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paintings. Throughout the book are pen and ink figures illustrating all the processes described in the text. I regret that the publisher did not use Gottsegen’s own sketches for these illustrations. I have seen the illustrative drawings he does for his classes and they are superior to the rather stiff drawings in the book. Nevertheless, the figures are clear and very helpful. This is certainly an important book for anyone using art materials or interested in current art materials and artists’ techniques. M.C. ESCHER: ART AND SCIENCE H.S.M. Coxeter et al., eds. Elsevier (North Holland),P.O. Box 1991,1000BZ, Amsterdam, The Netherlands, 1986. 400 pp., illus. Trade, $50.00. ISBN: 0 444 70011 0. Reviewedby Robert Dixon, 125Cricklade Avenue, London SW2, U.K. For 30 years now one scientist after another has been telling us that there is a great deal of interesting science in the visual art of M.C. Escher. See, for example, H.S.M. Coxeter’s Leonardo paper [I] on the print Circle Limit III, which credits the artist with deep and fresh insight into a non-Euclidean symmetry. Indeed Escher is the most known artist of our time to incorporate science in art in a way that seriously impressesscientists. Readers who wish to know more about this, particularly about the mathematics of symmetry and tessellation, should read the excellent M.C. Escher: Art and Science. The book is the result of an international conferenceon Escherwhich took place in Rome, March 1985, and contains a lively and well-illustrated selection of 36 papers, mostly about spatial mathematics. MicheleEmmer, the congress organiser and co-editor of the book, must be congratulated for managing to assemble such a complete gathering of the Escher scientists, includingH.S.M. Coxeter,Roger Penrose, Caroline Macgillavry, Bruno Ernst and Arthur Loeb, eachof whom had gotten to know and work with Escher at one time or another during the 1950s and 1960s. The contributors thus provide as many fond personal anecdotes as points of technical analysis. With so many excellent individual papers highlighting different topics it is hard to summarize the book’s contents, which range from geometry to psychology , and from surface ornament to picture-making. Doris Schattschneider guides us through Escher’s own notebooks on symmetry tilings. Richard Gregory explains how his long-standing admiration for Escher’s art ties in with the deepest questions that cognitive science has to ask about perception. J.F. Rigby and D.J. Dunham each demonstrate how to construct PoincarC’smodel of hyperbolic symmetries, which Escher used for his CircleLimit series. There are contributions on computer graphics, animationand colour. The book provides a substantial and authoritative review of Escher’s science. As well as being of interest to die-hard mathematicians, the book will engage those without mathematical training. Escher himself thought in pictures, and the mathematicians who are attracted to his work are more concerned to do the same than to reduce everything to formal code [2]. For those who want primarily to make pictures and patterns, the book offerspractical information together with a great deal of visual material. The usual barriers between artist and scientist are here dissolved by a gathering of mathematicians who freely admit that picture-making and pattern-making are good ways of doing, if not fundamental to, mathematics. George Escher, the artist’s eldest son, opens the book by describing his father’s working methods. H.S.M. Coxeter,Doris Schattschneider, Caroline Macgillavry, Branko Grunbaum , G.C. Shepard and others each presented papers on symmetry topics and plane tilings, providing the most substantial theoretical part of the book. Thesesymmetrytheorists make essentially the same remarkable point, that Escher the artist was often one step ahead of the mathematicians in a fieldof mathematical research which is still being explored today. Roger Penrose, Bruno Ernst, Richard Gregory and others dwell on the topic of ‘impossible objects’ and the range of tricks and ambiguities of perspective which Escher explored and demonstrated in a manner that no other artist has rivalled. Penrose recalls inventing the TRIBAR and passing the idea to Escher for embellishment in his famous belvedere, waterfall and staircase pictures. For Gregory, Escher’s puzzle pictures provide...


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