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Visualization, Explanation and Reasoning Styles in MathematicsThe Aesthetics of Mathematics: A Study

Visualization, Explanation and Reasoning Styles in Mathematics: The Aesthetics of Mathematics: A... REVIEL NETZ To the memory of Heda Segvic 1. THE PROBLEM MOTIVATED Let us start with atrivial example, whichhowever already suggests the out- lines of theproblem at hand.Imagine I have collected my lunch at a self- service cafeteriaso that now my tray holds, say, a paper plate with a sand- wich on it, another one withfruit, andfinally, a soda ina large cup (the kind known as “small”). Now, as I prepare to detach myself from the counter, I arrange thethree objects on the tray. This can be approached through several theoretical perspectives. First, there isthemathematical-physical perspective, employing the spe- cific field of statics (pioneered,as we shall note again below, byArchimedes). The task is to arrange three objects on a plane, so that their individual cen- tres of gravity, and the centre of gravity of the system as a whole, will ensure maximum stability. One should in particular consider the problem of the system’s robustness, i.e. how it may react with the disturbances it is likely to undergo as I move towards a table. This is a very complex problem, and the fact that we very often (not always) solve it in effective ways, may indicate our powers of unconscious http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Visualization, Explanation and Reasoning Styles in MathematicsThe Aesthetics of Mathematics: A Study

Part of the Synthese Library Book Series (volume 327)
Editors: Mancosu, Paolo; Jørgensen, Klaus Frovin; Pedersen, Stig Andur

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References (18)

Publisher
Springer Netherlands
Copyright
© Springer 2005
ISBN
978-1-4020-3334-6
Pages
251 –293
DOI
10.1007/1-4020-3335-4_10
Publisher site
See Chapter on Publisher Site

Abstract

REVIEL NETZ To the memory of Heda Segvic 1. THE PROBLEM MOTIVATED Let us start with atrivial example, whichhowever already suggests the out- lines of theproblem at hand.Imagine I have collected my lunch at a self- service cafeteriaso that now my tray holds, say, a paper plate with a sand- wich on it, another one withfruit, andfinally, a soda ina large cup (the kind known as “small”). Now, as I prepare to detach myself from the counter, I arrange thethree objects on the tray. This can be approached through several theoretical perspectives. First, there isthemathematical-physical perspective, employing the spe- cific field of statics (pioneered,as we shall note again below, byArchimedes). The task is to arrange three objects on a plane, so that their individual cen- tres of gravity, and the centre of gravity of the system as a whole, will ensure maximum stability. One should in particular consider the problem of the system’s robustness, i.e. how it may react with the disturbances it is likely to undergo as I move towards a table. This is a very complex problem, and the fact that we very often (not always) solve it in effective ways, may indicate our powers of unconscious

Published: Jan 1, 2005

Keywords: Mathematical Text; Greek Mathematics; Direct Awareness; Contemporary Literary Theory; Atical Text

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