leading masters of the art. He is noted for designs of great detail and realism, and his repertoire includes some of the most complex origami designs ever created. His work combines aspects of the Western school of mathematical origami design with the Eastern emphasis upon line and form to yield models that are at once distinctive, elegant, and challenging to fold. They have been shown in exhibitions in New York (Museum of Modern Art), Paris (Carrousel du Louvre), Salem (Peabody Essex Museum), San Diego (Mingei Museum of World Folk Art), and Kaga, Japan (Nippon Museum of Origami), among others.

In 1992 Dr. Lang became the first Westerner ever invited to address the Nippon Origami Association’s annual meeting; he has since been an invited guest at international origami conventions around the world. He lectures widely on origami and its connections to mathematics, science, and technology and teaches workshops on both artistic techniques and applications of folding in industrial design.

Dr. Lang is one of the pioneers of the cross-disciplinary marriage of origami with mathematics; he has been one of the few Western columnists for Origami Tanteidan Magazine, the journal of the Japan Origami Academic Society, and has presented several refereed technical papers on origami-math at mathematical and computer science professional meetings. He has consulted on applications of origami to engineering problems ranging from air-bag design to expandable space telescopes. He is the author or co-author of twelve books and numerous articles on origami art and design.

Dr. Lang was born in Ohio and raised in Atlanta, Georgia. Along the way to his current career as a full-time origami artist and consultant, he worked as a physicist, engineer, and R&D manager, during which time he authored or co-authored over 80 technical publications and 50 patents on semiconductor lasers, optics, and integrated optoelectronics. He is a Fellow of the Optical Society of America, a member of the IEEE Photonics Society, and served as Editor-in-Chief of the IEEE Journal of Quantum Electronics from 2007–2010. In 2009, he received the highest honor of Caltech, the Distinguished Alumni Award. Dr. Lang resides in Alamo, California.

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By Lily Zhou on April 27 2014
Format: Paperback
This is one of the most thorough books ever written on the mathematics of Origami. (Believe me or not, Mathematics is the basis of most of today's origami designs.) In it, Robert J. Lang, one of the world's most accomplished folders, describes decades of his experience, allowing a keen reader to use many of the techniques to create origami models of their own. Many of the models included are exclusive to the book.
However, amazing as it is, purchasing this book is not worth the investment if one buys it only for the models. The number of models in this book is few, and no one short of a professional can make any of the models in the second half of the book. Believe me; I've been folding for over a decade. Some creases require precision within 0.05 cm, such as when it asks you to make a crease 234/698th of the way through the paper in the Bull moose.
The beauty of this book lies in it's concepts. The mathematical concepts included in this book are extremely complex; nothing short of university level. Indeed, this book would be well-suited for a university student of mathematics. Theories such as the box pleat and geometric variations of common bases are covered, and require a mature mind.
In summary, believe me when I say that this book isn't for anyone who's not a serious folder. Also, if you are a child or adolescent, it's recommended that you stay away as well. The few models that can be folded by anyone short of professional are not worth the $55 investment.
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By chaosjordan on Dec 18 2011
Format: Paperback
This book was very heplful for me, a young origamist. It taught me precisely how to design origami models and there are awesome models to fold showed there :)
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By JN on Jan. 25 2013
Format: Paperback Verified Purchase
Excellent book but not so expensive! Love it so much! Amazing origami I have ever seen and made. Thanks the author so much for your fantastic work!
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Format: Paperback Verified Purchase
Love this book! I've just recently received it and love how well it explains everything- I'm soon to finish a moose!
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Most Helpful Customer Reviews on (beta) 30 reviews
17 of 19 people found the following review helpful
Beautiful, Complex! For the origami artist and math lover Dec 26 2011
By ThreeGentsand4Ladies - Published on
Format: Paperback
Wow! Got this book for Christmas and it is huge! Beautiful soft cover, 700+ pages (including indexes and glossary). The book opens with a lovely acknowledgment by Robert Lang and includes an excellent Introduction explaining the techniques of origami and it's development. The introduction also briefly explains each chapter, beginning with a review of design principals and basic folds, on to grafting and tileing and other rather complex origami techniques.

Another real joy of this book is the crease patterns of the models as well as the mathematical formulae (hence the "mathematical methods" in the title). The model diagrams themselves are very clear and in a brown/tan color pattern which makes following the diagrams easier to follow. The diagrams include for example, the astonishing Black Forest Cuckoo Clock, the elegant life-like Koi, and the Cyclomatus metallifer.

A big heavy book for the serious origami lover in your life (or yourself!), or even for the mathematician with an artistic bent. This book is definitely worth what you'll pay for it. Get this one and you won't be sorry you did!
7 of 7 people found the following review helpful
Origami's bible just got better June 18 2012
By Peter E. - Published on
Format: Paperback
Robert Lang's Origami Design Secrets, published in 2003, has become the bible of origami mathematical theory. Weighing in at 3-1/2 pounds and with 585 pages, it felt never-to-be-surpassed. But it has, as Lang has produced this expanded edition that tops the previous one by more than a pound and 170 new pages. If it gets any larger, it may go the way of the printed version of the Encyclopedia Britannica. Get it while you can still hold it in your hands.

