Why do mathematicians need different ways of presenting mathematical objects? The case of cayley graphs

Topoi 29 (1):41-51 (2010)
Abstract
This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed as exact mathematical constructions. Therefore, they are legitimate components of the theory (combinatorial and geometric group theory) and the pictures of Cayley graphs are a part of practical mathematical procedures.
Keywords Visualisation  Intuition  Geometry of groups  Cayley graphs
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