Using Analogical Representations for Mathematical Concept Formation

Alison Pease, Simon Colton, Ramin Ramezani, Alan Smaill, Markus Guhe

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

We argue that visual, analogical representations of mathematical concepts can be used by automated theory formation systems to develop further concepts and conjectures in mathematics. We consider the role of visual reasoning in human development of mathematics, and consider some aspects of the relationship between mathematics and the visual, including artists using mathematics as inspiration for their art (which may then feed back into mathematical development), the idea of using visual beauty to evaluate mathematics, mathematics which is visually pleasing, and ways of using the visual to develop mathematical concepts. We motivate an analogical representation of number types with examples of "visual" concepts and conjectures, and present an automated case study in which we enable an automated theory formation program to read this type of visual, analogical representation.

Original languageEnglish
Title of host publicationMODEL-BASED REASONING IN SCIENCE AND TECHNOLOGY: ABDUCTION, LOGIC AND COMPUTATIONAL DISCOVERY
EditorsL Magnani, W Carnielli, C Pizzi
Place of PublicationBERLIN
PublisherSpringer-Verlag GmbH
Pages301-314
Number of pages14
ISBN (Print)978-3-642-15222-1
Publication statusPublished - 2010

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