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

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