Treks into Intuitive Geometry : The World of Polygons and Polyhedra

• Autore: Akiyama Jin
• Pubblicazione: Singapore : , : Springer, , 2024; ©2024
• Edizione: 2nd ed.
• Descrizione fisica: 1 online resource (642 pages)
• Disciplina: 516
• Altri autori: MatsunagaKiyoko
• Nota di contenuto: Intro -- Preface -- Preface for the 2nd edition -- Acknowledgement -- Contents -- About the book ~ The Seven Pearls of the Book~ -- About the Authors -- Chapter 1 Art From Tiling Patterns -- 1. Geometric Patterns -- 2. Tilings -- 3. Conway Criterion -- 4. Math Behind Masterpieces -- Appendix 1.1.1 -- Appendix 1.2.1 -- References -- Chapter 2 The Tile-Maker Theorem and Its Applications to Art and Designs -- 1. How to Draw Repeated Patterns Like Escher's -- 2. Tile-Makers -- 3. Characteristics of a Net of an Isotetrahedron -- 4. Star-net, Star Unfolding and Completing the Polyhedral Tile-Maker Theorem -- 5. Dihedral Tile-Maker Theorem -- 6. Polyhedral Stampers -- 7. From Shark Heads to Tile-Makers -- 8. Knowledge and Terminologies for Topologically Extended Tile-Maker Theorem -- 9. Flat Closed-Surface Tile-maker Theorem -- 10. How to make Tiles from Flat Closed-Surface Tile-makers -- 11. Exhibition of Collage Art -- Appendix 2.3.1 -- Appendix 2.5.1 -- Appendix 2.10.1 -- References -- Chapter 3 Offshoots of the Fascinating Characteristics of Möbius Bands and Tori -- 1. The Möbius Love-Fate Fortune Telling -- 2. Various ways to cut Möbius bands in various manners -- 3. Experiments on Bisecting Möbius Flowers -- 4. General Properties of Bisection of Möbius Flowers -- 5. Investigation of bisection of n-Onions -- Appendix 3.4.1 -- Appendix 3.4.2 -- Appendix 3.5.1 -- References -- Chapter 4 Patchwork -- 1. Patchwork ― Equidecomposable Pairs of Polygons -- 2. How to Turn a Polygon into a Rectangle -- 3. Theorem of Equidecomposability -- References -- Chapter 5 Reversible Pairs of Figures -- 1. Envelope Magic -- 2. The Envelope Magic Trick -- 3. Trapezoidal Envelope Magic -- 4. Generalized Envelope Magic -- 5. Dudeney's Haberdasher's Puzzle -- 6. Reversible Transformation of Figures -- 7. Unveil All Reversible Pairs of Figures. ; 8. Everything about reversible pairs of figures appears in full view -- 9. Tessellability of reversible pairs of figures and superimposing method -- 10. Art Based on Reversible pairs of figures -- Appendix 5.5.1 -- Appendix 5.6.1 -- References -- Chapter 6 Reversibility and Foldability of Conway Tiles -- 1. Folding Nets of Platonic Solids -- 2. Terms and Properties of Conway tiles -- 3. Conway Polygons -- 4. Haberdasher's Puzzle from the point of view of Conway tiles -- 5. Easy-to-fold Conway tiles and others -- Appendix 6.1.1 -- Appendix 6.2.1 -- Appendix 6.3.1 -- Appendix 6.3.2 -- Appendix 6.4.1 -- Appendix 6.6.1 -- Appendix 6.6.2 -- Appendix 6.6.3 -- Appendix 6.6.4 -- References -- Chapter 7 Platonic Solids -- 1. The Platonic Solids -- 2. Euler's Formula for Polyhedra -- 3. Plato's Image for Platonic Solids -- 4. Duality Between a Pair of Polyhedra -- 5. The Cycle of Platonic Solids -- References -- Chapter 8 Cross-Sections of Polyhedra -- 1. CT Scanners and 3-D Copiers -- 2. Cross -Sections