{"id":225,"date":"2012-08-26T09:24:09","date_gmt":"2012-08-26T13:24:09","guid":{"rendered":"https:\/\/dividedspheres.com\/?page_id=225"},"modified":"2012-08-29T06:34:35","modified_gmt":"2012-08-29T10:34:35","slug":"selected-bibliography","status":"publish","type":"page","link":"https:\/\/dividedspheres.com\/?page_id=225","title":{"rendered":"Selected Bibliography"},"content":{"rendered":"

Bagchi, B. (1997). “How to Stay Away from Each Other in a Spherical Universe.” Resonance<\/span>(September): 18-26.Ball, W. W. R. and H. S. M. Coxeter (1987). Mathematical Recreations and Essays<\/span>. New York, Dover Publications.<\/p>\n

Bohlen, J. C. (1974). Trigonometric Relationships for Geodesic Domes with Special Reference to the Dodecahedron. Vancouver, BC, Western Forest Products Laboratory, Information Report VP-X-121.<\/p>\n

Clinton, J. D. (1970). Chord Factors and Angles. Domebook One<\/span>. L. Kahn. Los Gatos, CA, Pacific Domes: <\/strong>50-52.<\/p>\n

Clinton, J. D. (1971). Geodesic Math. Domebook 2<\/span>. L. Kahn. Bolinas, CA, Pacific Domes: <\/strong>106-113.<\/p>\n

Clinton, J. D. (2002). “A Group of Spherical Tessellations Having Edges of Equal Length.” Space Structures 5<\/span> 2<\/strong>(105): 995-1004.<\/p>\n

Clinton, J. D. (2002). A Limited and Biased View of Historical Insights for Tessellating a Sphere. Space Structures<\/span>. G. A. R. Park and P. Disney, Thomas Telford, London. 5<\/strong>.<\/p>\n

Collidge, J. L. (1971). A Treatise on the Circle and the Sphere<\/span>. Bronx, NY, Chelsea Pub. Co.<\/p>\n

Coxeter, H. S. M. (1936). “The Partition of a Sphere According to the Icosahedral Group.” Scripta Math<\/span> 4<\/strong>: 156-157.<\/p>\n

Coxeter, H. S. M. (1962). “The Problem of Packing a Number of Equal Non-Overlapping Circles on a Sphere.” Transactions of The New York Academy of Sciences (Dept. of Mathematics, University of Toronto)<\/span> 24<\/strong>: 320-331.<\/p>\n

Coxeter, H. S. M. (1971). Virus Macromolecules and Geodesic Domes. A Spectrum of Mathematics<\/span>. J. C. Butcher. Auckland, Auckland University Press: <\/strong>98-107.<\/p>\n

Coxeter, H. S. M. (1991). Regular Complex Polytopes<\/span>. New York, Cambridge University Press.<\/p>\n

Coxeter, H. S. M. and P. Du Val (1982). The Fifty-Nine Icosahedra<\/span>. New York, Springer-Verlag.<\/p>\n

Coxeter, H. S. M., M. Emmer, et al. (1985). M. C. Escher: Art and Science<\/span>. Proceedings of the International Congress on M.C. Escher, Rome, Italy, Elsevier Science Pub. Co.<\/p>\n

Coxeter, H. S. M., M. S. Longuet-Higgins, et al. (1954). “Uniform Polyhedra.” Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical & Engineering Sciences<\/span> 246<\/strong>(916): 401-450.<\/p>\n

Critchlow, K. (1970). Order in Space: A Design Source Book<\/span>. New York, Viking Press.<\/p>\n

Cromwell, P. R. (1997). Polyhedra<\/span>. Cambridge, U.K., Cambridge University Press.<\/p>\n

Cundy, H. M. and A. P. Rollett (1961). Mathematical Models<\/span>. Oxford, U.K., Clarendon Press.<\/p>\n

Dawson, R. J. M. (2005). “Some New Tilings of the Sphere with Congruent Triangles<\/a><\/strong>.”<\/p>\n

Doskas, G. (2011). Spherical Harmony – A Journey of Geometric Discovery<\/span>. LuLu Marketplace, Hedron Designs.<\/p>\n

Dutton, G. (1991). “Polyhedral Hierarchical Tessellations: The Shape of GIS to Come.” Geographical Information Systems<\/span> 1<\/strong>(3): 49-55.<\/p>\n

Dutton, G. (1999). A Hierarchical Coordinate System for Geoprocessing and Cartography<\/span>. New York, Springer.<\/p>\n

