Integer-Digit Functions: An Example of Math-Art Integration

Integer-Digit Functions: An Example of Math-Art Integration Integer-Digit Functions: An Example of Math- Art Integration ERNESTO ESTRADA ‘‘God made the integers, all else is the work of man.’’ L. Kronecker athematics and the visual arts mutually reinforce Digit Sum with ‘‘Memory’’ one another [10]. On the one hand, many math- A nonnegative integer N can be represented in a given base ematical objects appear in artistic or decorative M b according to the following expression works [5, 6]. In particular, mathematical curves and art have n n1 n2 N ¼ a b þ a b þ a b þ  þ a b þ a ; ð1Þ 1 2 3 n1 n a long-standing connection through the application of geometric principles [13, 20]. Simple curves such as the where a are nonnegative integers. We can represent a catenary are ubiquitous, for example in the work of the negative integer in a similar way if we multiply by 1 the Catalan architect Antoni Gaudı, as well as in ancient [19] right-hand-side part of the previous equation. For instance, and in modern architecture [12]. On the other hand, many the number N ¼ 257, expressed in the base b ¼ 10, is: mathematical objects display artistic appeal per http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Mathematical Intelligencer Springer Journals

Integer-Digit Functions: An Example of Math-Art Integration

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Publisher
Springer US
Copyright
Copyright © 2018 by The Author(s)
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Mathematical and Computational Engineering
ISSN
0343-6993
eISSN
1866-7414
D.O.I.
10.1007/s00283-017-9726-x
Publisher site
See Article on Publisher Site

Abstract

Integer-Digit Functions: An Example of Math- Art Integration ERNESTO ESTRADA ‘‘God made the integers, all else is the work of man.’’ L. Kronecker athematics and the visual arts mutually reinforce Digit Sum with ‘‘Memory’’ one another [10]. On the one hand, many math- A nonnegative integer N can be represented in a given base ematical objects appear in artistic or decorative M b according to the following expression works [5, 6]. In particular, mathematical curves and art have n n1 n2 N ¼ a b þ a b þ a b þ  þ a b þ a ; ð1Þ 1 2 3 n1 n a long-standing connection through the application of geometric principles [13, 20]. Simple curves such as the where a are nonnegative integers. We can represent a catenary are ubiquitous, for example in the work of the negative integer in a similar way if we multiply by 1 the Catalan architect Antoni Gaudı, as well as in ancient [19] right-hand-side part of the previous equation. For instance, and in modern architecture [12]. On the other hand, many the number N ¼ 257, expressed in the base b ¼ 10, is: mathematical objects display artistic appeal per

Journal

The Mathematical IntelligencerSpringer Journals

Published: Feb 15, 2018

References

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