Between Geometry and Architecture

Who can deny that the La Défense Arch in Paris is a "cube," the Pyramid at the Louvre is a "pyramid," and La Géode at La Villette is a "sphere"? But are these geometric forms truly architectural forms? When compared to structures designed by Frank Gehry with fluid forms, or fractal shapes developed by Benoît Mandelbrot, to what extent are these structures more "geometric"?

On this fine line between architecture and mathematics, what are the similarities and differences between the architect's "geometry" and the mathematician's geometry? How do the geometric foundations of a structure shape its architectural identity?

Mathematician-philosophers such as Descartes, Pascal, Desargues, Gauss, Bolzano, Poincaré, Mandelbrot, and Serfati, and philosophers of mathematics such as Jean-Jacques Gardies, Gilles-Gaston Granger, Jules Vuillemin, and Ludwig Wittgenstein have contributed to the ideas that form the basis of this book. At the same time, based on the works of important architects like Aalto, Brunelleschi, Durand, Gehry, Kahn, Bernini, Le Corbusier, Palladio, Philibert de l’Orme, Rietveld, Serlio, Utzon, Villard de Honnecourt, Viollet-le-Duc, and Wright, a concept of "appropriate" geometry for architecture is explored.

This book offers a comprehensive perspective for those who wish to understand the interaction between mathematics and architecture, the role of geometry in design processes, and how structural forms are shaped.