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Imagination in mathematics

In Amy Kind (ed.), Routledge Handbook on the Philosophy of Imagination. Routledge. pp. 463-477 (2016)

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  1. Diagrams in the Theory of Differential Equations (Eighteenth to Nineteenth Centuries).Dominique Tournès - 2012 - Synthese 186 (1):257-288.
    Diagrams have played an important role throughout the entire history of differential equations. Geometrical intuition, visual thinking, experimentation on diagrams, conceptions of algorithms and instruments to construct these diagrams, heuristic proofs based on diagrams, have interacted with the development of analytical abstract theories. We aim to analyze these interactions during the two centuries the classical theory of differential equations was developed. They are intimately connected to the difficulties faced in defining what the solution of a differential equation is and in (...)
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  • The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
    This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...)
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  • A Commentary on the First Book of Euclid's Elements.Glenn R. Proclus & Morrow - 1970
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  • La philosophie malebranchiste des mathématiques.Andre Robinet - 1961 - Revue d'Histoire des Sciences 14 (3-4):205-254.
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