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The shape of two-dimensional space

Mackay, Alan L. (2002) The shape of two-dimensional space. In: Hargittai, I. and Laurent, T. (eds.) Symmetry 2000 : proceedings from a symposium held at the Wenner-Gren Centre, Stockholm, in September 2000. Wenner-Gren International Series 80. London, UK: Portland Press, pp. 143-159. ISBN 1855781492.


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Genomics, so fashionable today, is only half of the secret of life. The other half of the secret is shape, form, morphogenesis and metamorphosis. The gene may prescribe what is synthesised, but the proteins appear and operate in a pre-existing environment which they then change. The first step towards life is the appearance of a micelle, a spherical membrane, a surface which separates the world into inside and outside. We are here concerned with surfaces, with a particular subset of two-dimensional manifolds embedded in three-dimensional Euclidean space, namely the non-self-intersecting, periodic minimal surfaces of cubic symmetry, which separate the world into two regions as an infinite plane would do, but with much more complex topologies. Like the Platonic solids , these cubic surfaces are geometrical absolutes and have distinctive topologies but entail no arbitrary parameters . The objective is to enumerate at least some of these surfaces, for probably an infinite number answer to this description, to draw attention to their geometry and to point to some of their applications and occurrences on various scales between mega-engineering and nano-technology. These objects are solutions looking for problems.

Item Type: Book Section
School or Research Centre: Birkbeck Schools and Research Centres > School of Science > Biological Sciences
Depositing User: Sandra Plummer
Date Deposited: 19 Dec 2005
Last Modified: 17 Apr 2013 12:32

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