‘‘God made the integers, all else is the work of man.’’
L. Kronecker
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References
A. Åström, and C. Åström, Circular knotworks consisting of pattern no. 295: a mathematical approach, Journal of Mathematics and the Arts 5 (2011), 185–197.
R. Bosch, Simple-closed-curve sculptures of knots and links, Journal of Mathematics and the Arts 4 (2010), 57–71.
R. Bosch, and U. Colley, Figurative mosaics from flexible Truchet tiles, Journal of Mathematics and the Arts 7 (2013), 122–135.
J. Briggs, Fractals: The patterns of chaos: a new aesthetic of art, science, and nature, Simon and Schuster (1992).
P. R. Cromwell, Celtic knotwork: mathematical art, The Mathematical Intelligencer 15 (1993), 36–47.
P. R. Cromwell, The search for quasi-periodicity in Islamic 5-fold ornament, The Mathematical Intelligencer 31 (2009), 36–56.
E. Estrada, and L. A. Pogliani, A new integer sequence based on the sum of digits of integers. Kragujevac Journal of Sciences 30 (2008), 45–50.
K. Fenyvesi, Bridges: A World Community for Mathematical Art, The Mathematical Intelligencer 38 (2016), 35–45.
F. A. Farris, Symmetric yet organic: Fourier series as an artist’s tool, Journal of Mathematics and the Arts 7 (2013), 64–82.
L. Gamwell, Mathematics and Art: A Cultural History, Princeton University Press (2015).
G. Irving, and H. Segerman, Developing fractal curves, Journal of Mathematics and the Arts 7 (2013), 103–121.
G. Kaplan, The Catenary: Art, Architecture, History, and Mathematics, Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture. Tarquin Publications (2008).
L. Koudela, Curves in the history of mathematics: the late renaissance, WDS’05 Proceedings of Contributed Papers, Part I (2005), pp. 198–202.
C. Mauduit, Substitutions et ensembles normaux, Habilitation Dir. Rech., Universit Aix-Marseille II, 1989.
C. H. Séquin, Topological tori as abstract art, Journal of Mathematics and the Arts 6 (2012), 191–209.
N. J. A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press. Web, edition at https://oeis.org.
N. J. A. Sloane, My Favorite Integer Sequences, in C. Ding, T. Helleseth, and H. Niederreiter, eds. Sequences and their Applications (Proceedings of SETA ’98), Springer-Verlag, pp. 103–130, 1999.
The Bridges Organization, Bridges, website, http://www.bridgesmathart.org/.
H. Yanai, and K. Williams, Curves in traditional architecture in East Asia, The Mathematical Intelligencer 23 (2001), 52–57.
R. C. Yates, A Handbook of Curves and their Properties, Literary Licensing, LLC (2012).
X. Zheng, and N. S. Brown, Symmetric designs on hexagonal tiles of a hexagonal lattice, Journal of Mathematics and the Arts 6 (2012), 19–28.
Acknowledgments
The author thanks artist Puri Pereira for useful discussions. He also thanks the Royal Society of London for a Wolfson Research Merit Award. Finally he thanks Gizem Karaali for her editorial assistance.
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Estrada, E. Integer-Digit Functions: An Example of Math-Art Integration. Math Intelligencer 40, 73–78 (2018). https://doi.org/10.1007/s00283-017-9726-x
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DOI: https://doi.org/10.1007/s00283-017-9726-x