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Book Reviews Archive: July 2000 to October 2002

Book Reviews Archive: 1994 to May 2000

Visualizing with CAD
An AUTOCAD Exploration of Geometric and Architectural Forms

by Daniela Bertol
Springer-verlag, Berlin, 1994, 359 pages, DM 84, with diskette included

Reviewed by Michele Emmer

"This book has been written for those who are afraid of mathematics, who would like to learn how to use it for the purpose of architecture and who do not want to spend more than a few weeks to achieve this goal. Discovering by himself, or with the help of a teacher, that it is easy to obtain quantitative answers to the problems of his daily practice, the architectural student will exorcise his fear of numbers and get ready to deal with the physical reality of architecture. He will learn at the same time the language of technology and thus establish the possibility of better communications with his consultants. The fulfilment of these needs is an essential condition of good architecture in today's technological era."
These are words from the famous structural engineer and architect Mario Salvadori (born in Rome in 1907) from his book "Mathematics in Architecture" (Prentice-Hall Int., London, 1968). More recently, in a meeting on "Architecture and Mathematics" ( Nexus Series, ed. by Kim Williams, edizione dell'Erba, Fucecchio, 1996) he was asked to introduce the meeting speaking on the theme "Can there be any relationship between Mathematics and Architecture?" (pp.9-13). He wrote: "Having proved that to look for relationships between as abstract as science as mathematics and as concrete as art as architecture is theoretically inconceivable.....I realize that all my disquisitions on the impossibility of relating mathematics and architecture vanish and, as a technologist, I must agree that the relationships between mathematics and architecture are so many and so important that, if mathematics had not been invented, architects would have had to invent it themselves. "
It is of course during the Renaissance that important connections were established among art, architecture and mathematics. To the Renaissance scientist, mathematics was the key to nature's behaviour. The conviction that nature is mathematical and that every natural process is subject to mathematical laws began to take hold in the twelfth century. It was a common belief that the book of nature was written in the language of geometry. Even an architect not very much interested in mathematics cannot ignore the importance of geometry in architecture. A wonderful example is what Morris Kline calls "The most original mathematical creation of the seventeenth century: projective geometry."("Mathematics in Western Culture", Oxford University Press, 1953).

The words of Salvadori were written 30 years ago. It is no doubt that many things have changed in this long period of time. Computers and telecommunications have revolutionized traditional perceptions of space and time. In particular "this transformed contemporary environment suggests the need for an investigation of physical form in their relation to our modified visual perceptions" wrote Daniela Bertol in the introduction to her volume . "The disciplines dealing with the exploration of forms, such as architecture and intuitive geometry, also need to address the implication of the new digital media." _The issue raised by this new way of dealing with visual forms in a digital world are the topic of this book._ Bertol has taken her degree in architecture at the University of Rome. She remembers very well the excitement of entering the ancient Roman temple of the Pantheon or when she was going each Sunday to Piazza San Pietro. Walking through Rome she has received the sense of architecture as the expression of a tangible geometry. She was fascinated by the treatises by Leon Battista Alberti, by the mathematician Luca Pacioli and by Sebastiano Serlio, who emphasized the relation between architecture and geometry. Bertol says that probably Serio writing his eight books of architecture today would have added a ninth book on computers. And probably would have also enclosed a computer diskette or a CD ROM with the electronic models of his temples and columns. This is really the key of the book of Bertol and her idea for writing it. She states that today computer visualization is probably as influential in architecture as perspective was in the Renaissance. "The linking of geometry, CAD, and architecture in the same book is similar to the inclusion of geometry, perspective, building technology and typologies and graphics in the treatises."

An ambitious project where the difference in the aesthetic of computer images versus traditional rendering inspired Bertol to use both to express two different processes that achieve the same result: the representation of three-dimensional objects through two-dimensional images.

Bertol recalls the analogies of her book with the Renaissance treatises and states the importance of relating contemporary technology with historical foundations. So the approach is that of an architect exploring space in terms of intuitive and visually constructable forms using CAD. Of course the aim of the author is to point on applications in architecture computer aided design, focusing on geometry and architecture as formal expression.

I hope it is now clear that the book of Bertol is not just a technical book on the use of CAD but is a successful essay to combine a deep understanding of the theoretical underpinnings of design and form, let's say geometry, with the understanding and treatment of CAD. This is the reason why you will find in the book chapter entitled "Considerations about space, architecture, design and computers" and questions like "What is space?". The role of geometry is investigated with an interest not so often found in architects. She wrote: (p.39): "Mathematics and geometry are related to architecture in two principal ways. First, they are a source of meaning for architecture. In Renaissance and Baroque architecture the use of geometric forms became a symbol of the power of human reason over nature. A philosophy of architecture based on mathematical principles. The other relationship between architecture and mathematics is more pragmatic. Geometric laws have practical applications in surveying, measuring, and stereotomy. Mathematics is indispensable in structural analysis. Two-dimensional architectural representations are made possible by geometric projections. "

The central part of the book is based on the problem of visualization through computer and computer models. The book includes a diskette to follow the suggestions of the book and to make experiments. An interesting book because it does not focus only on how to use a software but wants to investigate the reasons why we use the software to produce a certain form. It is this the real meaning of making a comparison between the book of Bertol and a treatise of Renaissance architecture. The ambitious of the book is to be a treatise, to discuss in deep the reasons why we use certain instruments and the philosophy hidden in them. This is the reason why it can be useful of course to students in architecture but can be very readable for people interested in geometry, in space, in forms. For any person with a wide range of cultural interest. A last note. I teach this year mathematics to the students of architecture at the University of Rome. It is a unique opportunity to have this incredible laboratory of forms, shapes and styles, the town of Rome, at students' disposal. Unfortunately the students sometimes do not realize the great advantage they have studying in Rome; this book can help them to rediscover their town.

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