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to attract significant collections and nurture public interest is increasingly being understood as a series of steady changes dating back to eighteenth-century collections such as those of Hans Sloane and Charles Willson Peale. Levin examines the Crystal Palace ofthe 1851 exposition in London as an historical precedent for temporary spaces in today’s museums, but he fails to realize that the Great Exposition influenced museums more through the direction that its chief executive, Henry Cole, brought to the museum field. In 1852, Cole took command of the museum that became the Victoria and Albert and used his exposition experience to attract popular audiences to the museum with educational displays, lectures, entertainments and publications . Perhaps a morejudicious treatment of such historical material might have helped Levin to place his study in clearer perspective. Reviewedby Robert I. Goler, Fraunces Tavern Museum, 54 Pearl Street, New York, NY 1OOO4, USA. Symmetry - An Analytic Treatment. J. Lee Kavanau. Science Software Systems Inc., Los Angeles, 1980. 650 pp., illus. Curves and Symmetry. J. Lee Kavanau. Science Software SystemsInc., Los Angeles, 1982.430pp.. illus. Structural Equation Geometry. J. Lee Kavanau . Science Software Systems Inc., Los Angeles, 1983. 505 pp., illus. J. Lee Kavanau has produced three heavy volumes designed to survey and classify geometric curves in terms of a novel ‘symmetry’ theory. This is actually an algebraic approach to the properties of curves and has little in common with the orthodox meaningof ‘symmetry’as ‘patterns ofidentical parts with identical complements’ which crystallographic theory classifies in terms of isometry groups. Herein liesthe first problem with Kavanau’s work. The reader must struggle with a new concept under an old label. Kavanau does not explain why he makes this terminological move that virtually ignores the important concept of classicalsymmetry. Perhaps he sees his work as embracing a higher generality of meaning. Or maybe it is an attempt to give a more precisemeaning to that occasional usage of ‘symmetry’which refers to vague notions of simplicityand regularity.Certainly he doesnot help his caseby failingto givea clear definition of what he means by ‘symmetry’, which he seems to be identifying with equational simplicity. The author states that he has in mind as a suitable reader the mathematics undergraduate who might otherwise miss the chance of doing some concretemathematics; I would not recommend these books to the mathematically uninitiated. Nevertheless, there are numerous pictures of computer-drawn curves which begin to hint at what Kavanau is trying to do and might well inspire a casual interest in their own right. We see circles, conics, cardioids, rose-curves, limacons, Cassinian ovals, Cartesian ovals and so on. By exploring these curves of various geometric transformations, Kavanau sets about demonstrating numerous hidden relationships and an overall systematic procedure for classifyingcurves into families. In fact he isdelvinginto an almost-forgotten goldmine of old-style geometric research. Thus, for example,who would suspectthat the cardioid (heart-shaped) is the mirror-image of the parabola, when the reflectionin question is taken in a circle,i.e. thetransformation known as inversion: (Y, 0) -(Vr,O)? But these books aredensely written and very awkward to follow. In the end I felt that the only service Kavanau is performing is providing drawings of traditional curves, produced through the modern facility of computer graphics. I would have preferred a much shorter text with many more drawings. I particularly likedthe eggobtained by inverting an ellipseabout an external point onthe major axis. Ironically, the author begins by justifiably calling for greater concrete expression of mathematics, but then falls short of this stated aim by burying a collection of diagrams under a mountain of text. Artists interested in exploring this area should turn instead to E.H. Lockwood’s classic A Book of Curves (Cambridge University Press, 1961) for a concise, comprehensive and lucid introduction. With the development of computer graphics, this ancient branch of mathematics has a new lease of life and provides an excellentsubject matter for novice programmers. But I very much doubt whether Kavanau’s treatment will find many readers. Reviewed by Robert Dixon, Department of Design Research, Royal College of Art, Kensington Grove, London SW7, U.K. Genetic Alchemy, Ihe Social History of the Recombinant DNA Controversy. Sheldon Krimsky...

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