239:, or for undergraduate research projects extending those subjects, although reviewer Mary Fortune cautions that "there is much preliminary material to be covered" before a student would be ready for such a project. Reviewer Georg Gunther summarizes the book as "a delightful addition to a wonderful corner of mathematics where art and geometry meet", recommending it as a reference for "anyone with a working knowledge of elementary geometry, algebra, and the geometry of complex numbers".
229:
Origamist David Raynor suggests that its methods could also be useful in constructing templates from which to cut out clean unfolded pieces of paper in the shape of the regular polygons that it discusses, for use in origami models that use these polygons as a starting shape instead of the traditional square paper.
228:
This book is quite technical, aimed more at mathematicians than at amateur origami enthusiasts looking for folding instructions for origami artworks. However, it may be of interest to origami designers, looking for methods to incorporate folding patterns for regular polygons into their designs.
219:
provides explicit folding instructions for 15 different regular polygons, including those with 3, 5, 6, 7, 8, 9, 10, 12, 13, 17, and 19 sides. Additionally, it discusses approximate constructions for polygons that cannot be constructed exactly in this way.
92:
using origami, and on finding the largest copy of a given regular polygon that can be constructed within a given square sheet of origami paper. With straightedge and compass, it is only possible to exactly construct regular
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69:. It goes on to show that, in this mathematical model, origami is strictly more powerful than straightedge and compass: with origami, it is possible to solve any
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168:. With a construction system that can trisect angles, such as mathematical origami, more numbers of sides are possible, using
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919:
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39:
165:
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44:
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85:, two problems that have been proven to have no exact solution using only straightedge and compass.
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49:
and published by
Arbelos Publishing (Shipley, UK) in 2008. The Basic Library List Committee of the
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The book is divided into two main parts. The first part is more theoretical. It outlines the
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The second part of the book focuses on folding instructions for constructing
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for mathematical origami, and proves that they are capable of simulating any
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may also be useful as teaching material for university-level geometry and
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has suggested its inclusion in undergraduate mathematics libraries.
457:(1988), "Angle trisection, the heptagon, and the triskaidecagon",
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30:, focusing on the ability to simulate and extend classical
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to be 3, 5, 6, 8, 10, 12, etc. These are called the
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77:. In particular, origami methods can be used to
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8:
443:on 2020-01-28 – via Arbelos Publishing
38:. It was written by Austrian mathematician
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18:Book on the mathematics of paper folding
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294:Fortune, Mary (March 2010), "Review of
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144:(powers of two plus one): this allows
32:straightedge and compass constructions
172:in place of Fermat primes, including
67:straightedge and compass construction
7:
747:Geometric Exercises in Paper Folding
768:A History of Folding in Mathematics
275:Mathematical Association of America
51:Mathematical Association of America
14:
460:The American Mathematical Monthly
215:equal to 7, 13, 14, 17, 19, etc.
668:Alexandrov's uniqueness theorem
419:Raynor, David (February 2009),
1:
606:Regular paperfolding sequence
754:Geometric Folding Algorithms
521:Mathematics of paper folding
386:Hajja, Mowaffaq, "Review of
341:Gunther, Georg (June 2013),
261:Caulk, Suzanne (July 2009),
28:mathematics of paper folding
936:
804:Margherita Piazzola Beloch
575:Yoshizawa–Randlett system
314:10.1017/s002555720000752x
775:Origami Polyhedra Design
433:British Origami Magazine
301:The Mathematical Gazette
915:2008 non-fiction books
565:Napkin folding problem
224:Audience and reception
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187:
166:constructible polygons
158:
130:
108:
210:
188:
159:
131:
109:
725:Fold-and-cut theorem
681:Steffen's polyhedron
545:Huzita–Hatori axioms
535:Big-little-big lemma
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177:
148:
120:
98:
63:Huzita–Hatori axioms
40:Robert Geretschläger
673:Flexible polyhedron
355:Crux Mathematicorum
854:Toshikazu Kawasaki
677:Bricard octahedron
652:Yoshimura buckling
550:Kawasaki's theorem
455:Gleason, Andrew M.
205:
183:
154:
136:is a product of a
126:
104:
910:Mathematics books
897:
896:
761:Geometric Origami
632:Paper bag problem
555:Maekawa's theorem
423:Geometric Origami
388:Geometric Origami
345:Geometric Origami
296:Geometric Origami
265:Geometric Origami
233:Geometric Origami
217:Geometric Origami
208:{\displaystyle n}
186:{\displaystyle n}
157:{\displaystyle n}
129:{\displaystyle n}
107:{\displaystyle n}
83:doubling the cube
26:is a book on the
23:Geometric Origami
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834:David A. Huffman
799:Roger C. Alperin
702:Source unfolding
570:Pureland origami
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436:, archived from
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308:(529): 189–190,
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814:Robert Connelly
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642:Schwarz lantern
627:Modular origami
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170:Pierpont primes
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849:Humiaki Huzita
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829:Rona Gurkewitz
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824:Martin Demaine
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707:Star unfolding
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540:Crease pattern
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467:(3): 185–194,
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140:with distinct
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79:trisect angles
71:cubic equation
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55:
17:
13:
10:
9:
6:
4:
3:
2:
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920:Paper folding
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718:Miscellaneous
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615:3d structures
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142:Fermat primes
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56:
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16:
889:Eve Torrence
819:Erik Demaine
780:
773:
766:
760:
759:
752:
745:
739:Publications
601:Möbius strip
591:Dragon curve
528:Flat folding
464:
458:
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438:the original
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422:
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387:
362:(6): 393–394
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232:
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138:power of two
87:
60:
22:
21:
20:
15:
874:KĹŤryĹŤ Miura
869:Jun Maekawa
844:KĂ´di Husimi
560:Map folding
421:"Review of
343:"Review of
271:MAA Reviews
263:"Review of
43: [
904:Categories
864:Anna Lubiw
697:Common net
622:Miura fold
402:1256.51001
243:References
116:for which
81:, and for
782:Origamics
661:Polyhedra
839:Tom Hull
809:Yan Chen
692:Blooming
596:Flexagon
322:27821925
481:0935432
36:origami
792:People
647:Sonobe
479:
400:
393:zbMATH
320:
57:Topics
34:using
441:(PDF)
428:(PDF)
350:(PDF)
318:JSTOR
193:-gons
114:-gons
47:]
195:for
687:Net
469:doi
398:Zbl
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310:doi
298:",
73:or
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477:MR
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