Abstract
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, underscoring the importance of proportion, symmetry and geometry in Renaissance Italy. This 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.
By … showing to what extent [Palladio] was a natural geometer, we do not make him less the great architect; on the contrary, we show, in a way that gives more than mere lip service to the proposition, how great architecture may flow from geometry (Hersey and Freedman 1992: 12).
First published as: Stephen R. Wassell , “The Mathematics of Palladio ”s Villas”, pp. 173–186 in Nexus II: Architecture and Mathematics, eds. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba.
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Notes
- 1.
For a detailed discussion of Palladio’s architecture, see Boucher (1994).
- 2.
For a complete discussion of Palladio ’s extensive rules governing the proportion of the orders, Palladio (1997: xiii–xix, 18–55).
- 3.
Howard and Longair (1982: 136). For the seven preferred room shapes, see Palladio ( 1997: I, xxi, 57). He recommends circles, squares and rectangles of proportions √2:l, 4:3, 3:2, 5:3 and 2:1. The last four are harmonic proportions; all are consistent with Vitruvius and/or Alberti , though circles are discussed only in terms of temples; see Vitruvius (1960: IV, viii, 122–124 and VI, iii, 177–179); Alberti (1955: VII, iv 138–139 and IX, v–vi, 197–199).
- 4.
Mitrović (1990: 289–291). Both decimal figures are close approximations of (l + √3)/2; for those interested in pure trigonometry, this equals \( \sin 30{}^{\circ}+ \cos 30{}^{\circ}=\sqrt{1+ \cos 30{}^{\circ}}=\sqrt{\frac{1+\sqrt{3}}{2}} \).
- 5.
Although Palladio did allow himself the use of approximations of the incommensurate ratio √2:1, he did not use it very often; see Howard and Longair (1982: Appendix, Table A4, 141–143), where this ratio is found only four times out of over one hundred entries.
- 6.
For more on the additive problem, see Scholfield (1958: 132–134).
- 7.
See also Ackerman and James (1967: 11–12).
- 8.
The latter was designed ca. 1567 but never completed, see Palladio (1997: II, iii, 94–95 and II, xv, 138); Puppi (1975: 384–388).
- 9.
To be precise, the rotational symmetry is broken in the Villa Trissino by the forecourt, the arcades of which project from the central block in quadrants as with the Villa Badoer . The Villa Rotonda , on the other hand, has essentially 90° rotational symmetry, except that the rectangular rooms do not quite align in 90° rotation.
References
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Acknowledgment
I would like to acknowledge Dr. Carroll William Westfall in gratitude for the fruitful discussions and invaluable suggestions that were crucial to the preparation of this manuscript.
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Wassell, S.R. (2015). The Mathematics of Palladio’s Villas. In: Williams, K., Ostwald, M. (eds) Architecture and Mathematics from Antiquity to the Future. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00143-2_7
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