This book was a labor of many years. It is both myearliest book and my latest book; I began writingup my ideas on how to design when I beganwhat became my first published book in the early1980s， but not until recently have I developed theframework for those ideas. Over the years， I have been influencedby many scientists and artists， both inside and outsideof origami， all of whom contributed， one way or another， to thepresent tome. It is impossible for me to identify everyone whohas contributed to my work， but some of the larger pieces comefrom the following， who I thank:Neal Elias， for his encouragement and for introducing meto the magic of box pleating and the realization that anythingwas possible in origami.Lillian Oppenheimer and Alice Gray， for introducing meto the wide， wild world of origami fanatics.Akira Yoshizawa， who started it all， then showed that therewas more to origami art than just clever designs.Dave Brill， who showed that you could have both cleverdesign and high art in the same model.John Montroll， who took origami design to an unequaledlevel and who has been a constant source of inspiration andfriendship.Michael LaFosse， who took origami art to an unequaledlevel and Richard Alexander; both have been equally greatfriends.John Smith， James Sakoda， and especially David Lister forsharing a wealth of information about the history of origami，both privately and on the origami-L mailing list; David Lister，as well for numerous private comments and corrections withrespect to origami history; and Joan Sallas， for information onearly napkin-folding and for providing one of the figures.Toshiyuki Meguro， Jun Maekawa， and Fumiaki Kawahata，who developed circle and tree methods in Japan and who allprovided crucial insights to my own work along the way.Marshall Bern， who encouraged me to write my first origamicomputer science technical paper.Barry Hayes， who， with Marshall， proved mathematicallythat origami is really， really hard (lest there be any doubt).Erik and Martin Demaine， who have been friends andcollaborators in computational origami; in particular， themathematical theory that led to Chapters 12–14 is as muchtheirs as mine.Thomas Hull， who， as the focal point of origami math， hasdone more to bring origamists and mathematicians togetherthan anyone else.Koshiro Hatori， who provided translations of several ofthe references.Dave Mitchell， for his One-Crease Elephant.Dr. Emmanuel Mooser， for his Train.Raymond W. McLain and Raymond K. McLain， for theirgenerous permission to reproduce the latter’s Train diagramsand Raymond K.’s recollections of the early days of Americanorigami.In addition to the above， numerous other insights， encouragement，ideas， concepts， and criticisms came from PeterEngel， Robert Geretschl?ger， Chris Palmer， Paulo Barreto，Helena Verrill， Alex Bateman， Brian Ewins， Jeremy Shafer，Issei Yoshino， Satoshi Kamiya， Jason Ku， Brian Chan， HideoKomatsu， Masao Okamura， and Makoto Yamaguchi. A particularthank you goes to Toshi Aoyagi who for many years actedas matchmaker and translator between me and many of myJapanese colleagues and to Koshiro Hatori， Koichi Tateishi，Marcio Noguchi， and Anne LaVin， who have all helped withtranslation and advice.I am particularly indebted to Peter Engel， Marc Kirschenbaum，and Diane Lang for proofreading the text and thediagrams and making numerous suggestions for correctionsand improvements (and Diane did so twice， for both editions).Needless to say， any errors that remain are entirely my own.There are fewer errors in this printing than in the first edition，however， and I am most grateful for the eagle eyes of Yu LinYang， Roberto Gretter， Gadi Vishne， and Tom Hull in identifyinga few elusive typos; also for fruitful discussions with Erikand Marty Demaine that allowed me to make a more precisestatement of the tree theorem in Chapter 11 and that helpedcrystallize many of the concepts of polygon packing.I would like to tha
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