Abstract
In order to understand and to reconstruct the shape of many objects of the geometric world, mathematicians have focused their attention on singularities and deformations. The purpose of this article is to present these usual topological concepts and tools to artists being a priori unfamiliar with mathematics, with the hope that new beautiful creations will appear in the artistic world.
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Notes
- 1.
The topological dimension of a point is 0, of a line, 1, of a surface 2, of our usual space 3, of the space-time 4, etc.
- 2.
“Blowing up” is a standard mathematical term (in French “éclatement”). Mathematicians call the inflated part the “blowup” of the singular part.
References
Bruter, C.P.: Deux Universaux de la Décoration http://math-art.eu/pdfs/ConferenceSaverne.pdf (2010). Accessed 10 April 2010
Faber, E., Hauser, H.: Today’s menu: Geometry and resolution of singular algebraic surfaces. Bull. Am. Math. Soc. 47(3), 373–417 (2010)
Francis, G.K.: A Topological Picturebook. Springer, New York (1987)
Acknowledgments
I am deeply indebted to Jean Constant who gave up so much time to correct all my Franglish ESMA papers, including that one. Many thanks also to Dick Palais and Simon Salamon and an anonymous author who did the same work on the text of the Preface.
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© 2012 Springer-Verlag Berlin Heidelberg
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Bruter, C.P. (2012). An Introduction to the Construction of Some Mathematical Objects. In: Bruter, C. (eds) Mathematics and Modern Art. Springer Proceedings in Mathematics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24497-1_4
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DOI: https://doi.org/10.1007/978-3-642-24497-1_4
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