Research
Journal Article – Journal of Mathematics and the Arts
April 23, 2020
My journal article, “Structure from appearance: topology with shapes, without points,” appears in the Journal of Mathematics and the Arts.
Abstract
This journal article on mathematics and the arts presents a new methodological approach to study the topology of shapes made with lines, planes or solids. Topologies for shapes traditionally follow the classical theory of point-sets. This paper formalizes topologies with shapes without a point-set representation, using structures defined with visible parts. It introduces an interpretative aesthetic dimension according to which the topology of a shape is not inherited from an ambient space but is induced based on how its appearance is interpreted into parts.
This methodological approach provides a more natural, spatial framework to study the mathematical structure of design objects in art and design. It shows how objects of art and design can directly lead to mathematical constructs (here, topology). This is opposite of a more common approach, where objects of art and design conform to canonical mathematical constructs.
Context
The results that this paper presents contribute broadly to the intersection of mathematics and architecture. Specifically, the paper contributes to the areas formed by studies on topology and configurations, shape grammars, and architectural morphology. For further work on mathematics and architecture, please see my existing and upcoming publications.