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E-grāmata: Star Origami: The Starrygami(TM) Galaxy of Modular Origami Stars, Rings and Wreaths

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Star Origami: The Starrygami(TM) Galaxy of Modular Origami Stars, Rings and WreathsPalielināt
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"Star Origami is a festival of folding fun that is sure to inspire. Tung Ken's stellar designs are rich with invention, and as always, his works are beautifully illustrated and written by him. Those eager for the math behind the designs will not be disappointed." Michael LaFosse (Origamido® Studio), author of over 50 origami books including Geometric Origami: The Art of Modular Paper Sculpture

"Tung Ken Lam is one of the worlds leading exponents of modular origami design. His books never disappoint." David Mitchell, author of Mathematical Origami and founder of origamiheaven.com

"Perfect for teachers to guide students to explore the relationships between the properties of rectangles and the folded stars. The curious and motivated student will find hours of mathematical buried treasure through folding." Charlene Morrow, Director, SummerMath, Mount Holyoke College and Past Board Chair, OrigamiUSA

"Star Origami provides a treasure trove of relevant math foundations, and suggestive pathways for the creative journey. It has already stimulated new directions for my own star structures." Arnold Tubis, author of Unfolding Mathematics with Origami Boxes and Tessellation Inspired Origami Box Designs

Star Origami: The Starrygami Galaxy of Modular Origami Stars, Rings and Wreaths is an exciting collection of origami rings, stars and wreaths made using the modular technique, including clear instructions for making them.

Features











Over sixty paper stars, all made without cutting, gluing or decorating using the modular origami technique





Hundreds of clear step-by-step instructions show you how, based on the technique of folding a small number of simple units and joining them together as a satisfying puzzle





Secret tips to make new shapes just by varying a few lengths and angles





Suitable for teaching and learning art, geometry and mathematics. Teachers will appreciate the practical advice to succeed in using origami for education.

Recenzijas

"Star Origami is a festival of folding fun that is sure to inspire. Ken's stellar designs are rich with invention and, as always, his works are beautifully written and illustrated. Those eager for the math behind the designs will not be disappointedthis is one of Tung Ken Lam's most exemplary efforts and not to be missed! Michael LaFosse (Origamido® Studio) author of over 50 origami books including Geometric Origami: The Art of Modular Paper Sculpture

"The modular origami-star creator faces an unlimited world of design possibilities, from random fidgeting to myriad explorations guided by mathematics. For the latter, Star Origami provides a treasure trove of relevant math foundations, and suggestive pathways for the creative journey. It has already stimulated new directions for my own star structures." Arnold Tubis, Author of Unfolding Mathematics with Origami Boxes and Tessellation Inspired Origami Box Designs

"Tung Ken Lam is one of the worlds leading exponents of modular origami design. His books never disappoint." David Mitchell, author of Mathematical Origami and founder of www.origamiheaven.com"A handy catalog of classes of rectangles and their mathematical properties. Perfect for teachers who can guide students in an exploration of the relationship between the properties of rectangles and stars that can be formed from them by folding. The curious and motivated student will find hours of mathematical buried treasure through folding." Charlene Morrow, Director, SummerMath, Mount Holyoke College and Pas Board Chair, OrigamiUSA

"[ T]he combination of artistic creativity and mathematical precision is both astounding and inspirational in equal measures." Sep Riahi, CEO, Global Tinker "A beautifully written and easy to navigate guide to folding a wonderful range of modular origami stars, from simple models suitable for children and beginners, to more complex models to challenge and delight the experienced folder.

This is a wonderful compendium for teachers of mathematics, containing many simple but pleasing models suitable for children and beginners, several of which can be made from A4 printer paper, perfect for the busy teacher! Tung Ken Lam also includes a comprehensive section to support teachers to manage the activities in a classroom, showing how to gently draw out the mathematics inherent in the paper folding process. There are also instructions for exploring the designs in computer graphics and dynamic geometry programs.

Truly a treasure of a book!" Clarissa Grandi, author of the Artful Maths books and ArtfulMaths.com.

"Profusely and effectively illustrated step-by-step instructions, Star Origami: The Starrygami Galaxy of Modular Origami Stars, Rings and Wreaths is an ideal introduction to the mathematics of creating origami stars" Midwest Books Review

"In every book, we look for something unique, something that draws our attention or gives us some added value beyond only the models. This book is surprising in a few aspects. First, the extra material around the models is huge. The author even went far and wrote code lines for Turtle-Graphic on a PC so the reader can create the polygons he is talking about. The first 40 pages have many gems and a lot of relevant knowledge to help the casual folder learn the deeper secrets of model creation or the students in a class to learn the mathematical features hidden in a sheet of paper. I must recommend the Note for Teachers chapter. It is highly useful for making sure the class will succeed in folding the models and learning relevant aspects from the geometric domain.

