Abstract
A wallpaper map is a conformal projection of a spherical earth onto regular polygons with which the plane can be tiled continuously. A complete set of distinct wallpaper maps that satisfy certain natural symmetry conditions is derived and illustrated. Though all of the projections have been published before, some generalize to one-parameter families in which the sphere is pre-transformed by a conformal automorphism.
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References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Applied Mathematics Series, vol. 55. National Bureau of Standards (1965)
Adams, O.A.: Elliptic Functions Applied to Conformal World Maps. Special publication no. 112, U.S. Coast and Geodetic Survey (1925)
Adams, O.A.: Conformal Projection of the Sphere within a Square. Special publication no. 153, U.S. Coast and Geodetic Survey (1929)
Adams, O.A.: Conformal map of the world in a square. Bulletin Géodèsique, 461–473 (1936)
Bieberbach, L.: Conformal Mapping. Chelsea (1953), translated by F. Steinhardt
Coxeter, H.S.M.: Regular Polytopes. Dover, New York (1973), reprint of Macmillan edition of 1963
Guyou, E.: Sur un nouveau système de projection de la sphère. Comptes Rendus de l’Acad/’emie des Sciences 102, 308–310 (1886)
Lee, L.P.: Conformal Projections based on Elliptic Functions. Cartographica Monograph 16 (1976)
McIlroy, M.D.: Power series, power serious. Journal of Functional Programming 9, 325–337 (1999)
McIlroy, M.D.: Wallpaper maps (2011), an extended version of the present paper, http://www.cs.dartmouth.edu/~doug/wallpaper.pdf
Pedoe, D.: Geometry: A Comprehensive Course. Dover, New York (1988)
Peirce, C.S.: A quincuncial projection of the sphere. American Journal of Mathematics 2, 394–396 and one unpaginated plate (1879)
Schwarz, H.A.: Über einige abbildungsaufgaben. Journal für die reine un angewandte Mathematik 70, 105–120 (1869)
Snyder, J.P.: Flattening the Earth. University of Chicago Press, Chicago (1997)
Snyder, J.P., Voxland, P.M.: An Album of Map Projections. Professional Paper 1453, U.S. Geological Survey (1989)
Weyl, H.: Symmetry. Princeton University Press, Princeton (1952)
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© 2011 Springer-Verlag Berlin Heidelberg
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McIlroy, M.D. (2011). Wallpaper Maps. In: Jones, C.B., Lloyd, J.L. (eds) Dependable and Historic Computing. Lecture Notes in Computer Science, vol 6875. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24541-1_27
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DOI: https://doi.org/10.1007/978-3-642-24541-1_27
Publisher Name: Springer, Berlin, Heidelberg
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