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.

• 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

Winner of the 2012 PROSE Award in Architecture & Urban Planning, Association of American Publishers One of Choice's Outstanding Academic Titles for 2013 "[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 "I cannot recommend this book highly enough. This is a lucidly written, beautifully illustrated, hugely informative volume... Mathematics apart, this book is just plainly an absorbing and informative read... The book is lavishly illustrated--both its architectural and mathematical strands come pretty much alive in the abundance of drawings and diagrams. From this perspective, the book must be very suitable for an advanced Liberal Arts mathematics course; however the aesthetic focus of the book makes it a cultural phenomenon. I would suggest consulting the book before a trip to Europe, Middle East, or Australia. Technical details and depth of coverage brought to you by Alexander Hahn are certain to complement more common travel guides."--CTK Insights "Rich, insightful and detailed, the book is a pleasurable excursion if you want to go beyond a peek at the buildings. Drawings and colour images add understanding to the narration."--Vaidehi Nathan, Organiser "It is not only a picture book but also a book that is a pleasure to read from cover to cover and I can imagine that after reading it, after a while one will pick it up again and again to just enjoy the illustrations or reread sections and chapters."--A. Bultheel, European Mathematical Society "A great building has a formal beauty, and it is no surprise that one can understand such buildings through mathematics. Hahn considers numerous buildings such as the Parthenon, the Hagia Sophia, the US Capitol, and the Sydney Opera House, providing a tour through the history of architecture with care and appropriate detail... The author balances the richness of the buildings with the generous development of the mathematical topics, including polygonal geometry, trigonometry, symmetry, conic sections, perspective, and the calculus--all leavened with the problems of transferring loads and stable structures... Hahn has served up a beautiful mix of mathematics, architecture, and history, and he has made it accessible to most readers. This book belongs in every library; it is a treasure trove of wonders."--Choice "The book is very readable and well written as a textbook. Readers only need to know some basic high school mathematics. It is very well illustrated with graphics that follow the text and plates in color of the most important buildings that are considered. At the end of each chapter, there are problems and discussions that help the reader to better understand the underlying mathematics. The discussions are particularly interesting because they provide a lot of background information. They cover a range of topics, from the golden rectangle, symmetry and the geodesic triangle to medieval building practices and Gaudi's forms. The book also contains a glossary of architectural terms for the reader's convenience."--Vesna Velickovic, Mathematical Reviews Clippings "Many exercises contained in the book are a great material for interdisciplinary courses and teacher's training."--D. Ciesielska, Zentralblatt MATH "I commend this book for its interesting and original insights into Archimedes' far-reaching discoveries."--Phill Schultz, Australian Mathematical Society "I recommend this book for advanced survey courses or special topics courses."--Craig McBride, Mathematics Teacher

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.

