# 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
42 pages

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# References (18)

Publisher
Springer Netherlands
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