From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines this with an in-depth look at their aesthetics, history, and structure. Whether using trigonometry and vectors to explain why Gothic arches are structurally superior to Roman arches, or showing how simple ruler and compass constructions can produce sophisticated architectural details, Alexander Hahn describes the points at which elementary mathematics and architecture intersect.
Beginning in prehistoric times, Hahn proceeds to guide readers through the Greek, Roman, Islamic, Romanesque, Gothic, Renaissance, and modern styles. He explores the unique features of the Pantheon, the Hagia Sophia, the Great Mosque of Cordoba, the Duomo in Florence, Palladio's villas, and Saint Peter's Basilica, as well as the U.S. Capitol Building. Hahn celebrates the forms and structures of architecture made possible by mathematical achievements from Greek geometry, the Hindu-Arabic number system, two- and three-dimensional coordinate geometry, and calculus. Along the way, Hahn introduces groundbreaking architects, including Brunelleschi, Alberti, da Vinci, Bramante, Michelangelo, della Porta, Wren, Gaudí, Saarinen, Utzon, and Gehry.
Rich in detail, this book takes readers on an expedition around the globe, providing a deeper understanding of the mathematical forces at play in the world's most elegant buildings.
Alexander J. Hahn is professor of mathematics at the University of Notre Dame. His books include Basic Calculus: From Archimedes to Newton to Its Role in Science.
"[Hahn] conducts an opulent historical and geographical tour."--Jascha Hoffman, New York Times Book Review
"Modern architects rely on algebra and calculus. Hahn turns these tools on historical structures from the Parthenon to the Hagia Sophia to St. Paul's Cathedral, revealing how they hold up and explaining the causes of visible contortions and cracks. . . . More engrossingly, Hahn employs mathematics to explore how architects have conceived of buildings through the ages. In the case of Milan's cathedral, Hahn's discussion is especially rich because his maths plays out against a backdrop of detailed historical documentation, including the testimony of the German [master builder]."--Jonathon Keats, New Scientist
"[H]andsomely produced and lavishly illustrated. . . . Hahn tends to avoid discussing some of the aesthetic versus engineering limitations in favor of explaining how things work. And in that area he can be very helpful to the experienced architecture fan and the novice as well. . . . The mathematical sections are well illustrated and pictures of buildings abound. . . . No effort has been spared to make this an informative and aesthetically pleasing book. And the problems are fun too."--Gerald L. Alexanderson, MAA Reviews
Table of Contents:
Chapter 1 Humanity Awakening: Sensing Form
and Creating Structures 1
Chapter 2 Greek Geometry and Roman Engineering 12
Chapter 3 Architecture Inspired by Faith 53
Chapter 4 Transmission of Mathematics and Transition in Architecture 97
Chapter 5 The Renaissance: Architecture and the Human Spirit 138
Chapter 6 A New Architecture: Materials, Structural Analysis, Computers, and Design 205
Chapter 7 Basic Calculus and Its Application to the Analysis of Structures 265
Glossary of Architectural Terms 301
Photo Sources 318