The Mathematics of Palladio's Villas

Much has been written about the mathematical qualities of Andrea Palladio's architecture, including his own I quattro libri dell'architettura. Often this has been analyzed within the context of a larger collection of architectural treatises, including Vitruvius' De architectura and Alberti's De re aedificatoria, as well as works by contemporaries of Palladio, such as Daniele Barbaro, Cesare Cesariano, Sebastiano Serlio and Giacomo Barozzi da Vignola. These cinquecento writings underscore the importance of proportion, symmetry and geometry in Renaissance Italy: for example, Barbaro maintains that "some arts have more of science and others less", and the "more worthy [are] those wherein the art of numeracy, geometry and mathematics is required". Lionello Puppi concludes, "Architecture obviously came into this category...Palladio...bring[s] to the concrete stage of his planning operation a single-minded scientific approach, arrived at through 'lofty speculation' into number and proportion". Rudolph Wittkower asserts, "The conviction that architecture is a science, and that each part of a building, inside as well as outside, has to be integrated into one and the same system of mathematical ratios, may be called the basic axiom of Renaissance architects". Many modern authors have analyzed Wittkower's thesis that harmonic proportions derived from musical scales played a central role in the minds and designs of Renaissance theorists and architects. Central to this debate is Palladio's oeuvre--his architecture and his Quattro libri.

Prof. Wassell's essay provides a review of the mathematical aspects of Palladio's work as it has been discussed in the literature and offers a novel perspective on his mathematical approach to architectural design. The author argues that, given the amount of discussion already focused on the role that harmonic proportions played in the Palladio's architecture, it is now time to search further for other mathematical facets of his design philosophy. The analysis is arranged in three sections: geometry, proportion and symmetry."

ABOUT THE AUTHOR

Steve Wassell received a B.S. in architecture in 1984, a Ph.D. in mathematics (mathematical physics) in 1990, and an M.C.S. in computer science in 1999, all from the University of Virginia. He is a Professor of Mathematical Sciences at Sweet Briar College, where he joined the faculty in 1990. Steve's primary research focus is on the relationships between architecture and mathematics. He has presented papers at Nexus 1998 and Nexus 2000, published articles in The Mathematical Intelligencer and the Nexus Network Journal as well as a book (with Kim Williams) entitled On Ratio and Proportion (a translation and commentary of Silvio Belli, Della proportione et proportionalità), and taught a course at SBC entitled Architecture and Mathematics. Steve's overall aim is to explore and extol the mathematics of beauty and the beauty of mathematics.

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