Easton, R. and L. Kahn (1970). Domebook One<\/span>. Los Gatos, CA, Pacific Domes.<\/p>\n

Edmondson, A. C. (1987). A Fuller Explanation – The Synergetic Geometry of R. Buckminster Fuller<\/span>. Boston, Birkh\u00e4user (reprinted Pueblo, CO: Back-In-Action Book Series 2007).<\/p>\n

Fearnley, C. J. (2011). “CJ Fearnley’s List of Buckminster Fuller Resources on the Internet<\/a><\/strong>.”<\/p>\n

Fowler, P. W., T. Tarnai, et al. (2002). “From Circle Packing to Covering on a Sphere with Antipodal Constraints.” Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical & Engineering Sciences<\/span> 458<\/strong>(2025): 2275-2287.<\/p>\n

Fuller, R. B. (1946). Cartography. USPTO. United States.<\/p>\n

Fuller, R. B. (1954). Building Construction. USPTO. United States.<\/p>\n

Fuller, R. B. (1959). Geodesic Tent. USPTO. United States.<\/p>\n

Fuller, R. B. (1959). Self-Strutted Geodesic Plydome. USPTO. United States.<\/p>\n

Fuller, R. B. (1961). Synergetic Building Construction. USPTO. United States.<\/p>\n

Fuller, R. B. (1962). Tensile-Integrity Structures. USPTO. United States.<\/p>\n

Fuller, R. B. (1965). Geodesic Structures. USPTO. United States.<\/p>\n

Fuller, R. B. (1965). Laminar Geodesic Dome. USPTO. United States.<\/p>\n

Fuller, R. B. (1967). Octahedral Building Truss. USPTO. United States.<\/p>\n

Fuller, R. B. and E. J. Applewhite (1975). Synergetics: Explorations in The Geometry of Thinking<\/span>. New York, Macmillan.<\/p>\n

Fuller, R. B. and S. Sh\u014dji (1992). Fuller Projection Dymaxion Air-Ocean World. Los Angeles, Buckminster Fuller Institute.<\/p>\n

Gabriel, J. F. o., Ed. (1997). Beyond the Cube: The Architecture of Space Frames and Polyhedra<\/span>. New York, John Wiley.<\/p>\n

Goldberg, M. (1937). “A Class of Multi-Symmetric Polyhedra.” Tohoku Mathematics Journal<\/span> 43<\/strong>: 104-108.<\/p>\n

Goldberg, M. (1967). “Viruses and a Mathematical Problem.” Journal of Molecular Biology<\/span> 24<\/strong>(2): 337-338.<\/p>\n

Gray, R. W. (2009). “Great Circle and LCD Triangle Info<\/a><\/strong>.” The Projects of R. W. Gray<\/span>.<\/p>\n

Hart, G. W. (1998). Icosahedral Constructions. Bridges – Mathematical Connections in Art, Music and Science<\/span>. Southwestern College, Winfield, KA: <\/strong>195-202.<\/p>\n

Hart, G. W. (2008). “The Encyclopedia of Polyhedra<\/a><\/strong>.”<\/p>\n

Hart, G. W. (2008). “Pavilion of Polyhedreality<\/a><\/strong>.”<\/p>\n

Hart, G. W. and H. Picciotto (2001). Zome Geometry : Hands-on Learning with Zome Models<\/span>. Emeryville, CA, Key Curriculum Press.<\/p>\n

Heartney, E. and K. D. Snelson (2009). Kenneth Snelson – Forces Made Visible<\/span>. Lenox, MA, Hard Press Editions.<\/p>\n

Henderson, D. W. and E. Moura (1996). Experiencing Geometry: On Plane and Sphere<\/span>. Englewood Cliffs, NJ, Prentice Hall.<\/p>\n

Henderson, D. W. and D. Taimin\u0326a (2005). Experiencing Geometry: Euclidean and Non-Euclidean with History<\/span>. Upper Saddle River, NJ, Pearson Prentice Hall.<\/p>\n

Hoberman, C. (1990). Reversibly Expandable Doubly-Curved Truss Structure. USPTO. United States.<\/p>\n

Holden, A. (1991). Shapes, Space and Symmetry<\/span>. New York, Dover Publications.<\/p>\n

Howard, T. C. (1958). Possible Ways the Random Geometric Grid Developed by Lincoln Laboratories may be Covered by Patent 2,682,235 Owned by Inventor R. Buckminster Fuller. Raleigh, NC, Geodesics, Inc.<\/p>\n

