Curvature Against the Grain

DOI

10.2991/gaf.k.200124.004How to use a DOI?

Keywords

Curvature; Casorati curvature; curvedness

Abstract

In mathematics “curvature” is described in various ways, but perhaps the most common is as a rate of spatial attitude. Such a definition is similar to the deviation from flatness, where flatness might again be understood (in various ways) in terms of congruence. In classical physics the notion of curvature occurs in kinematics and in the theory of elastic continuous media. The latter aspect is perhaps closest to what might be the notion of “curvature as a gut feeling.” It is least likely that hands-on experience with elastic materials in visuomotor interaction was at the root of the curvature as a proto-concept. One guesses it developed roughly in parallel with the development of spoken language, although “curvature” no doubt was present as a quality of experience with the Neanderthal, say. I consider relations between the very diverse notions of “curvature.” Curvature as a gut feeling survives even today in artistic intuition, it applies to most of us who appreciate sculpture.

Copyright

© 2020 The Authors. Published by Atlantis Press SARL

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Jan Koenderink
PY  - 2020
DA  - 2020/02/23
TI  - Curvature Against the Grain
JO  - Growth and Form
SP  - 9
EP  - 19
VL  - 1
IS  - 1
SN  - 2589-8426
UR  - https://doi.org/10.2991/gaf.k.200124.004
DO  - 10.2991/gaf.k.200124.004
ID  - Koenderink2020
ER  -