The Secrets of Ancient Geometry—and Its Use by Tons Brunés (review)

362 Books fields, primarily for grade school teachers, it could also serve those curious about color and without any scientific training. The succession of topics is logical and proceeds from biological sources and necessity for color to social uses and, finally, to physical and psychological aspects. The easily read, clearly written text is obviously by one enthusiastically involved in the use of color and disturbed by the apparent insensitivity of most people to the possibilities it offers for a richer visual environment. A popularizing balance has been struck between scientific depth and utilitarian exposition. While more accurate, useful and better organized than ‘Light, Color, and Environment’ by Faber Birren, I still feel there is considerable rigidity and error in Verity’s text. Perhaps certain details of the physics of color are not particularly important but personal impressions need not be propagated carelessly. 1 find no grounds for the statement: ‘The Red/Yellow/ Blue association appears to be a fundamental psychological relationship of colours.’ The wide variety of yellows that one can name is amazing but to neglect the greens as something less fundamental appears baseless. In fact, all systematized color-naming arrangements are conveniences, with still unmeasured scales, relating them to psychological parameters. In most cases the color illustrations are persuasive and say more to the perceptive than the text; however , one wonders if they really earn their keep. The text is quite explicit in directing attention to color relationships with which one is familiar but the pictures are often more important for unmentioned reasons (lightness contrast rather than color effects or artifacts of colour photography rather than color vision). For those who desire support for their interest in color, this would be a useful introduction. I would still recommend one of the more scientific discussions on the use of color, the perception of color or the physics of color, if one really wants a more generally accepted explanation and set of data. The Secretsof Ancient Geometry-and Its Use. Tons Brunes. Translated from the original Danish manuscript by C. M. Napier. Rhodos, International Science Publishers, Copenhagen, 1967. Two Volumes, 585 pp., illus. Reviewed by: Crockett Johnson* The reviewer’s impression is that the publication of this work in 1967was an event belatedly heard of in art circles by way of sparse and garbled accounts of reviews in architectural and engineering journals. With the volumes in hand, it can be said the publication of the work was indeed an event, not perhaps the event it would have been fifty years ago but still an event of considerable magnitude. The reasonable belief that there existed a geometric key to familiar and, therefore, esthetically * 14 Rowayton Avenue, Rowayton, Conn. 06853, U.S.A. acceptable proportions in art and architecture has been a persistent one. Most popularly the fascinating golden section has been applied to ancient works of many kinds. But, as its use would imply an appreciation of its uniqueness that calls for a grasp of geometry as recent at least as Pythagoras, one is not surprised that its applications to ancient works have not been convincing and that it certainly has given little indication of offering anything resembling a universal fit. The approach of Brunts, a Danish engineer, has been to invent a geometry that does fit and then to demonstrate by evidence of that very fit that such a geometry certainly existed. The basis of the system, a proportion the author calls the sacred cut, is d 2 (the geometric number 1.4142135 . . .) and its relation to 1, 2 and a circle with a diameter of 2. A square with sides of 2 contains the circle and the circle contains a square with sides of d2. And, of course, 4 2 is the diagonal of a square with sides of 1 (Fig. I(a) ). On this frame is woven a net of connecting lines with intersecting points (Fig I(b), (c) and (d)) that is applied, each time with remarkable persuasion, to the Pyramids, Egyptian art, Cuneiform, the modern alphabet, Moses’ Tabernacle, Greek temples, Roman arches, the Pantheon, Cologne Cathedral, jars and vases, a Viking fort, the game of chess and stylizations of the human figure. The argument against coincidence...