Huybers, P. (1993). “Computer-Aided Design of Polyhedral Building Structures.” Design Studies<\/span> 14<\/strong>(1).<\/p>\n

Huybers, P. (1997). The Polyhedral World. Beyond the Cube: The Architecture of Space Frames and Polyhedra<\/span>. J. F. o. Gabriel. New York, John Wiley & Sons, Inc.: <\/strong>243-279.<\/p>\n

Kahn, L. (1974). Domebook Two<\/span>. Bolinas, CA, Shelter Publications.<\/p>\n

Kahn, L., Ed. (1989). Refried Domes<\/span>. Bolinas, CA, Shelter Publications.<\/p>\n

Kahn, L. (1989). The Wonder of Jeana. Refried Domes<\/span>. Bolinas, CA, Shelter Publications, Inc.: <\/strong>12-13.<\/p>\n

Kells, L. M., W. F. Kern, et al. (1943). Plane and Spherical Trigonometry<\/span>. New York, McGraw-Hill Book Co., Inc.<\/p>\n

Kenner, H. (2003). Geodesic Math and How to Use It<\/span>. Berkeley, CA, University of California Press.<\/p>\n

Kitrick, C. J. (1990). “A Unified Approach to Class I, II and III Geodesic Domes.” International Journal of Space Structures<\/span> 5<\/strong>(3-4): 223-246.<\/p>\n

Lalvani, H. (1996). Space Structures with Non-Periodic Subdivisions of Polygonal Faces. USPTO. United States.<\/p>\n

Leighton, H. L. C. (1943). Solid Geometry and Spherical Trigonometry<\/span>. New York, NY, D. Van Nostrand.<\/p>\n

Leytem, C. (1996). “Hidden Symmetries in the Snub Dodecahedron.” European Journal of Combinatronics<\/span> 17<\/strong>(5): 451-460.<\/p>\n

Livio, M. (2002). The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number<\/span>. New York, Broadway Books.<\/p>\n

Loeb, A. L. (1976). Space Structures: Their Harmony and Counterpoint<\/span>. Reading, MA, Addison Wesley Pub. Co.<\/p>\n

Lorance, L. (2009). Becoming Bucky Fuller<\/span>. Cambridge, MA, MIT Press.<\/p>\n

MacLean, K. J. M. (2007). A Geometric Analysis of the Platonic Solids and Other Semi-Regular Polyhedra: With an Introduction to the Phi Ratio – for Teachers, Researchers and the Generally Curious<\/span>. Ann Arbor, MI, Loving Healing Press.<\/p>\n

Makai, E. J. (1975). On Some Geometrical Problems of Single-Layered Spherical Grids with Triangular Network. II International Conf. on Space Structures<\/span>. University of Surrey, Guilford, England: <\/strong>1975.<\/p>\n

Maor, E. (1998). Trigonometric Delights<\/span>. Princeton, NJ, Princeton University Press.<\/p>\n

Marks, R. W. and R. B. Fuller (1973). The Dymaxion World of Buckminster Fuller<\/span>. Garden City, NY, Anchor Books.<\/p>\n

Matsko, V. J. (2009). “Polyhedra and Geodesic Structures<\/a><\/strong>.”<\/p>\n

Messer, P. W. (1999). Mathematical Formulas for Geodesic Domes. Spherical Models<\/span>. M. J. Wenninger. New York, Dover: <\/strong>145-149.<\/p>\n

Morgan, G. J. (2003). “Historical Review: Viruses, Crystals and Geodesic Domes.” Trends in Biochemical Sciences<\/span> 28<\/strong>(2): 86-90.<\/p>\n

Museum of Modern Art (1960). Three Structures by Buckminster Fuller in the Garden of the Museum of Modern Art. New York, Museum of Modern Art.<\/p>\n

Otero, C. and R. Togores (2002). Computational Geometry and Spatial Meshes. International Conference Computational Science ICCS 2002 Part II<\/span>. M. A. Sloot. Amsterdam: <\/strong>315-324.<\/p>\n

Pearce, P. (1978). Structure in Nature is a Strategy for Design<\/span>. Cambridge, MA, MIT Press.<\/p>\n

Pearce, P. and S. Pearce (1978). Polyhedra Primer<\/span>. New York, Van Nostrand Reinhold.<\/p>\n

Pearson, F. (1984). Map Projection Methods<\/span>. Blacksburg, VA, Sigma Scientific, Inc. Computer Science Corporation.<\/p>\n

