Why do mathematicians need different ways of presenting mathematical objects? The case of cayley graphs
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
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Topoi 29 (1):41-51 (2010)
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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References found in this work BETA
Charles Parsons (2007). Mathematical Thought and its Objects. Cambridge University Press.
Solomon Feferman (2000). Mathematical Intuition Vs. Mathematical Monsters. Synthese 125 (3):317-332.
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