Alfonso Ramírez Ponce
National University of Mexico
Faculty of Architecture
C.U., MEXICO D.F.

Rafael Ramírez Melendez
Pompeu Fabra University
Technology Department
Ocata 1, Barcelona, SPAIN

The comprehensive knowledge of materials and their corresponding building techniques has become a vital necessity, given the backdrop of an ever increasing demand for living space, particularly housing. Morever, it has become vitally important to rationalise the building process in order to achieve the lowest possible cost. This paper aims to describe, analyse, and formalise some of the fundamental properties of a popular construction technique for building brick vaults and domes without any use of scaffolding or centering or any additional reinforcements whatever. The technique is of collective invention in Mexico and dates back to the nineteenth century. Brick vaults, made only of pieces of clay and the intuition of skillful hands of craftsmen, apart from offering an economical solution even to this day to the housing problem, possess both an architectonic and a mathematical beauty.

The "leaning brick" is a popular construction technique which is at the same time millennary and modern. This technique is used for building building roofs with bricks without any framework, making it a very economical way of building. It can be used between floors of a housing block or to cover an open area such as a terrace. It is an ingenious technique, not invented by architects or engineers, but instead the fruit of common knowledge, all too often ignored or disregarded by professionals and academics.

As a first step towards a mathematical analysis of the vaults we have formalised their surface as a function of two real variables. We have explored two cases: the surface of a vault constructed on a rectangular perimeter, and the surface of a vault constructed on four circular arches resulting in the section of a sphere. We have also indicated how to calculate the area of the surface in both cases.

ABOUT THE AUTHORS
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The correct citation for this paper is:
Alfonso Ramírez Ponce and Rafael Ramírez Melendez , "Curves of Clay: Mexican Brick Vaults and Domes", pp. 143-154 in Nexus V: Architecture and Mathematics, ed. Kim Williams and Francisco Delgado Cepeda, Fucecchio (Florence): Kim Williams Books, 2004.