Divided Spheres (2 ed)
Geodesics and the Orderly Subdivision of the Sphere

By (author) Edward S. Popko,Chrisopher J. Kitrick,Christopher J. Kitrick

ISBN13: 9780367680039

Imprint: CRC Press

Publisher: Taylor & Francis Ltd

Format: Hardback

Published: 19/08/2021

Availability: POD

Description
New to the Second Edition New Foreword by Joseph Clinton, life-long Buckminster Fuller collaborator A new chapter by Chris Kitrick on the mathematical techniques for developing optimal single-edge hexagonal tessellations, of varying density, with the smallest edge possible for a particular topology, suggesting ways of comparing their levels of optimization An expanded history of the evolution of spherical subdivision New applications of spherical design in science, product design, architecture and entertainment New geodesic algorithms for grid optimization New full-color spherical illustrations created using DisplaySphere to aid readers in visualizing and comparing the various tessellations presented in the book. Updated Bibliography with references to the most recent advancements in spherical subdivision methods.
1. Divided Spheres. 1.1. Working with Spheres. 1.2. Making a Point. 1.3. An Arbitrary Number. 1.4. Symmetry and Polyhedral Designs. 1.5. Spherical Workbenches. 1.6. Detailed Designs. 1.7. Other Ways to Use Polyhedra. 1.8. Summary. Additional Resources. 2. Bucky's Dome. 2.1. Synergetic Geometry. 2.2. Dymaxion Projection. 2.3. Cahill and Waterman Projections. 2.4. Vector Equilibrium. 2.5. Icosa's 31. 2.6. The First Dome. 2.7. Dome Development. 2.8. Covering Every Angle. 2.9. Summary. Additional Resources. 3. Putting Spheres to Work. 3.1. The Tammes Problem. 3.2. Spherical Viruses. 3.3. Celestial Catalogs. 3.4. Sudbury Neutrino Observatory. 3.5. Cartography. 3.6. Climate Models and Weather Prediction. 3.7. H3 Uber's Hexagonal Hierarchical Geospatial Indexing System. 3.8. Honeycombs for Supercomputers. 3.9. Fish Farming. 3.10. Virtual Reality. 3.11. Modeling Spheres. 3.12. Computer Aided Design. 3.13. Octet Truss Connector. 3.14. Dividing Golf Balls. 3.15. Spherical, Throwable Pan n (TM) Panoramic Camera. 3.16. Termespheres. 3.17. Space Chip's (TM). 3.18. Hoberman's MiniSphere (TM). 3.19. V-Sphere (TM). 3.20. Gear Ball - Meffert's Rotation Brain Teaser. 3.21. Rhombic Tuttminx. 3.22. Rafiki's Code World. 3.23. Japanese Temari Balls. 3.24. Art and Expression. Additional Resources. 4. Circular Reasoning. 4.1. Lesser and Great Circles. 4.2. Geodesic Subdivision. 4.3. Circle Poles. 4.4. Arc and Chord Factors. 4.5. Where Are We? 4.6. Altitude-Azimuth Coordinates. 4.7. Latitude and Longitude Coordinates. 4.8. Spherical Trips. 4.9. Loxodromes. 4.10. Separation Angle. 4.11. Latitude Sailing. 4.12. Longitude. 4.13. Spherical Coordinates. 4.14. Cartesian Coordinates. 4.15. Coordinates. 4.16. Spherical Polygons. 4.17. Excess and Defect. 4.18 Summary. Additional Resources. 5. Distributing Points. 5.1. Covering. 5.2. Packing. 5.3. Volume. 5.4. Summary. Additional Resources. 6. Polyhedral Frameworks. 6.1. What Is a Polyhedron? 6.2. Platonic Solids. 6.3. Symmetry. 6.4. Archimedean Solids. 6.5. Circlespheres and Atomic Models. 6.6. Atomic Models. Additional Resources. 7. Golf Ball Dimples. 7.1. Icosahedral Balls. 7.2. Octahedral Balls. 7.3. Tetrahedral Balls. 7.4. Bilateral Symmetry. 7.5. Subdivided Areas. 7.6. Dimple Graphics. 7.7. Summary. Additional Resources. 8. Subdivision Schemas. 8.1. Geodesic Notation. 8.2. Triangulation Number. 8.3. Frequency and Harmonics. 8.4. Grid Symmetry. 8.5. Class I: Alternates and Ford. 8.6. Class II: Triacon. 8.7. Class III: Skew. 8.8. Covering the Whole Sphere. Additional Resources. 9. Comparing Results. 9.1. Kissing-Touching. 9.2 Sameness or Nearly So. 9.3. Triangle Area. 9.4. Face Acuteness. 9.5. Euler Lines. 9.6. Parts and T. 9.7. Convex Hull. 9.8. Spherical Caps. 9.9. Stereograms. 9.10. Face Orientation. 9.11. King Icosa. 9.12. Summary. Additional Resources. Subdivision Schemas. Geodesic Math. 10. Self-Organizing Grids. 10.1. Reduced Constraint Networks. 10.2. Symmetry. 10.3. Self-Organizing - Key Concepts. 10.4. Hexagonal Grids. 10.5. Rotegrities. 10.6. Future Directions. 10.7. Summary. Additional Resources. A. Stereographic Projection. B. Coordinate Rotations. C. Geodesic Math. Bibliography. Index.
  • Mathematics
  • Mathematical foundations
  • Geometry
  • Professional & Vocational
  • Tertiary Education (US: College)
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