The Sequence of Fibonacci and the Palazzo della Signoria in Florence

In Florence, the sequence of Fibonacci gave precise rules for the design of the plan of one of the most important buildings of Gothic architecture : the Palazzo della Signoria, later widened and transformed into Palazzo Vecchio. The Fibonacci sequence (a sequence of numbers, each of which is the sum of the two preceding numbers) and the following Lucas sequence give couples of numbers that can describe Fibonacci rectangles.

A Fibonacci rectangle can be divided into two parts: a square and a new Fibonacci rectangle; moreover, by adding a square to its longest side, it can generate another rectangle. These features appeared consistent with the requirements of a medieval city hall: on the ground floor, to have a spatious room for a large number of people coming together to make decisions, and an open space with porticos for various activities; on upper floors, to divide the large room into two smaller rooms with the same ratio, a square and a rectangle. This is what happens in Palazzo della Signoria, where dimensions are taken exactly from numbers of the sequence. The tower as well took its proportions from the numbers of the sequence in a hidden way. The final trapezium of the plan (a triangle was added to the rectangle) gave logic to the peculiar forms of the courtyard.

Comparing the elevation of Palazzo della Signoria with that of Palazzo Strozzi, built two centuries later, it is possible to understand how important the use of the sequences became in Florentine architecture

ABOUT THE AUTHOR
Architect Maria Teresa Bartoli, is Professore straordinario of Architectural Surveying since 2002 at the Faculty of Architecture in Florence, where she has been working since 1983, first as a ricercatore, then as Professore associato teaching drawing, surveying and geometry for architects. She has taken part (as a member of the team or as the leader) in the survey of important monuments in Florence such as Palazzo Strozzi, Palazzo Medici, Palazzo Vecchio, the Convent of Carmine, and Villa Medici, on behalf of the Public Administration. Her research fields include: the history of Renaissance perspective; the links between architecture and geometry; metrology and history of geometrical paradigms in architecture. Since 1973 she has published many articles and essays in specialized reviews, and has been a speaker at many international meetings. In 1994 she was invited by the Dibner Institute for the Science and Technology in Cambridge, Massachussets, as speaker in a workshop on Renaissance Perspective. Her most representative publication is the volume Le ragioni geometriche del segno architettonico (Florence: Alinea, 1997). Recent publications include: "Un laboratorio dell'architettura gotica: Firenze, la città, le mura, il Palazzo" in Città, Architettura, le matrici di Arnolfo, ed. M.T.Bartoli, S. Bertocci (Florence: Edifir, 2004); "L'architetto di Palazzo Medici-2 in Firenze Architettura, 1 and 2 (2002); "Il disegno come conoscenza dell'Architettura", in the biennial periodical of the Dipartimento di Progettazione dell'Architettura, pp. 4-13.

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