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Diagrams and Proofs in Analysis

Diagrams and Proofs in Analysis This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept formation as well as representations of proofs. In addition we note that ‘visualization’ is used in two different ways. In the first sense ‘visualization’ denotes our inner mental pictures, which enable us to see that a certain fact holds, whereas in the other sense ‘visualization’ denotes a diagram or representation of something. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Studies in the Philosophy of Science Taylor & Francis

Diagrams and Proofs in Analysis

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References (16)

Publisher
Taylor & Francis
Copyright
Copyright Open Society Foundation
ISSN
1469-9281
eISSN
0269-8595
DOI
10.1080/02698590903467085
Publisher site
See Article on Publisher Site

Abstract

This article discusses the role of diagrams in mathematical reasoning in the light of a case study in analysis. In the example presented certain combinatorial expressions were first found by using diagrams. In the published proofs the pictures were replaced by reasoning about permutation groups. This article argues that, even though the diagrams are not present in the published papers, they still play a role in the formulation of the proofs. It is shown that they play a role in concept formation as well as representations of proofs. In addition we note that ‘visualization’ is used in two different ways. In the first sense ‘visualization’ denotes our inner mental pictures, which enable us to see that a certain fact holds, whereas in the other sense ‘visualization’ denotes a diagram or representation of something.

Journal

International Studies in the Philosophy of ScienceTaylor & Francis

Published: Mar 1, 2010

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