• 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

Winner of the 2012 PROSE Award in Architecture & Urban Planning, Association of American Publishers One of Choice's Outstanding Academic Titles for 2013 "[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 "I cannot recommend this book highly enough. This is a lucidly written, beautifully illustrated, hugely informative volume... Mathematics apart, this book is just plainly an absorbing and informative read... The book is lavishly illustrated--both its architectural and mathematical strands come pretty much alive in the abundance of drawings and diagrams. From this perspective, the book must be very suitable for an advanced Liberal Arts mathematics course; however the aesthetic focus of the book makes it a cultural phenomenon. I would suggest consulting the book before a trip to Europe, Middle East, or Australia. Technical details and depth of coverage brought to you by Alexander Hahn are certain to complement more common travel guides."--CTK Insights "Rich, insightful and detailed, the book is a pleasurable excursion if you want to go beyond a peek at the buildings. Drawings and colour images add understanding to the narration."--Vaidehi Nathan, Organiser "It is not only a picture book but also a book that is a pleasure to read from cover to cover and I can imagine that after reading it, after a while one will pick it up again and again to just enjoy the illustrations or reread sections and chapters."--A. Bultheel, European Mathematical Society "A great building has a formal beauty, and it is no surprise that one can understand such buildings through mathematics. Hahn considers numerous buildings such as the Parthenon, the Hagia Sophia, the US Capitol, and the Sydney Opera House, providing a tour through the history of architecture with care and appropriate detail... The author balances the richness of the buildings with the generous development of the mathematical topics, including polygonal geometry, trigonometry, symmetry, conic sections, perspective, and the calculus--all leavened with the problems of transferring loads and stable structures... Hahn has served up a beautiful mix of mathematics, architecture, and history, and he has made it accessible to most readers. This book belongs in every library; it is a treasure trove of wonders."--Choice "The book is very readable and well written as a textbook. Readers only need to know some basic high school mathematics. It is very well illustrated with graphics that follow the text and plates in color of the most important buildings that are considered. At the end of each chapter, there are problems and discussions that help the reader to better understand the underlying mathematics. The discussions are particularly interesting because they provide a lot of background information. They cover a range of topics, from the golden rectangle, symmetry and the geodesic triangle to medieval building practices and Gaudi's forms. The book also contains a glossary of architectural terms for the reader's convenience."--Vesna Velickovic, Mathematical Reviews Clippings "Many exercises contained in the book are a great material for interdisciplinary courses and teacher's training."--D. Ciesielska, Zentralblatt MATH "I commend this book for its interesting and original insights into Archimedes' far-reaching discoveries."--Phill Schultz, Australian Mathematical Society "I recommend this book for advanced survey courses or special topics courses."--Craig McBride, Mathematics Teacher

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.

• 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

Winner of the 2012 PROSE Award in Architecture & Urban Planning, Association of American Publishers One of Choice's Outstanding Academic Titles for 2013 "[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 "I cannot recommend this book highly enough. This is a lucidly written, beautifully illustrated, hugely informative volume... Mathematics apart, this book is just plainly an absorbing and informative read... The book is lavishly illustrated--both its architectural and mathematical strands come pretty much alive in the abundance of drawings and diagrams. From this perspective, the book must be very suitable for an advanced Liberal Arts mathematics course; however the aesthetic focus of the book makes it a cultural phenomenon. I would suggest consulting the book before a trip to Europe, Middle East, or Australia. Technical details and depth of coverage brought to you by Alexander Hahn are certain to complement more common travel guides."--CTK Insights "Rich, insightful and detailed, the book is a pleasurable excursion if you want to go beyond a peek at the buildings. Drawings and colour images add understanding to the narration."--Vaidehi Nathan, Organiser "It is not only a picture book but also a book that is a pleasure to read from cover to cover and I can imagine that after reading it, after a while one will pick it up again and again to just enjoy the illustrations or reread sections and chapters."--A. Bultheel, European Mathematical Society "A great building has a formal beauty, and it is no surprise that one can understand such buildings through mathematics. Hahn considers numerous buildings such as the Parthenon, the Hagia Sophia, the US Capitol, and the Sydney Opera House, providing a tour through the history of architecture with care and appropriate detail... The author balances the richness of the buildings with the generous development of the mathematical topics, including polygonal geometry, trigonometry, symmetry, conic sections, perspective, and the calculus--all leavened with the problems of transferring loads and stable structures... Hahn has served up a beautiful mix of mathematics, architecture, and history, and he has made it accessible to most readers. This book belongs in every library; it is a treasure trove of wonders."--Choice "The book is very readable and well written as a textbook. Readers only need to know some basic high school mathematics. It is very well illustrated with graphics that follow the text and plates in color of the most important buildings that are considered. At the end of each chapter, there are problems and discussions that help the reader to better understand the underlying mathematics. The discussions are particularly interesting because they provide a lot of background information. They cover a range of topics, from the golden rectangle, symmetry and the geodesic triangle to medieval building practices and Gaudi's forms. The book also contains a glossary of architectural terms for the reader's convenience."--Vesna Velickovic, Mathematical Reviews Clippings "Many exercises contained in the book are a great material for interdisciplinary courses and teacher's training."--D. Ciesielska, Zentralblatt MATH "I commend this book for its interesting and original insights into Archimedes' far-reaching discoveries."--Phill Schultz, Australian Mathematical Society "I recommend this book for advanced survey courses or special topics courses."--Craig McBride, Mathematics Teacher