Star Origami: The Starrygami™ Galaxy of Modular Origami Stars, Rings and Wreaths (AK Peters/CRC Recreational Mathematics Series)

Description

"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 world’s 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. Cover Half Title Series Page Title Page Copyright Page Contents 1. Introduction 1.1. Stars 1.2. Origami stars and how this book is organised 1.3. How to use this book 1.3.1. For beginning folders 1.3.2. For intermediate and experienced folders 1.3.3. For potential and experienced creators 1.3.4. To use specific paper or make a particular subject 1.3.5. For teachers 1.4. The models 1.5. Difficulty 1.5.1. Difficulty of folding the units 1.5.2. Difficulty of assembly 2. Stars 2.1. Regular polygons 2.2. Overlapping regular polygons 2.3. Stellating a regular polygon 2.4. Joining the diagonals of a regular polygon to make a star polygon 2.5. Taking the midpoints of the edges of a regular polygon and moving them towards or away from the centre 2.6. Rosette 2.7. Kaleidoscope mirrors 2.8. Taking a shape and rotating it around a centre of rotation 3. Special Rectangles 3.1. The square 3.2. The silver rectangle 3.3. The leftover rectangle 3.4. The bronze rectangle 3.5. The double bronze or half bronze rectangle 3.6. The golden rectangle 3.7. The double square or half square 3.8. The 1:3. rectangle 3.9. The 4:5. rectangle 3.10. Landscape-portrait (LP) rectangles 3.11. Other rectangles 4. Folding and Generalising Stars 4.1. Variation and creation 4.2. Varying and generalising a flat star 4.2.1. Changing the number of units without changing the unit 4.2.2. Embedding in a different rectangle without changing the key angle 4.2.3. Embedding in a different rectangle and changing the key angle 4.3. Varying and generalising a single model 4.3.1. Varying Star 8 Octad 4.3.2. Six types of variation from a single model: Star 4, Square From Silver Rectangle 4.3.3. Sliders 4.3.4. Overlapped and interlaced regular polygons 4.4. Summary 4.4.1. Dividing an edge into equal parts 4.4.2. Dividing a right angle into equal parts 4.4.3. Dividing 180◦ and 360◦ into equal parts 5. Tips on Paper and Folding 5.1. Paper 5.2. Paper colour and patterns 5.3. Paper size 5.4. Preparing paper 5.5. Folding the modules 5.6. Assembling the modules 5.7. Following the instructions 6. Symbols and Procedures 7. Ring Stars 7.1. Star 4, Square From Silver Rectangle * * 7.2. Star 6, Square From Silver Rectangle * * 7.3. Star 7, Square From Silver Rectangle * * 7.4. Star 5, 3 by 4 from Square ** ** 7.5. Star 5, 5 by 6 from Square Blintz ** ** 7.6. Poly Diag Star 6 ** ** 7.7. Poly Diag Star 5 ** ** 7.8. Poly Diag Star 8 ** ** 7.9. Boat Unit 5 Pentagram ** ** 7.10. Boat Unit 6 Hexagram ** ** 7.11. Boat Unit 7 Heptagram ** ** 8. Wreaths 8.1. Swirl 10, Square From Silver Rectangle * * 8.2. Octagram Wreath * * 8.3. Octagram Paper Cup - Kite Wheel ** ** 8.4. Kite Wheel 10 *** ** 8.5. Decagon Ring * * 8.6. Handshake Wreath 8 * * 8.7. Hook and Roll Wreath 8 ** ** 8.8. Star 8 Octad * * 8.9. Starburst 8 Octad * * 8.10. Starburst 8 60◦ ** * 8.11. Starburst 6 * * 9. Stars 9.1. Star 3, Square From Silver Rectangle * * 9.2. Silver Star 7 ** ** 9.3. Star 6 * * 9.4. Pentagram ** *** 9.5. Star 6, Bronze Rectangle from Square ** * 9.6. Handshake Star 6 * * 9.7. Star 4, Kite from Silver Rectangle * * 9.8. Star 5 From Half Silver Rectangle * * 9.9. Star 4 Leftover Wrap * * 9.10. Star 6 Bronze Wrap * * 9.11. Star 8 Leftover Wrap 45◦ * ** 9.12. Star 8 Leftover Wrap 22.5◦ ** ** 9.13. Medallion Star ** *** 9.14. Star 6 Fancy Wrap *** *** 9.15. Star 6, Equilateral Triangle from Rectangle * * 9.16. Star 6 Bronze Triangle Wheel ** ** 9.17. Intersecting Squares ** ** 9.18. Quilt Star ** ** 9.19. Three Four Dodecagon Squares ** ** 10. Sliders 10.1. Star 4 Slider, Square Silver From Rectangle * * 10.2. Square Pointer Slider ** ** 10.3. Pinwheel Square Slider ** ** 10.4. Pinwheel Square 3D Slider *** ** 10.5. Octagram Slider * * 10.6. Floppy Slider 8 * * 10.7. Floppy Slider 6 * * 10.8. Slider N 8 ** ** 10.9. Slider N 6 ** ** 10.10. Slider N 5 ** ** 11. 3D Stars 11.1. Starfish * * 11.2. XYZ Rhombic * * 11.3. Star Ball ** *** 11.4. WXYZ *** *** 11.5. Blintz Icosidodecahedron ** **** 12. Notes for Teacher 12.1. Common folding problems and how to avoid them 12.2. General tasks 12.2.1. Use mathematical vocabulary 12.2.2. Identify the mathematical properties of shapes 12.2.3. Use reverse engineering for teaching and learning 12.2.4. Practical work with fractions of length, angle and area 12.2.5. Scale a design for a specific size 12.2.6. Explore the properties of A series paper 12.2.7. Generalise a design 12.2.8. Identify the symmetries of a model 12.2.9. Identify the transformations as a model changes shape 12.2.10. Find the relationships, if any, between perimeter, area and volume 12.2.11. Make a model in dynamic geometry software 12.3. Specific mathematical topics 12.3.1. Folding 60◦ angles 12.3.2. Nolids 12.3.3. The regular icosahedron and other regular polyhedra 13. Further Reading 13.1. Origami 13.2. Mathematics and geometry 13.3. Origami and mathematics 13.4. Origami and mathematics education Bibliography Index About the Author Online Materials