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Using analogical representations for mathematical concept formation

Using analogical representations for mathematical concept formation

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

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Authors

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

Research units

Info

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
StatePublished - 2010
EventModel-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery - Campinas, Brazil

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

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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