Publisher’s Synopsis :
Unique and wildly creative, this mathematical approach to origami was invented by a Japanese master of the art. Jun Maekawa regards paperfolding from a perspective guided by geometric and aesthetic principles. In this captivating how-to book, he illustrates his point of view with directions for constructing 34 fabulous items, including cubes, towers, and geometric shapes as well as puzzles and figures of everyday items.
This is the first publication outside Japan of these original models, offering advanced beginners and serious origamists a combination of simple and complex figures and an intriguing blend of art and science. Rather than the square-shaped paper familiar to American folders, all models employ rectangular sheets of paper - that is, sheets with an aspect ratio of 1:1.41, or 1 to the square root of 2. Instructions for making rectangular origami paper are included. (Please do not let the mathematical references worry you - see booksellers comments below).
Preface to the book :
It is not generally known that origami conceals one of its richest veins in the rectangle with this aspect ratio. We have some traditional models made of rectangular sheets with proportions close to the ratio. In the modern era, some pioneers such as Eiji Nakamura and Koya Ohashi have explored this field of origami, and Kunihiko Kasahara recently published a series of enjoyable books titled Chohokei-de Oru (Folding Rectangles). I myself have also designed many origami models using these proportions. Whereas many regard the square as canonical in origami, I find "harmony of form," which is the most important appeal of origami for me, in many figures other than the square. Among them, I am fascinated by the 1: the square root of 2 rectangle no less than the square.
Moreover, the number the square root of 2 itself is so fascinating that some have written books dedicated exclusively to it. I have also included in this book some mathematical topics about the number. Since I am not an expert in math or math education, I have limited them to those that are interesting to me and poem I have something to do with the origami models, so that I will not annoy you. As a fan of mathematics, however, I would be pleased if you enjoy amusing mathematics, different from painful mathematics taught at school, by reading them along with folding paper.
So, welcome to the beautiful world of the square root of 2.
Introduction to the book:
The book contains origami models that are made from the 1: the square root of 2 rectangle with some exceptions, and consists of these three chapters:
In Chapter 1, I will explain four properties of the 1: the square root of 2 rectangle: it has matching angles; it is the most common rectangle; it relates to the cube; and it has repeating structures. Relatively easy "angle-matching" models will be diagrammed in Chapter 2. Chapter 3 contains relatively complex "angle-matching" models having longer sequences.
I have inserted some tips for making models and columns regarding them, presented in boxes like this one, into the diagrams. Some of the columns relate to background information about the models rather than making them.
You can, of course, skip reading the columns and start to make any models you like without paying attention to the order of the book. I have omitted detailed explanations of folds and techniques. I am sure, however, that you will be able to enjoy the book by itself. When you stumble upon a step, look up the symbols and basic folds, and observe the diagram of the next step. Reading the instructions will also help you solve the problem.
To make models in the book, you will need to use sheets in international standard sizes, whose ratio of the longer side to the shorter one is around the square root of 2 (about 1.414), rather than square origami paper. You can use copy paper, letter paper, flyer, notepad, or other kinds of paper of this aspect ratio. Refer to the beginning of Chapter 1 (page 14) for details about the standard paper sizes.
Although you can use generic A4 copy paper for most models in this book, I have specified the best paper size for each model, such as A4 or A5. You can obtain two A5 sheets by cutting one A4 sheet in half, as the numbers in the names of standard sizes rise by 1 every time they become half their size.
You may be able to purchase different types of standard-sized paper at large stores. At the end of this book, I have appended information about the paper I used for the models in the pictures at the beginning of the book. One type of paper I recommend is 50-70 g/m2 craft paper as it is relatively easy to obtain and good to fold. It is used for brown envelopes and other purposes. You can also use sales flyers or wrapping paper, Flyer though you need to check the aspect ratio because such sheets do not tend to come in standard sizes. I have explained how to check the aspect ratio at the beginning of Chapter 1.
There are 34 amazing models to be made from this book and PLEASE do not let all the mathematical references and discussions worry you. Bottom line is you can use standard ISO 216 paper size, i.e. A4, A3, etc. You will get a lot of fun out of this book.
See also B1343 – Genuine Japanese Origami – Book 1 by the same author that covers origami insects, leaves, plants, trees, animals and fantastic creatures.
1st edition, 2012, paperback, 128pp, fully illustrated with clear instructions throughout, 21 x 28cm