Architecture and Mathematics from Antiquity to the Future

Volume I: Antiquity to the 1500s

  • Kim Williams
  • Michael J. Ostwald

Table of contents

  1. Front Matter
    Pages i-xix
  2. Michael J. Ostwald, Kim Williams
    Pages 1-21
  3. Mathematics in Architecture

  4. From 2000 B.C. to 1000 A.D.

  5. Theories of Measurement and Structure

    1. Front Matter
      Pages 243-243
    2. Paul A. Calter
      Pages 261-269
    3. Alfonso Ramírez Ponce, Rafael Ramírez Melendez
      Pages 309-324
    4. Javier Barrallo, Santiago Sanchez-Beitia
      Pages 325-332
  6. From 1100 A.D.–1400 A.D.

  7. Theories of Proportion, Symmetry, Periodicity

    1. Front Matter
      Pages 547-547
    2. Peter Saltzman
      Pages 585-602
    3. István Hargittai, Magdolna Hargittai
      Pages 603-618
    4. Marco Frascari, Livio G. Volpi Ghirardini
      Pages 619-626
  8. From 1400 A.D.–1500 A.D.

    1. Front Matter
      Pages 627-627
    2. Michael R. Ytterberg
      Pages 629-644

About this book


The aim of this collection of essays is to present a broad portrait of the ways in which two seemingly different disciplines are interconnected. The diversity and varied texture of the essays richly illustrates the affinity between architecture and mathematics. As the almost 100 papers presented in this two-volume publication show, every age and every culture has relied on principles of mathematics incorporated in their works of architecture to imbue their built environment with meaning and order. Included are discussions of geometry, proportional systems, linear algebra, periodic and aperiodic tilings, fractals, perspective, computer science and mechanics. Western architecture of every period is examined: Egyptian, Roman, Medieval, Renaissance, Baroque, Enlightenment, twentieth-century and beyond, as is the architecture of Turkey, China, India, Japan, Australia and Islam. The mathematical nature of the architecture of Leon Battista Alberti, Andrea Palladio and Frank Lloyd Wright is examined, and the philosophical background behind Renaissance architecture is explored. Contributors come from a wide range of disciplines and cultural backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators from the world over. Architecture may be seen and understood in a new light, by professionals as well as non-professionals.


architecture and mathematics periodic and aperiodic tilings theories of proportion

Editors and affiliations

  • Kim Williams
    • 1
  • Michael J. Ostwald
    • 2
  1. 1.Kim Williams BooksTorinoItaly
  2. 2.School of Architecture and Built EnvironmentThe University of NewcastleCallaghanAustralia

Bibliographic information