The Dogana courtyard in Palazzo Vecchio, the detail that enlightens the rule

Abstract

The apparent irregularity in the trapezium of the Dogana courtyard in Palazzo Vecchio hides an uncommon precise geometrical rule. Such a rule requires the knowledge of the triangle which the trapezium belongs to. The search of that triangle throws new light on the length measures of the elder Arnolfo Palace. A design method based on geometrical theorems becomes evident, in which plan length measures are achieved through first and second degree equations. The plan offers directions to the three-dimensional palace development and to the surrounding urban design. The presence of the same triangle in the coeval Santa Maria Novella square gives evidence both for similarity in design of these two Florentine Republic plans and for relevance of new science knowledge in Gothic architecture.

Keywords

• mathematics and gothic architecture, new knowledge from surveying and digital drawing