Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings


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, Gaudé, 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.


The Mathematical Excursions into the world of architecture that this book undertakes are organized around two historical narratives. the primary narrative has a focus on aspects of architectural form (the role of geometry, symmetry, and proportion) and structure (matters of thrusts, loads, tensions, compressions) of some of the great buildings of western architecture from the pyramids of Egypt to iconic structures of the twentieth century. Some of the high points of this narrative are the Parthenon in Athens, the Colosseum and Pantheon in Rome, the Hagia Sophia, historic mosques, great Romanesque, Gothic, and Renaissance cathedrals, Palladio’s villas, the U.S. Capitol, the Sydney Opera House, and the Guggenheim Museum in Bilbao. (This narrative is not comprehensive, but instead seeks to illustrate important architectural features with compelling examples.)

A second narrative develops current elementary mathematics from a historical perspective. This includes selected aspects of Euclidean geometry, trigonometry, the properties of vectors, coordinate geometry in two and three dimensions, and (at the very end) basic calculus. It is the raison d’être of this book to intertwine these two stories and to demonstrate how they inform each other. the mathematics provides clarifying insights into the architecture, and, in turn, the architecture is a stage that gives visibility to applications of abstract mathematics. To be clear, the two narratives meet around topical issues and not when they happen to be aligned chronologically. in fact, the chronological alignment between mutually informing architecture and mathematics is rare. (Greek geometry and architecture is an exception.) the reality is that the elementary mathematics that might have clarified the understanding of a complex structure was almost always beyond the reach of the builders of the time.

The collage of historic buildings (all at the same scale) of Plate 1—refer to the section of colorplates after chapter 4—provides a snapshot of this book. It studies many of these buildings and focuses its mathematical analysis on their domes, arches, columns, and beams.

The prerequisites that you will need to bring to this book are a working knowledge of some basic high school math (such as elementary algebra and a little geometry) as well as an interest in learning about architecture and its vocabulary (as the Glossary presents it). You will be able to use the book in different ways. To a large extent, your choices will be influenced by your . . .

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