Popko, E. S. (1968). Geodesics<\/span>. Detroit, University of Detroit Press.<\/p>\n

Puderbaugh, H. L. (1964). “Projections for a Geodesic Sphere.” Architectural Science Review<\/span>(March): 19-26.<\/p>\n

Pugh, A. (1976). Polyhedra – A Visual Approach<\/span>. Berkeley, CA, University of California Press.<\/p>\n

Radin, C. (2006). “Review of The Pursuit of Perfect Packing.” The Mathematical Association of America<\/span> 113<\/strong>: 88-90.<\/p>\n

Richeson, D. S. (2008). Euler’s Gem: the Polyhedron Formula and the Birth of Topology<\/span>. Princeton, NJ, Princeton University Press.<\/p>\n

Roberts, S. (2006). King of Infinite Space – Donald Coxeter, the Man Who Saved Geometry<\/span>. New York, Walker & Company.<\/p>\n

Sadao, S. (2011). Buckminster Fuller and Isamu Noguchi: Best of Friends<\/span>. Milan, 5 Continents Editions.<\/p>\n

Saff, E. B. and A. B. J. Kuijlaars (1997). “Distributing Many Points on the Sphere.” Mathematical Intelligencer<\/span> 12<\/strong>(1): 5-11.<\/p>\n

Sahr, K., D. White, et al. (2003). “Geodesic Discrete Global Grid Systems.” Cartography and Geographic Information Science<\/span> 30<\/strong>(2): 121-134.<\/p>\n

Sherwood, A. (2007). “How can I arrange N points evenly on a sphere<\/a>?<\/strong>” A collection of links for sphere arrangement problems<\/span>.<\/p>\n

Skilling, J. (1975). “The Complete Set of Uniform Polyhedra.” Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical & Engineering Sciences<\/span> 278<\/strong>: 111-135.<\/p>\n

Snelson, K. D. (1965). Continuous Tension, Discontinuous Compression Structures. USPTO. United States.<\/p>\n

Snelson, K. D. (2002). “Circles, Spheres and Atoms.” Symmetry: Culture and Science<\/span> 13<\/strong>(1): 1-18.<\/p>\n

Snyder, J. P. (1987). Map Projections – A Working Manual. Washington, U. S. Geological Survey.<\/p>\n

Sobel, D. (1995). Longitude: the True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time<\/span>. New York, Walker.<\/p>\n

Song, L., J. Kimerling, et al. (2002). Developing An Equal Area Global Grid by Small Circle Subdivision. Discrete Global Grids<\/span>. Santa Barbara, CA, University of California, National Center for Geographic Information & Analysis.<\/p>\n

Spunt, L. (1976). Modular Dome Structures. IASS World Congress on Space Enclosures<\/span>. Montreal, Build. Res. Centre Concordia, University Montreal. 1: <\/strong>235-240.<\/p>\n

State University Colorado (2001). “Geodesics Climate Model Uses Different Mapping Techniques, Coordinates and Supercomputing to Improve Predictions<\/a><\/strong>.” ScienceDaily<\/span>.<\/p>\n

Stuart, D. R. (1962). “Polyhedra.” Student Publications of the School of Design North Carolina State University<\/span> 3<\/strong>(1).<\/p>\n

Stuart, D. R. (1963). “The Orderly Subdivision of Spheres.” The Student Publications of the School of Design, North Carolina State University<\/span> 5<\/strong>: 23-33.<\/p>\n

Sutton, D. (2002). Platonic & Archimedean Solids<\/span>. New York, Walker & Co.<\/p>\n

Szalay, A. S., J. Gray, et al. (2005). Indexing the Sphere with the Hierarchical Triangular Mesh. Redmond, WA, Microsoft Corp. Research Advanced Technology Division, Technical Report MSR-TR-2005-123.<\/p>\n

Tammes, P. M. L. (1930). “On the Origin of Number and Arrangement of the Places of Exit on the Surface of Pollen-Grains.” Recueil des Travaux Botaniques N\u00e9erlandais<\/span> 27<\/strong>: 1-84.<\/p>\n

Tarnai, T. (1974). “Spherical Grids of Triangular Network.” Acta Technica Academiae Scientiarum Hungaricae<\/span> 76<\/strong>: 307-336.<\/p>\n

Tarnai, T. (1983). “Geodesic Dome with Three Different Bar Lengths.” Structural Topology<\/span> 8<\/strong>: 23-24.<\/p>\n

