Civil Engineering Association

Mathematical Excursions to the World's Great Buildings >> By Alexander J. Hahn

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.

Endorsements:

"The mathematical analysis of building structures is essential to the understanding of architecture. Yet most texts available are abstract and not specific to the importance of such study. At last, Alexander Hahn has provided a thorough and beautifully illustrated mathematical look at the world's greatest buildings that will remedy this void and provide a relevant and absorbing study for architects and others interested in the art of building. I particularly found the description of the amazing structural problem of the Sydney Opera House not only interesting but exciting."--John Burgee, fellow of the American Institute of Architects

"Readers who enjoy connecting mathematics to real-world applications will find this book intriguing, as will anyone who wants to learn more about the forces and mathematics behind the construction of the world's great buildings."--Michael Huber, author of Mythematics

"Clear and engaging, this terrific book contains interesting and authentic mathematical applications. Mathematical Excursions to the World's Great Buildings is a book you can curl up with and enjoy."--Marc Frantz, Indiana University

Table of Contents:

Preface vii
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
References 307
Index 311
Photo Sources 318

Subject Areas:

Mathematics
Art and Architecture