Bottom line: Highly recommended for teachers and for folders who want more than a few more models!" Ilan Garibi, The Fold, OrigamiUSA

1 Introduction
1(4)
1.1 Stars
1(1)
1.2 Origami stars and how this book is organised
1(1)
1.3 How to use this book
2(1)
1.3.1 For beginning folders
2(1)
1.3.2 For intermediate and experienced folders
2(1)
1.3.3 For potential and experienced creators
2(1)
1.3.4 To use specific paper or make a particular subject
2(1)
1.3.5 For teachers
3(1)
1.4 The models
3(1)
1.5 Difficulty
4(1)
1.5.1 Difficulty of folding the units
4(1)
1.5.2 Difficulty of assembly
4(1)
2 Stars
5(10)
2.1 Regular polygons
5(2)
2.2 Overlapping regular polygons
7(1)
2.3 Stellating a regular polygon
7(2)
2.4 Joining the diagonals of a regular polygon to make a star polygon
9(3)
2.5 Moving midpoints of the edges towards or away from the centre
12(1)
2.6 Rosette
13(1)
2.7 Kaleidoscope mirrors
14(1)
2.8 Taking a shape and rotating it around a centre of rotation
14(1)
3 Special Rectangles
15(12)
3.1 The square
17(1)
3.2 The silver rectangle
18(1)
3.3 The leftover rectangle
19(1)
3.4 The bronze rectangle
20(2)
3.5 The double bronze or half bronze rectangle
22(1)
3.6 The golden rectangle
22(1)
3.7 The double square or half square
23(1)
3.8 The 1:3 rectangle
24(1)
3.9 The 4:5 rectangle
25(1)
3.10 Landscape-portrait (LP) rectangles
25(1)
3.11 Other rectangles
26(1)
4 Folding and Generalising Stars
27(10)
4.1 Variation and creation
27(1)
4.2 Varying and generalising a flat star
27(2)
4.2.1 Changing the number of units
28(1)
4.2.2 Embedding without changing the key angle
28(1)
4.2.3 Embedding and changing the key angle
28(1)
4.3 Varying and generalising a single model
29(5)
4.3.1 Varying Star 8 Octad
29(2)
4.3.2 Six types of variation from Star 4
31(2)
4.3.3 Sliders
33(1)
4.3.4 Overlapped and interlaced regular polygons
33(1)
4.4 Summary
34(3)
4.4.1 Dividing an edge into equal parts
34(1)
4.4.2 Dividing a right angle into equal parts
35(1)
4.4.3 Dividing 180° and 360° into equal parts
36(1)
5 Tips on Paper and Folding
37(4)
5.1 Paper
37(1)
5.2 Paper colour and patterns
37(1)
5.3 Paper size
38(1)
5.4 Preparing paper
38(1)
5.5 Folding the modules
38(1)
5.6 Assembling the modules
39(1)
5.7 Following the instructions
39(2)
6 Symbols and Procedures
41(4)
7 Ring Stars
45(14)
7.1 Star 4, Square From Silver Rectangle * *
46(2)
7.2 Star 6, Square From Silver Rectangle * *
48(2)
7.3 Star 7, Square From Silver Rectangle * *
50(1)
7.4 Star 5, 3 by 4 from Square ** **
51(1)
7.5 Star 5, 5 by 6 from Square Blintz ** **
52(1)
7.6 Poly Diag Star 6 ** **
53(1)
7.7 Poly Diag Star 5 ** **
54(1)
7.8 Poly Diag Star 8 ** **
55(1)
7.9 Boat Unit 5 Pentagram ** **
56(1)
7.10 Boat Unit 6 Hexagram ** **
57(1)
7.11 Boat Unit 7 Heptagram ** **
58(1)
8 Wreaths
59(13)
8.1 Swirl 10, Square From Silver Rectangle * *
60(2)
8.2 Octagram Wreath * *
62(1)
8.3 Octagram Paper Cup - Kite Wheel ** **
63(1)
8.4 Kite Wheel 10 *** **
64(1)
8.5 Decagon Ring * *
65(1)
8.6 Handshake Wreath 8 * *
66(1)
8.7 Hook and Roll Wreath 8 ** **
67(1)
8.8 Star 8 Octad * *
68(1)
8.9 Starburst 8 Octad * *
69(1)
8.10 Starburst 8 60° ** *
70(1)
8.11 Starburst 6 * *
71(1)
9 Stars
72(20)
9.1 Star 3, Square From Silver Rectangle * *
