In his classic Architectural Principles in the Age of Humanism, Rudolf Wittkower convincingly argues that an understanding of the roots of Renaissance architecture designed by masters such as Alberti and Palladio can be developed only by appreciating the relationships between architecture, music and mathematics as seen through the eyes of Renaissance architects and theorists. Crucial to developing this appreciation is the ability approach the world of knowledge as Renaissance scholars would have, without inherently accepting the artificial division of this world into arts and sciences-and the compartmentalized disciplines within each.

Lionel March suggests "…the Renaissance might be called the era of conspicuous erudition in which patrons, scholars, and artists displayed their breadth of classical learning in various works and commissions." The foundation of learning upon which artists of the Renaissance built was constructed through a determined search for reason in aesthetics, logic in beauty and rational explanations to intangible phenomena, a search involving at least implicit use of mathematics.

This present paper briefly discusses Neolithic speculative geometry; the beginnings of history in the Middle East; the Greeks, first true mathematicians; the Romans, masters of engineering; and the Middle Ages. In the years immediately preceding the Renaissance, the qualitative view of neo-Platonic metaphysics slowly gave way to a more quantitative view of reality that would eventually allow science to progress at a steady pace. This transition was slow, and Renaissance scholars were still heavily influenced by long-held ideas on number symbolism and sacred geometry.

As did their predecessors, Renaissance artists sought to incorporate meaning into their design by using a rational approach towards aesthetics. Some of the most prominent theorists -- Barbaro, Pacioli, and Dürer -- focused their efforts largely on concerns of geometry and proportion, often doing so within the context of the ideas described in this paper. Indeed, this was completely natural before the divorce of arts and sciences in the Age of Reason! It is crucial, therefore, to be able to put oneself in this same context if one is truly to understand Renaissance architecture.

ILLUSTRATION: Stonemason's mark from the Cathedral of Strasburg.

ABOUT THE AUTHOR
Stephen R. Wassell is an Associate Professor of Mathematical Sciences at Sweet Briar College in Virginia (USA). He has received a Bachelor of Science degree in Architecture, a Ph.D. in Mathematics, and a Master's degree in Computer Science from the University of Virginia. After publishing several articles in his doctoral research area, mathematical physics, he is now studying the relationships between architecture and mathematics. At present, Steve's primary focus is on Palladian architecture, since its roots--Palladio's own architecture, his Quattro Libri, and the scholarly interests of his intellectual circle--exhibit on an obvious appreciation of the mathematical underpinnings of aesthetics. (This work has been partially supported by a grant from the Graham Foundation for Advanced Studies in the Fine Arts as well as numerous grants from Sweet Briar College.) Steve's overall mission is to explore and extol the mathematics of beauty and the beauty of mathematics. He is the author of "The Mathematics of Palladio's Villas Workshop '98", now available in the NNJ volume 1 in print, and the review of Branko Mitrovic's translation of Giacomo Barozzi Da Vignola, Canon of the Five Orders of Architecture. He presented "The Mathematics of Palladio's Villas" at Nexus 98, published in Nexus II: Architecture and Mathematics.