### 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 language | English |
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Title of host publication | Model-Based Reasoning in Science and Technology |

Subtitle of host publication | Abduction, Logic, and Computational Discovery |

Editors | Lorenzo Magnani, Walter Carnielli, Claudio Pizzi |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 301-314 |

Number of pages | 14 |

ISBN (Electronic) | 9783642152238 |

ISBN (Print) | 9783642152238 |

DOIs | |

Publication status | Published - 2010 |

Event | Model-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery - State University of Campinas , Campinas, Brazil Duration: 17 Dec 2009 → 19 Dec 2009 http://www-3.unipv.it/webphilos_lab/courses/progra4.html |

### Publication series

Name | Studies in Computational Intelligence |
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Volume | 314 |

### Conference

Conference | Model-Based Reasoning in Science and Technology: Abduction, Logic, and Computational Discovery |
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Abbreviated title | MBR'09_Brazil |

Country | Brazil |

City | Campinas |

Period | 17/12/09 → 19/12/09 |

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