| Description |
1 online resource (xi, 129 pages) : illustrations (some color) |
| Contents |
Cover -- Half-title Page -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgements -- 1 Parallel Folds -- 1.1 Card Notation -- 1.2 Rhombus Card -- 1.3 Circular Arc Equations -- 1.4 Parallelograms -- 1.5 Cut Variations -- 1.6 Pop-Up Letters -- 1.7 Tents -- 1.8 Artistic Designs -- 1.9 Creases as Centerlines -- Notes -- 2 V-Folds and Rotary Motion -- 2.1 Geometry of V-Folds -- 2.2 Vertical y-Motion -- 2.3 "Flat'' Rotary Motion -- Notes -- 3 The Knight's Visor -- 3.1 The Knight's Visor Pop-Up -- 3.2 Flat Visor Curve -- 3.3 The Nephroid -- 3.4 Visor Curve in 3D -- 3.5 Parabolic Visor -- Notes -- 4 Pop-Up Spinner -- 4.1 Pop-Up Spinner -- 4.2 Linkages and Fixed-Angle Polygonal Chains -- 4.3 Unit 90°-Chain in Spinner -- 4.4 Minimal Spinner -- Notes -- 5 Polyhedra: Rigid Origami and Flattening -- 5.1 Polyhedra -- 5.2 Rigid Origami -- 5.3 Continuous Flattening -- 5.4 Pop-Up Cubes -- 5.5 Pop-Up Octahedron at 90° -- 5.6 Rubber Band Pop-Ups -- 5.7 Pop-Up Tetrahedron at 180° -- Notes -- 6 Algorithms for Pop-Up Design -- 6.1 Introduction -- 6.2 Orthogonal Polygons and Polyhedra -- 6.3 Algorithm 1: Orthogonal Polygons -- 6.4 Algorithm 2: General Polygons -- 6.5 Algorithm 3: Orthogonal Polyhedra -- Notes -- 7 Pop-Up Design is Hard -- 7.1 NP-Hard Problems -- 7.2 Proving a Problem is NP-Hard -- 7.3 Reducing 3-SAT to Pop-Up Design -- Notes -- 8 Solutions to Exercises -- Chapter 1 Exercises -- Chapter 2 Exercises -- Chapter 3 Exercises -- Chapter 4 Exercises -- Chapter 5 Exercises -- Chapter 6 Exercises -- Chapter 7 Exercises -- Symbols -- Bibliography -- Index |
| Summary |
Anyone browsing at the stationery store will see an incredible array of pop-up cards available for any occasion. The workings of pop-up cards and pop-up books can be remarkably intricate. Behind such designs lies beautiful geometry involving the intersection of circles, cones, and spheres, the movements of linkages, and other constructions. The geometry can be modelled by algebraic equations, whose solutions explain the dynamics. For example, several pop-up motions rely on the intersection of three spheres, a computation made every second for GPS location. Connecting the motions of the card structures with the algebra and geometry reveals abstract mathematics performing tangible calculations. Beginning with the nephroid in the 19th-century, the mathematics of pop-up design is now at the frontiers of rigid origami and algorithmic computational complexity. All topics are accessible to those familiar with high-school mathematics; no calculus required. Explanations are supplemented by 140+ figures and 20 animations |
| Notes |
Description based on online resource; title from digital title page (viewed on June 28, 2022) |
| Subject |
Geometry.
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Three-dimensional greeting cards.
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geometry.
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Geometría
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Geometry
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Three-dimensional greeting cards
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| Form |
Electronic book
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| ISBN |
9781009093095 |
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1009093096 |
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