Tarnai, T. (1984). “Spherical Circle-Packing in Nature, Practice and Theory.” Structural Topology<\/span> 9<\/strong>: 39-58.<\/p>\n

Tarnai, T. (1992). Dense Sphere Packing on a Sphere. First International Seminar on Structural Morphology<\/span>. R. Motro and T. Wester. Montpellier – Le Grand Motte, France: <\/strong>53-62.<\/p>\n

Tarnai, T. (1993). “Geodesic Domes and Fullerenes.” Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical & Engineering Sciences<\/span> 343<\/strong>(1667).<\/p>\n

Tarnai, T. (1993). Geodesic Domes and Golf Balls. Space Structures<\/span>. 4: <\/strong>1176-1183.<\/p>\n

Tarnai, T. (2002). “Polymorphism in Multi Symmetric Close Packings of Equal Spheres on a Spherical Surface.” Structural Chemistry<\/span> 13<\/strong>(3-4): 289-295.<\/p>\n

Tarnai, T. and Z. G\u00e1sp\u00e1r (1985). Covering the Sphere with Equal Circles. Colloquium on Intuitive Geometry<\/span>. Balatonsz\u00e9plak, Hungary.<\/p>\n

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Thompson, D. A. W. (1992). On Growth and Form<\/span>. New York, Dover.<\/p>\n

Tickoo, S. and V. Sing (2008). CATIA V5R18 for Designers<\/span>. Schererville, IN, CADCIM Technologies.<\/p>\n

Tomlow, J., Ed. (1997). Polyhedra from Pythagoras to Alexander Graham Bell<\/span>. Beyond the Cube: The Architecture of Space Frames and Polyhedra. New York, John Wiley & Sons, Inc.<\/p>\n

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Unger, K. (1991). “The Invention Behind the Invention.” Synergetica Journal, Buckminster Fuller Institute<\/span> 1<\/strong>(1).<\/p>\n

University of Minnesota Science and Technology Center (2008). “The Geometry Center – A Project of the National Science Foundation<\/a><\/strong>.”<\/p>\n

University of New South Wales (2008). “Distributing Points on the Sphere<\/a><\/strong>.” School of Mathematics and Statistics<\/span>.<\/p>\n

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Wenninger, M. J. (1971). Polyhedron Models<\/span>. Cambridge [Eng.], University Press.<\/p>\n

Wenninger, M. J. (1983). Dual Models<\/span>. New York, Cambridge University Press.<\/p>\n

Wenninger, M. J. (1999). Spherical Models<\/span>. Mineola, NY, Dover.<\/p>\n

Wertz, J. R. and W. J. Larson (1999). Space Mission Analysis and Design<\/span>. El Segundo, CA, Microcosm.<\/p>\n

Weyl, H. (1952). Symmetry<\/span>. Princeton, NJ, Princeton University Press.<\/p>\n

White, D. (2000). “Global Grids from Recursive Diamond Subdivisions of the Surface of an Octahedron or Icosahedron.” Environmental Monitoring and Assessment<\/span> 64<\/strong>(1): 93-103.<\/p>\n

White, D., A. J. Kimerling, et al. (1992). “Cartographic and Geometric Components of a Global Sampling Design for Environmental Monitoring.” Cartography and Geographic Information Systems<\/span> 10<\/strong>(1): 5-22.<\/p>\n

Xiaochong, T., B. Jin, et al. (2002). The Expression of Spherical Entities and Generating of Voronoi Diagrams Based on Truncated Icosahedron DGG. Zhengzhou, China, Institute of Surveying and Mapping.<\/p>\n

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Bagchi, B. (1997). “How to Stay Away from Each Other in a Spherical Universe.” Resonance(September): 18-26.Ball, W. W. R. and H. S. M. Coxeter (1987). Mathematical Recreations and Essays. New York, Dover Publications. Bohlen, J. C. (1974). Trigonometric Relationships for Geodesic Domes with Special Reference to the Dodecahedron. Vancouver, BC, Western Forest Products Laboratory, Information […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":22,"menu_order":2,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-225","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/pages\/225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dividedspheres.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=225"}],"version-history":[{"count":10,"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/pages\/225\/revisions"}],"predecessor-version":[{"id":233,"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/pages\/225\/revisions\/233"}],"up":[{"embeddable":true,"href":"https:\/\/dividedspheres.com\/index.php?rest_route=\/wp\/v2\/pages\/22"}],"wp:attachment":[{"href":"https:\/\/dividedspheres.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}