73(1)
9.2 Silver Star 7 ** **
74(1)
9.3 Star 6 * *
75(1)
9.4 Pentagram ** ***
76(1)
9.5 Star 6, Bronze Rectangle from Square ** *
77(1)
9.6 Handshake Star 6 * *
78(1)
9.7 Star 4, Kite from Silver Rectangle * *
79(1)
9.8 Star 5 From Half Silver Rectangle * *
80(1)
9.9 Star 4 Leftover Wrap * *
81(1)
9.10 Star 6 Bronze Wrap * *
82(1)
9.11 Star 8 Leftover Wrap 45° * **
83(1)
9.12 Star 8 Leftover Wrap 22.5° ** **
84(1)
9.13 Medallion Star ** ***
85(1)
9.14 Star 6 Fancy Wrap *** ***
86(1)
9.15 Star 6, Equilateral Triangle from Rectangle * *
87(1)
9.16 Star 6 Bronze Triangle Wheel ** **
88(1)
9.17 Intersecting Squares ** **
89(1)
9.18 Quilt Star ** **
90(1)
9.19 Three Four Dodecagon Squares ** **
91(1)
10 Sliders
92(12)
10.1 Star 4 Slider, Square Silver From Rectangle * *
93(1)
10.2 Square Pointer Slider ** **
94(1)
10.3 Pinwheel Square Slider ** **
95(1)
10.4 Pinwheel Square 3D Slider *** **
96(2)
10.5 Octagram Slider * *
98(1)
10.6 Floppy Slider 8 * *
99(1)
10.7 Floppy Slider 6 * *
100(1)
10.8 Slider N 8 ** **
101(1)
10.9 Slider N 6 ** **
102(1)
10.10 Slider N 5 ** **
103(1)
11 3D Stars
104(8)
11.1 Starfish * *
105(1)
11.2 XYZ Rhombic * *
106(1)
11.3 Star Ball ** ***
107(2)
11.4 WXYZ *** ***
109(2)
11.5 Blintz Icosidodecahedron ** ****
111(1)
12 Notes for Teachers
112(17)
12.1 Common folding problems and how to avoid them
112(4)
12.2 General tasks
116(8)
12.2.1 Use mathematical vocabulary
116(1)
12.2.2 Identify the mathematical properties of shapes
116(1)
12.2.3 Use reverse engineering for teaching and learning
116(1)
12.2.4 Practical work with fractions of length, angle and area
117(1)
12.2.5 Scale a design for a specific size
117(1)
12.2.6 Explore the properties of A series paper
117(2)
12.2.7 Generalise a design
119(2)
12.2.8 Identify the symmetries of a model
121(1)
12.2.9 Identify the transformations as a model changes shape
121(1)
12.2.10 Find the relationships between perimeter, area and volume
122(1)
12.2.11 Make a model in dynamic geometry software
122(2)
12.3 Specific mathematical topics
124(5)
12.3.1 Folding 60° angles
124(3)
12.3.2 Nolids
127(1)
12.3.3 The regular icosahedron and other regular polyhedra
128(1)
13 Further Reading
129(2)
13.1 Origami
129(1)
13.2 Mathematics and geometry
130(1)
13.3 Origami and mathematics
130(1)
13.4 Origami and mathematics education
130(1)
Bibliography 131(3)
Index 134(3)
About the Author 137(1)
Online Materials 137
Tung Ken Lam is an origami creator, author, and qualified mathematics teacher.

His best-known works are WXYZ (p. 108) and Jitterbug. He is the author of Action Modular Origami to Intrigue and Delight (Tarquin, 2018), and coauthor of Learning Mathematics with Origami (Association of Teachers of Mathematics, 2016).

He has taught and presented his origami work in France, Italy, Sweden, Japan, and USA. He has run many events for teachers, learners, and the general public. He accepts commissions for origami projects and creating bespoke origami to order. Clients have included Bletchley Park Trust, The Bodleian Library, University of Oxford, EuroStemCell (formerly the Scottish Centre for Regenerative Medicine) and Honda UK.
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