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Using Analogical Representations for Mathematical Concept Formation

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Model-Based Reasoning in Science and Technology

Part of the book series: Studies in Computational Intelligence ((SCI,volume 314))

Abstract

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.

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Author information

Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Informatics Forum, 10 Crichton Street, Edinburgh, EH8 9AB, United Kingdom

    Alison Pease, Alan Smaill & Markus Guhe

  2. Department of Computing, Imperial College London, 180 Queens Gate, London, SW7 2RH, United Kingdom

    Simon Colton & Ramin Ramezani

Authors
  1. Alison Pease
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  2. Simon Colton
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  3. Ramin Ramezani
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  4. Alan Smaill
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  5. Markus Guhe
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Editor information

Editors and Affiliations

  1. Università di Pavia, Pavia, Italy

    Lorenzo Magnani

  2. CLE State University of Campinas, Campinas, Brazil

    Walter Carnielli

  3. Università di Siena, Siena, Italy

    Claudio Pizzi

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Pease, A., Colton, S., Ramezani, R., Smaill, A., Guhe, M. (2010). Using Analogical Representations for Mathematical Concept Formation. In: Magnani, L., Carnielli, W., Pizzi, C. (eds) Model-Based Reasoning in Science and Technology. Studies in Computational Intelligence, vol 314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15223-8_17

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  • DOI: https://doi.org/10.1007/978-3-642-15223-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15222-1

  • Online ISBN: 978-3-642-15223-8

  • eBook Packages: EngineeringEngineering (R0)

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