![]() ![]() Everyone has probably folded at least a boat or an airplane in their lifetime. This ancient art of paper folding started in Japan and China, but origami is now a household word around the world. As most origami enthusiasts already know, it is based on two Japanese words oru (to fold) and kami (paper). To understand origami, one should start with its definition. What started as a simple desire to share photos of my folding unfolded into the writing of this book. Ever since I started exhibiting photos of my origami designs on the Internet, I began to receive innumerable requests from the fans of my website to write a book. Preface Never did I imagine that I would end up writing an origami book. Suggested Reading Suggested Websites About the Author ‡ (Created June 2004) Umbrella Dodecahedron Whirl Dodecahedron Jasmine Dodecahedron 1 Jasmine Dodecahedron 2 Jasmine Dodecahedron 3 Swirl Dodecahedron 1 Swirl Dodecahedron 2Ħ Miscellaneous (Created 2001–2003) Lightning Bolt Twirl Octahedron Star WindowsĪppendix Rectangles from Squares Homogeneous Color Tiling Origami, Mathematics, Science and Technology.‡ (Created May 2004) Daisy Dodecahedron 1 Daisy Dodecahedron 2 Daisy Dodecahedron 3ĥ Patterned Dodecahedra IIâ.‡ (Created June 2003) Poinsettia Floral Ball Passion Flower Ball Plumeria Floral Ball Petunia Floral Ball Primrose Floral BallĤ Patterned Dodecahedra Iâ.‡ (Created October 2003) Cosmos Ball Cosmos Ball Variation Calla Lily Ball Phlox Ball FanTastic Stellaģ Floral Ballsâ.‡ (Created 1997–2001) Daisy Sonobe Striped Sonobe Snow-Capped Sonobe 1 Snow-Capped Sonobe 2 Swan Sonobe Spiked Pentakis DodecahedronĢ Enhanced Sonobesâ.Preface Acknowledgments Photo Credits Platonic & Archimedean Solids Origami Basics Folding Tipsġ Sonobe Variationsâ Back cover: Poinsettia Floral Ball (top) and Cosmos Ball Variation (bottom). Library of Congress Cataloging-in-Publication Data Mukerji, Meenakshi, 1962– Marvelous modular origami / Meenakshi Mukerji. No part of the material protected by this copyright notice may be reproduced or utilized in any form, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without written permission from the copyright owner. 5 Commonwealth Road, Suite 2C Natick, MA 01760 Copyright © 2007 by A K Peters, Ltd. (See pages 50 and 54.)Įditorial, Sales, and Customer Service Office A K Peters, Ltd. These 3D shapes have a lot of symmetry, though not as much as the Platonic solids.Jasmine Dodecahedron 1 (top) and 3 (bottom). Questions about larger models will lead you to the Archimedean solids and the Johnson solids. Questions about coloring will lead you to the mathematics of graphs and networks (and big questions that remained unsolved for many centuries). One seemingly innocent question can easily lead to a mathematical rabbit hole. Once you've mastered the basic structure of each 3D shape, you may find yourself (as others have done) pondering deeper mathematical questions.Ĭan you arrange the sonobe units so two units of the same color never touch, if you only have three colors?Īre larger symmetric shapes possible? (Answer: yes!)Īre there relationships between the different 3D shapes? (For example, the icosahedron is basically built of triangles, but can you spot the pentagons lurking within? Or the triangles in the dodecahedron?) ![]() Sonobe units, like these ones piled in a stack, can be put together to create 3D shapes. So, for a little effort you are rewarded with a vast number of models to explore. Many modular origami patterns, although they may use different units, have a similar method of combining units into a bigger creation. The building blocks, called units, are typically straightforward to fold the mathematical skill comes in assembling the larger structure and discovering the patterns within them. That's where you use several pieces of folded paper as "building blocks" to create a larger, often symmetrical structure. Any piece of origami will contain mathematical ideas and skills, and can take you on a fascinating, creative journey.Īs a geometer (mathematician who studies geometry), my favorite technique is modular origami. I'm a mathematician whose hobby is origami, and I love introducing people to mathematical ideas through crafts like paper folding. Both activities, however, share similar skills: precision, the ability to follow an algorithm, an intuition for shape, and a search for pattern and symmetry. ![]()
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