Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami (AK Peters/CRC Recreational Mathematics Series)

I like the content of this book and I will spend time on it, but I do not recommend others to buy this at Amazon. I received a wrong binding book, the cover and the content are inverted. In addition, the edge of my book is damaged.

Robert Lang is the origami guy you go to if you are a beginner or origami pro. He is the definitive authority on origami.

This book is a masterpiece. Lang delves deep into the mathematics behind origami tessellations, a complex genre of origami that has seen a surge of interest in the 21st century. Of particular interest are twist-folds, which are collections of creases that literally allow one to "twist" a section of the paper and then have everything collapse back into a flat, folded form. Square twists have been a standard origami move for decades --- they can be seen in many origami roses, for example. But twists can be made from other polygons as well, not just squares, and as such they can be made to tile a sheet of paper, giving a repetitive crease pattern that will have a similar, "tiled" geometric look when folded. Lang fully describes the math behind how twist folds work and when they can (and when they can't) be made into a full tessellation. But he doesn't stop there, giving full exposure to origami tessellation patterns that have been extensively studied in origami engineering applications, like the famous Miura-ori and the Yoshimura pattern. He also explores and details special families of origami tessellations, like flagstone woven tessellations. He even describes 3D origami tessellations, where the finished model is structurally 3D, not a flat model. While there are many, many crease patterns and some instructions in this book, it really is a book meant for serious students of origami art. If you're an origami artist who wants to really see what tessellations can add to your work, and who isn't afraid of seeing some (or lots!) of mathematical equations at the same time, you must buy this book! But you don't really need to understand all the math to learn a whole lot about how tessellation folds work. If you **want** to see all the math behind such geometric origami, then you absolutely must get your hands on this book. Along with Lang's famous "Origami Design Secrets" book and Erik Demaine & Joe O'Rourke's text "Geometric Folding Algorithms", this book is the next in a progression of work that distills much of the advanced research that has been going on in origami math & science into a coherent, readable form. Highly, highly recommended for serious origami artists, origami scientists and engineers, and students of origami mathematics.

Yet another comprehensive and extremely well written monograph from Robert J. Lang which aspires to become a seminal work of origami, and of folding in general. Where his now classic Origami Design Secrets revolves around how to design (figurative) origami models with any number and kind of flaps, this new book revolves around tessellations, in general 2D and 3D periodic patterns from single sheets. Lang first extensively describes vertices, periodicity, twists, and tiles, in short, all the ground work of tessellations, firmly set in math, but with clear origami motivations and plenty of examples, as well as some historical notes. Mostly flat foldable patterns of traditional tessellations, but also cylindrical shapes like lamp shades and a fun spring action model, and some beautiful works of art that go beyond the flat or cylindrical world. Lang then goes on to handle more specialised topics. Rigid foldability explains why some patterns are easy to collapse, whereas others seem to resist the folding. Basically, the easy collapses are rigid, i.e. they can be made with materials that do not bend like paper is able to. The final three chapters leave the realm of flat-foldability and enters 3D folds and rotational shapes, the latter accompanied by stunning illustrations. The treatment builds heavily on math and addresses the mathematically interested, but the very visual and material aspects folding may make the book relevant to a wider audience, also because Lang motivates everything with practical goals of origami and foldability. Large parts can be understood with basic high school math, and the rest by the math of technical college levels. Lang is careful to mark all sections with one of three levels of math required (* lower high school, ** upper high school, and *** college level). The majority of the sections are marked * or **. The Spherical and 3D analysis (two chapters out of ten) have few examples and both $require levels ** or ***. The final chapter with rotational shapes requires ***, but is rich on patterns and examples that may be explored with little mathematical knowledge. Overall, the book is written in such a way that one may focus on some chapters in isolation, and even study some of the sections individually. All chapters end with a list of terms, and the book has clear list of contents as well as an extensive index and list of literature.In summary, if you want an origami book with a lot of models ready to fold, this is not for you.But if you like to understand what really goes on in origami and to be able to design advanced models, or even transfer the knowledge to other, technological areas, this book is a must at least as important as Origami Design Secrets.

Although it has a big chunk of pages, it is more heavy on math than his previous book. Does not cover all tessellation examples & no diagrams really either. Difficult to grasp if not a math expert, non friendly design concepts: once again more emphasis on the math whichis high. Maybe a 20% would understand it. As an origami enthusiast, I am only gaining by trying the patterns instead.

Does anybody know what the story is about this book. It has been "forthcoming" for years now. As of today, the publisher is saying Apr 2016 and will cost $60.

Wrote the author said his book was coming out next year. I'm not sure who is jerking us around the author or the publisher. Been hearing this same story for quite some time. Some one is jerking us around. Once again capitalism replaces honesty.

certainly NOT worth a thousand dollars!!!!!

There is not much to say about the contents, it does cover everything you could wish for. Almost all topics are in there and a number of contemporary artists and their work also found way into this book.However, you must be aware that this is a math text book. It is not a classical origami book. You won't find many projects nor diagrams. But that is not the intention of this book anyways. In a very strict and complete way Robert navigates through the very young topic of mathematical origami. He takes you along on a very comprehensive journey that will enable an eager student to apply and understand the principles.There are but a few drawbacks that make it difficult for me personally to give it 5 stars. I do find the layout of the book rather strange. The pages have an enormous margin, intended for notes i presume. Yet on almost every page the formulas and figures are sticking out of said margins. That is in my opinion extremely sloppy and admittedly triggers me in a way that reading through the otherwise interesting text is made unnecessarily difficult. Theorems are not very visible, the font barely changes so you will have a hard time finding them (they are numbered though). All these problems could have been solved very easily. Considering that the paperback version, that came damaged btw, is overprized at 60+ EUR. The hardback version is unaffordable in my opinion. I would not recommend buying that at all.To sum up, it is an interesting book with a terrible layout. You have to be quite committed to read and understand everything but that shouldn't keep an enthuistic student from enjoying it. If you have a solid math background on high school level and maybe a bit above you will have many hours of interesting insights into origami ahead of you.

It is pure Origami and math and no this is not a beginner book,not even advance, it is for the Origami professional to seek new places without borders.