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Diagrammatic Reasoning in Mathematics

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Springer Handbook of Model-Based Science

Part of the book series: Springer Handbooks ((SHB))

Abstract

The objective of the present chapter will be to review the most recent studies about diagrammatic reasoning in mathematics. Section 22.3 will focus on the very much discussed topic of the role and of the features of diagrams and diagrammatic reasoning in Euclidean geometry. Section 22.4 will be devoted to the proposal of considering diagrams as representations that are introduced in support of other symbolic practices and whose power resides in their ambiguity. In Sect. 22.5, the attention will turn toward studies discussing diagrammatic reasoning in contemporary mathematics. In Sect. 22.6 , computational perspectives on how to implement diagrammatic reasoning in computer programs will be introduced, both for Euclidean geometry and theory of numbers. In Sect. 22.7, it will be discussed how the study of diagrammatic reasoning can shed light onto the nature of mathematical thinking in general. Finally, in Sect. 22.8, some brief conclusions about diagrammatic reasoning in mathematics will be drawn. The choice of reviewing the research about diagrammatic reasoning along these lines is of course at least in part arbitrary. The aim of such a regrouping is to provide the reader with a map that can be helpful for exploring the various and already copious literature that has been recently produced on the subject. The ambition is that such a map will be as extensive as possible.

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Abbreviations

DIAMOND:

diagrammatic reasoning and deduction

GRM:

Gaussian random matrix

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Acknowledgements

My thanks go to the people quoted in the text, for their work and for the fruitful discussions in which I have taken part at recent conferences and workshops. I am particularly indebted to Mario Piazza and Silvia De Toffoli, with whom I have extensively reflected upon the topic of diagrammatic reasoning in mathematics. I am also grateful to Albrecht Heeffer, who gave me the occasion of working on this chapter and to the Université de Lorraine and the Région Lorrainefor having sustained my research.

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  1. Laboratoire d’Histoire des Sciences et de Philosophie – Archives Henri-Poincaré, UMR 7117 CNRS – Université de Lorraine, 91 avenue de la Libération, 54001, Nancy Cedex, France

    Valeria Giardino

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  1. Valeria Giardino
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Correspondence to Valeria Giardino .

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  1. Department of Humanities, University of Pavia, Piazza Botta 6, 27100, Pavia, Italy

    Lorenzo Magnani  & Tommaso Bertolotti  & 

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Giardino, V. (2017). Diagrammatic Reasoning in Mathematics. In: Magnani, L., Bertolotti, T. (eds) Springer Handbook of Model-Based Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-30526-4_22

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  • DOI: https://doi.org/10.1007/978-3-319-30526-4_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30525-7

  • Online ISBN: 978-3-319-30526-4

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