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Mathematical Excursions to the World's Great Buildings Hardcover – July 22, 2012

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Product Details

  • Hardcover: 336 pages
  • Publisher: Princeton University Press (July 22, 2012)
  • Language: English
  • ISBN-10: 0691145202
  • ISBN-13: 978-0691145204
  • Product Dimensions: 1 x 8.7 x 9.4 inches
  • Shipping Weight: 2.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (11 customer reviews)
  • Amazon Best Sellers Rank: #146,357 in Books (See Top 100 in Books)

Editorial Reviews


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

From the Inside Flap

"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

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Customer Reviews

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Most Helpful Customer Reviews

9 of 10 people found the following review helpful By R. Hardy HALL OF FAMETOP 500 REVIEWER on September 6, 2012
Format: Hardcover
In his autobiography, Bertrand Russell wrote of his passion for mathematics, "I have tried to apprehend the Pythagorean power by which number holds sway about the flux." The Pythagoreans held all things to be numbers, and it wouldn't be surprising if Alexander J. Hahn, a professor of mathematics, held them in the same reverence. If all things are numbers, so all buildings are numbers, and Hahn's _Mathematical Excursions into the World's Great Buildings_ (Princeton University Press) is an attempt to show mathematical and architectural principles together through history. Both subjects are vast, but Hahn hits highlights of both as he ties the two together. This is a good-looking volume, large format, with plenty of illustrations consisting of old and new pictures of famous buildings and force diagrams and curves in the Cartesian plane. It also could be a text for a course in mathematics; every chapter ends in a list of "Problems and Discussions," exercises to be solved by the student, with answers not given. Since these range from the Pythagorean theorem to full scale calculus, they may be more than the general reader (such as this one) might want to attempt. Some of the math within the text is daunting, too, but Hahn's explanations are clear and his enthusiasm is obvious.

There are themes that run through the chapters here to make the book a consistent whole. One is the idea of the arch. You will here find analysis of the forces on the "voussoirs" (stones making the arch, with the keystone the top one), the friction between them, and the outward thrust. The Romans did little calculation for making their half-circle arches, but of course used the mathematics of geometry.
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2 of 2 people found the following review helpful By Ann Marie Wagrez on November 24, 2012
Format: Kindle Edition Verified Purchase
It was exactly what I was looking for. There is a comparison on mathematical concepts between the Greeks and Romans that I enjoyed to read.
From begining to end, it is a real pleasure to go through the different concepts and periods in architecture.
I will consider to buy a print version of this book.
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1 of 1 people found the following review helpful By Ikaros Bigi on April 28, 2013
Format: Hardcover
My review of Hahn's book `The Mathematical Excursions to the Word's Great Buildings':
It is a wonderful book! You can see my `real' judgment that I paid for this book quickly with my own money, not to find it on our library or pay from my research funds. I keep it in my office to read parts from it after teaching classes and before working on my research. I work on physics, but as a theorist I know something about math.
Around the century ago physics had focused more and more not for finding elementary particles, but on the underlying `symmetries'. I have to give the credit to the mathematics to think about it - and in real world how to produce wonderful buildings and crucially to help the architecture & architects. Professor Hahn shows in excellent ways to show the crucial collaboration between the people from mathematics & architecture and the tools with building those designs; it follows the traditions what these people see a goal of their works.
Finally I think it is wonderful to see `geometry' and `algebra' and the connections between different ways from churches, mosques and even opera house and the correlations with Greek, Roman and Arabic/Islam buildings and their patterns. Many people talk `only' about Greek & Roman architecture and others `only' about Arabic & Islam architecture. In this book you can see the history of connections between different cultures based on mathematics.

I have to disagree with the author only on two points:
(a) I believe that Gauss was a genius not `only' in mathematics, but in general -- in particular also in physics.
(b) `La Sagrada Familia' in Barcelona is wonderful, but I will give `Palau Guell' `top' position for Gaudi's work. In some January ago I was able to walk around also on the `landscape' of the roof.

Ikaros Islam Bigi, Grace-Rupley II Professor, Notre Dame du Lac
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1 of 1 people found the following review helpful By Miguel Angel Vazquez on April 24, 2013
Format: Hardcover
In Spain, years ago, when you were 14 years old you have to choose between studying Humanities or Science. For those who chose the first, maths began to fade out swiftly in their student curricula. I am one of those "Humanities guys".

I'd always wanted to recover my old student relationship with maths, so I got excited when I was told that there was a path to do it using something widely known by a Humanities "expert": art and architecture. I bought Hahn's book with big hopes. The book was even better than expected.

There's a world inside the world of art. One has always known of its existence, but never had been able to touch it, see it, understand it. Loving art and architecture (the Humanities approach) is basically a question of pleasure. You just feel strong emotions facing a cathedral's façade, and you do not exactly know why. From know on, thanks to this book, I've seen a new dimension: not only loving, but, sorry for the Ucases, UNDERSTANDING it. Knowing how it was made.

Maybe some readers would consider the book too tough. Maybe it is, specially for someone who do not work with maths. But exactly in the same degree in which a math expert can enjoy an obscure Apollinaire's poem or James Joyce page, a Humanities lover would find, this is my opinion, pleaure in re-reading passages and getting, in the end, to the sweet shelter of knowledge.

I truly admire this book's author and, also, the bunch of giants who live in its pages: the builders, the freemasons, the architects, the engineers. Specially those between them who, actually, lacked of protocolised knowledge and learned how to build beauty, as Henri de Violet le Duc remembers us in his own book about Middle Age construction methods, just trying, then failing, then trying again.
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