Origami Design Secrets is an extraordinary codification of the mathematical tools used by Lang and an increasing number of other folders to design complex origami figures, those with slender legs and antennas, articulated body parts, textured scales and feathers, and other features not easily generated by means of traditional origami bases or trial and error. The essence of the mathematical approach is optimization. Complex models need to use paper efficiently in order to generate all those long, thin appendages, or else the paper will bunch up and your gazelle will look like a hippo.

Lang's analytical approach ensures that the paper is apportioned in the most efficient manner to achieve the desired result. Over the decades, Lang and other theorists have developed a profound understanding of how a square of paper folds up at the macro level (how efficient forms derive from the shape of a square), the micro level (what happens at each individual intersection of creases in the interior of the paper), and in between. Lang is generous in sharing credit for those discoveries, many of which are his. The culmination of Lang's approach is his creation of computer programs that lay out the points and creases of the intended design on the actual square of paper. He sometimes uses a laser cutter to produce the patterns on handmade paper for his museum-quality models, an interesting mix of the crafted and the machined.

While Lang's writings suggest that his design process is driven by efficiency and rigor and thus largely premeditated, in person he puts it somewhat differently. Mathematics, he says, drives the generation of possibilities, and chance and serendipity arise from his process of iterating designs and looking for fortuitous alignments, coincidences, and elegances of form and structure. As a result, many of Lang's finished creations are extremely beautiful, both on the surface and in the elegance of their folding process. Regrettably, his writing rarely touches on the artistry of the design process, and despite his attempt to make his mathematical theories and computer programs accessible to all, many other folders who implement his approach produce (in this reviewer's eyes) little of aesthetic value.

Now to the book itself, and to the expanded edition. The format is based on building up origami mathematical theory chapter by chapter, with nearly every chapter followed by instructions for folding several models of Lang's own design. As the theory grows more complex, so do the models, and some of the later ones may take readers hours to construct. Those new to origami may hit a wall after just the first few chapters. This is one origami book that is not being marketed to beginners.

Because of Origami Design Secrets' formidable mathematical achievements, other of its accomplishments are rarely remarked on. First, Lang's prose is colloquial and accessible, and he truly endeavors to explicate rather than obfuscate, which would have been the easier course. And second, his diagrams--both the step-by-step diagrams for folding the models and the analytical drawings, many of them in 3-D--are equally lucid. In the absence of Lang's excellent communication skills, attempting to explain this complex material to the mathematical near-layman would not have been worth the effort.

Readers who own the first edition will naturally wonder whether to purchase the second one. If you can afford it and have room on your bookshelf, I highly recommend it. The new edition contains two new chapters (on uniaxial box pleating and polygon packing), expanded and revised portions of other chapters, four new sets of diagrams (including instructions for a beautiful dancing crane), and a dozen mind-bogglingly complex and beautiful crease patterns to arthropods so creepy and real (a scorpion, a camel spider, a scarab beetle) that they will haunt your dreams. Origami Design Secrets edition number two will clearly remain the final word on its subject--until, of course, Lang comes out with edition number three.
4 of 4 people found the following review helpful
The next step in origami May 20 2013
By will - Published on
Format: Paperback Verified Purchase
I love the way Robert Lang writes. This book talks about individual techniques in building origami designs. Little tricks that can be used to make scales, fingers, wings, etc. This is a book ABOUT origami, not just OF origami directions.

Having said that, there are plenty of models to make in the book with directions. These are very impressive, and some are supremely difficult.

A lot of the techniques described in this book are difficult, and take lots of practice. But I think someone who's only made some paper cranes or with very basic experience with origami could slowly work their way through the book and master everything with practice.

There is one thing that could be improved. The diagrams in the instructions are usually quite clear, however some times adding extra diagrams showing incomplete models from extra angles would make following the directions easier, and would make climbing the learning curve easier.
2 of 2 people found the following review helpful
a must for any origamist's library Dec 25 2012
By Poison Wood - Published on
Format: Paperback
I've been folding origami since I was perhaps 7 years old, but it's always been a bit of a black box to me. I've never really understood how designers come up with their designs. This book, far more than any other I've encountered, explains the theory of origami design. Even if you don't plan to do your own designs, it's very enlightening to get an understanding of the reasoning behind steps in various folds.

This book is a large, lengthy volume. Each chapter has instructions for two or three folds, and each chapter explains a new theory that the instructions then put into practice. I wasn't sure I'd enjoy reading all the theory, but I ended up really enjoying going through it. As always, Lang offers very readable diagrams with clear instructions. The designs in this book range from easy (not very easy) to challenging. He includes explanations of how to make the fish with scales shown on the front but not step-by-step instructions, and that would be a *very* challenging project. This book is appropriate for a beginner, but you'll find the projects quite challenging at first. I think it's best for an advanced beginner or better; I don't think there's an upper limit on skill in terms of getting benefit from the book.
1 of 1 people found the following review helpful
Must buy for those to prefers to create their own models May 10 2013
By HS Lim - Published on
Format: Paperback Verified Purchase
First, this book is not for beginners. If you are a beginner, you can still get it but it would be more useful to use as you gain experience.

The book is divided into sections. Each section explains a technique, then further illustrated on how the technique was used by providing folding examples, which you can fold. You can gain understanding of each technique, combined them to create your own models.

This book shows how complicated models were designed and created, so even if you are not interested in folding complicated models, understanding how other creative people create their own models will leave your jaw dropping.