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The construction of a 16-sided mazzocchio. Drawing by Richard Talbot
This paper stems from a study of one of the most complex and well-known examples of early renaissance perspective drawings, the Chalice - a drawing that has become almost iconic within the history of perspective, although neither the author nor the exact date of its execution are certain. It is a study of both the design of the Chalice and of the geometry underlying its perspective construction and asks whether there is any relationship between its design - its elevation, and the geometric constructions and procedures that would have been required for its depiction.
Close examination of the drawing reveals the progression of its construction as well as the method of its perspective projection and suggests that the large octagonal mazzocchio was the first element to be drawn. Measurements taken from this and an associated mazzocchio drawing, 1756A in the Uffizi, show that their proportions - specifically the relationship between their octagonal section and their diameter are identical. Further measurement and reconstruction shows that these proportions have their origin in the geometric constructions necessary for the depiction of the mazzocchi.
The construction of the plan of the 32 sided mazzocchio, with its octagonal vertical cross section, would have required drawing a square, constructing an octagon within that square, further division to give 16 and then the 32 sections that describe the circumference. The paper argues that it is these constructions that relate directly to the elevation of the Chalice.
The central proposition of this paper is, therefore, that the design of the Chalice - its elevation, is not arbitrary. It is derived from the same geometric constructions and procedures required for the construction and depiction of the large octagonal mazzocchio.
About the author
The correct citation for this paper is:
Richard Talbot, "Design and perspective construction: Why is the Chalice the shape it is?", pp. 121-134 in Nexus VI: Architecture and Mathematics, eds. Sylvie Duvernoy and Orietta Pedemonte Turin: Kim Williams Books, 2006.