MATHEMATICS IN M.C. ESCHER’S GALLERY
Keywords:
M.C. Escher, Complex transformation, Wallpaper Group, Symmetry, Spiral, InfinityAbstract
M.C. Escher, a Dutch graphic artist, is renowned for his masterful integration of mathematical concepts into his art. His work, particularly the piece Gallery exemplifies the seamless blend of art and mathematics, showcasing the beauty and complexity inherent in both fields. This paper delves into the mathematical structures underlying Escher's Gallery exploring the principles of complex transformations and wallpaper groups. By analyzing these elements, we aim to uncover the profound connections between art and mathematics, and how Escher's work challenges our perception of reality.References
[1] Locher J, Veldhuysen W. The Magic of M.C. Escher. Thames & Hudson, London, 2013.
[2] Schattschneider D. Visions of Symmetry. Harry N Abrams, New York, 2004.
[3] Escher M C, Vermeulen, J W. Escher on Escher: Exploring the Infinite. Harry N Abrams, New York, 1989.
[4] Escher M C. The Official Website: https://mcescher.com/gallery/
[5] Kaplan C S. Escher-like spiral tilings. https://isohedral.ca/escher-like-spiral-tilings/
[6] Dixon R. Two conformal mappings. Leonardo, 1992, 25(3/4): 263-266.
[7] Ahlfors L V. Conformal Invariants: Topics in Geometric Function Theory. McGraw-Hill, New York, 1973.
[8] Nehari Z. Conformal Mapping. McGraw-Hill, New York, 1952.
[9] Conway J H, Burgiel H, Goodman-Strauss C. The Symmetries of Things. A.K. Peters/CRC Press, Boca Raton, FL, 2008.
[10] Coxeter H S M. Regular Polytopes. Dover Publications, Mineola, NY, 1973.
[11] Carter N C, Grimes S M, Reiter C A. Frieze and wallpaper chaotic attractors with a polar spin. Comput. Graph, 1998, 22(6): 765-779.
[12] Grünbaum B, Shephard, G C. Spiral tilings and versatiles. Math. Teach, 1979, 88, 50-51.