Abstract
The Leaning Tower of Pisa consists of a ground floor with a blind arcade, six tiers of open arches, and a smallish tamburo. The 15-fold and 30-fold symmetry of the Leaning Tower is extremely rare, if not unique. The Baptistery consists of four levels, and counting a garland of arches, there are five elements to be analyzed. The Romanesque ground floor consists of a blind arcade of 20 arches resting on 20 pilasters. The second level displays a striking “symmetry clash”: a 12-fold symmetry. The third level returns to a 20-fold symmetry. The symmetry clashes help reconstruct the history of the Baptistery construction. In 1185 the original plan for the exterior was replaced by that of Guidolotto. His design involved the regular pentagon and pentadecagon, which had appeared for the first time in the construction of the Leaning Tower. Circa 1221, the quarrels ended with the 12-fold symmetry triumphant. A third reversal, circa 1278, revived the icosagonal symmetry.
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First published as: David Speiser , “The Symmetries of the Baptistery and the Leaning Tower of Pisa ”, pp. 135–146 in Nexus I: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1996. This is a slightly abridged text of an earlier publication: “The Symmetries of the Baptistery and the Leaning Tower of Pisa,” Annali della Scuola Normale Superiore di Pisa, Classe di Lettere e Filosofia Serie III, vol. XXIV, 2–3 (1994): 511–564, with 7 plates.
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Notes
- 1.
There are many leaning towers besides the one in Pisa, but to the best of my knowledge, the 15-fold symmetry is never mentioned in any book or scientific paper. Even the Baedeker, that faithful companion, fails to mention this fundamental fact. For the only correct reference that I can find, see Carli (1989).
- 2.
I found this construction in an Italian journal of design shortly after the war. Unfortunately I have forgotten the names of the authors and of the journal, so I cannot give proper credit.
- 3.
For a very careful description of the Baptistery, see Smith (1978).
- 4.
The architect of the Tower is not known: could it have been Guido himself?
References
Carli, E. 1989. Il Campanile. Pp. 219–226 in E. Carli, ed. Il Duomo di Pisa, Florence: Nardini.
Grassi, Ranieri. 1831. Le frabbriche principali id Pisa ed alcune vedute della stessa città, 24 tavole. Pisa: Edizioni Ranieri Prosperi.
Pierotti, Piero. 1990. Una torre da non salvare. Pisa: Pacini Editore.
Smith, Christine. 1978. The Baptistery of Pisa. New York: Garland.
Acknowledgment
I should like to thank Prof. Luigi A. Radicati di Brozolo, who made this work possible.
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Speiser, D. (2015). The Symmetries of the Baptistery and the Leaning Tower of Pisa . In: Williams, K., Ostwald, M. (eds) Architecture and Mathematics from Antiquity to the Future. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-00137-1_36
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