Using analogical representations for mathematical concept formation

Alison Pease (Lead / Corresponding author), Simon Colton (Lead / Corresponding author), Ramin Ramezani, Alan Smaill, Markus Guhe

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

    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.
    Original languageEnglish
    Title of host publicationModel-Based Reasoning in Science and Technology
    Subtitle of host publicationAbduction, Logic, and Computational Discovery
    EditorsLorenzo Magnani, Walter Carnielli, Claudio Pizzi
    Place of PublicationBerlin
    PublisherSpringer
    Pages301-314
    Number of pages14
    ISBN (Electronic)9783642152238
    ISBN (Print)9783642152238
    DOIs
    Publication statusPublished - 2010
    EventModel-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery - State University of Campinas , Campinas, Brazil
    Duration: 17 Dec 200919 Dec 2009
    http://www-3.unipv.it/webphilos_lab/courses/progra4.html

    Publication series

    NameStudies in Computational Intelligence
    Volume314

    Conference

    ConferenceModel-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery
    Abbreviated titleMBR'09_Brazil
    CountryBrazil
    CityCampinas
    Period17/12/0919/12/09
    Internet address

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  • Cite this

    Pease, A., Colton, S., Ramezani, R., Smaill, A., & Guhe, M. (2010). Using analogical representations for mathematical concept formation. In L. Magnani, W. Carnielli, & C. Pizzi (Eds.), Model-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery (pp. 301-314). (Studies in Computational Intelligence; Vol. 314). Springer . https://doi.org/10.1007/978-3-642-15223-8_17