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Diagrammatics in Art and Mathematics by Radmila Sazdanovic

Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA; E-Mail: radmilas@math.upenn.edu; Tel.: +1-215-898-6285; Fax: +1-215-898-2010

Received: 8 March 2012; in revised form: 25 April 2012 / Accepted: 28 April 2012 /

Published: 22 May 2012

This paper explores two-way relations between visualizations in mathematics and mathematical art, as well as art in general. A collection of vignettes illustrates connection points, including visualizing higher dimensions, tessellations, knots and links, plotting zeros of polynomials, and new and rapidly developing mathematical discipline, diagrammatic categorification.

This begins with some math-art and stuff about non-Euclidean geometries, then knot theory.

4. Diagrammatic Categorification

In this section we will describe a few research level results for which the visualizations are essential and relevant to mathematics. A nice example where diagrammatics naturally lends itself to mathematical concepts is the bijection (the bijection is between sets) between unoriented one dimensional topological field theories over some field k and the finite dimensional k-vector spaces with a non-degenerate bilinear form.

The paper then shows some artistic interpretations of these, integral diagrams.

This relates a little to Giaquinto. I’m not sure whether the case is made for a two-way math-art relationship but the value, cognitive and aesthetic, of diagramming is underlined.

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