of a Cube -- 3. Universal Tilers -- 4. Mitsubishi and the Star of David -- References -- Chapter 9 Symmetry of Platonic Solids -- 1. Diagonal Weights -- 2. A Ball and and a F ullerene -- 3. The Platonic Solids through Reflecting Mirrors -- References -- Chapter 10 Double Duty Solids -- 1. TetraPak -- 2. Double Duty Solids -- 3. Finding More Double Duty Solids -- 4. Eleven Types of e-Nets of a Cube -- References -- Chapter 11 Nets of Small Solids with Minimum Perimeter Lengths -- 1. Minimum Steiner Tree Problem -- 2. Melzak's Algorithm -- 3. Minimum Perimeter Nets for a Regular Octahedron -- 4. Minimum Perimeter Net for a Cube C -- 5. Soap Experiments for Minimum Steiner Trees -- 6. Soap Experiments for Nets with Minimum Perimeter Lengths for Small Solids -- References -- Chapter 12 Tessellation Polyhedra -- 1. Regular Faced Polyhedra. ; 2. Tessellation Polyhedra -- 3. Art -- References -- Chapter 13 Universal Measuring Boxes -- 1. How to Measure Water Using a 6 dL Box -- 2. Changing the Shape of the Box -- 3. Orthogonal Measuring Boxes -- 4. An Application of the Ternary System -- 5. Non-Orthogonal Universal Measuring Boxes -- Appendix 13.4.1 -- References -- Chapter 14 Wrapping a Box -- 1. Wrapping Technique of the Experts -- 2. Point Symmetric Skew Wrapping -- 3. Patchwork Surgery -- 4. Investigating Efficient Wrappings -- 5. Six Remarkable Wrappings Obtained by Patchwork Surgery -- 6. The Most Saving But Mummy-Like Wrapping -- References -- Chapter 15 Bees, Pomegranates and Parallelohedra -- 1. How to Pack Cans Efficiently -- 2. Honeycombs and Pomegranate Seeds -- 3. Applications of Sphere Packing -- 4. Rhombic Dodecahedron -- 5. Truncated Octahedron -- 6. Lattices and Voronoi Domains -- 7. Parallelohedra -- References -- Chapter 16 Reversible Polyhedra -- 1. A Pig to a Ham, a Fox to a Snake, and Panda Magic -- 2. Transformation of a Pig to Ham -- 3. How to Make a Fox-Snake Solid -- 4. Make a Fox-Snake Solid with Paper -- 5. Making Panda Magic! -- 6. How to Make Reversible Polyhedra -- 7. Who Will Come Out of the U.F.O.? -- 8. P1-lattices and (P, Q)-Chimera Superimpositions -- 9. P1-Reversible Pairs Among Canonical Parallelohedra -- 10 . Reversibility for Parallelohedra and the Double-Reversal-Plates Method -- References -- Chapter 17 Elements of Polygons and Polyhedra -- 1. The Power of Triangulation -- 2. Element Sets and Element Numbers -- 3. Hilbert's Third Problem and Dehn Theorem -- 4. An Element Set and the Element Number for Platonic Solids -- 5. Another Element Set for the Platonic Solids -- References -- Chapter 18 The Pentadron -- 1. Atoms for Parallelohedra -- 2. Another Way to Find a Pair of Pentadra -- 3. The Chart for Composing Five Parallelohedra with Pentadra. ; 4. Pentadral Complices -- 5. A Bridge Between Platonic Solids and Parallelohedra -- 6. Art and Design -- Appendix 18.1.1 -- References -- Figure Permissions -- © J Art 2015 -- © J Art 2023 -- Copyright -- Endnote -- Key Word Index -- Index -- Symbol.
• Titolo autorizzato: Treks into intuitive geometry
• ISBN: 981-9986-08-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910864199603321
• Lo trovi qui: Univ. Federico II