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Mathematical Excursions to the World's Great Buildings

Mathematical Excursions to the World's Great Buildings

Copyright Date: 2012
Edition: STU - Student edition
Pages: 352
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  • Book Info
    Mathematical Excursions to the World's Great Buildings
    Book Description:

    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.

    eISBN: 978-1-4008-4199-8
    Subjects: Mathematics, Architecture and Architectural History

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Preface
    (pp. vii-x)
    Alexander Hahn
  4. 1 Humanity Awakening: Sensing Form and Creating Structures
    (pp. 1-11)

    The earliest ancestors of humans began to emerge about 7 million years ago, and the human species has existed for about 100,000 years. For most of this period humans were preoccupied with acquiring food and securing shelter. They lived in caves, made stone tools and weapons, and hunted and foraged for food. Some 10,000 years ago, an important transition occurred. By that time, the Ice Age that had started about 60,000 years ago was over. The ice sheets that covered Europe and Asia had receded to make room for forests, plains, and deserts. Seeing how plants sprang forth and grew...

  5. 2 Greek Geometry and Roman Engineering
    (pp. 12-52)

    By the beginning of the last millennium B.C., the city-states of Greece started to flourish. These trading towns along the Aegean and southern Italian coasts were ruled by an independent, politically aware merchant class. Their growing trade made them wealthy and connected them with other lands on the shores of the Mediterranean and beyond. The new social order that they established spawned a new rational approach. Rather than the acceptance of “mythos,” the account that gods and demi-gods controlled nature and unleashed its forces on a whim, there was a realization that observed phenomena operated in accordance with a rational...

  6. 3 Architecture Inspired by Faith
    (pp. 53-96)

    The Roman emperor Constantine recognized the Christian faith in the fouth century and it became Rome’s state religion soon thereafter. In refocusing attention from this world to the next, Christianity offered biblical narratives and supernatural explanations to guide the course of human action. Neither the inquisitive mindset with which Greek philosophy and mathematics analyzed the world nor the confident spirit with which Roman engineering shaped it received much promotion. When Constantine moved the imperial capital from Rome to Byzantium (soon thereafter renamed Constantinople), the Roman Empire and its Christian faith split into western and eastern parts. The split between Christian...

  7. 4 Transmission of Mathematics and Transition in Architecture
    (pp. 97-137)

    Fundamental changes occurred in the territories around the Mediterranean Sea and to its north and east during the period from the twelfth to the fifteenth centuries. The energy of the Islamic Dominions was diminishing. A Christian Reconquest ended the Islamic occupation of Spain in the west, and Mongol invasions ended the influence of the Seljuk Turkish dynasty in the east. The Byzantine Empire, its territories under constant pressure from Islamic expansion, was stagnating and no longer creative. A rising Ottoman Turkish dynasty finally ended its existence in the fifteenth century. However, for Catholic Christian Europe, this was a dynamic period...

  8. 5 The Renaissance: Architecture and the Human Spirit
    (pp. 138-204)

    During the fourteenth and fifteenth centuries, five major political powers took control of the Italian peninsula: the three major city-states of Florence, Venice, and Milan, the States of the Vatican with Rome as center, and the kingdom of Naples. In a time of constant warfare and shifting alliances and borders, the fortunes of smaller city-states, such as Siena, Genoa, and Pisa, rose and fell. In spite of this, manufacturing increased in towns and cities, their markets grew, and commercial activity expanded. Soon a class of merchants and bankers shared wealth, lands, and influence with nobles and aristocrats. As commerce grew,...

  9. [Illustrations]
    (pp. None)
  10. 6 A New Architecture: Materials, Structural Analysis, Computers, and Design
    (pp. 205-264)

    An Industrial Revolution begins in the middle of the eighteenth century, develops quickly in the nineteenth, and ushers in a new age. The machines that the steam engine and the utility of iron make possible dramatically change the scale and range of human activity. Powerful steamships and locomotives are able to transport large quantities of cargo and people. Machine-powered foundries, mills, and other factories employing large numbers of workers produce goods made of metals, fabrics, artificial fibers, and plastics economically and in great quantities. The hoists, lifts, and cranes deployed in building projects and the vehicles that bring the materials...

  11. 7 Basic Calculus and Its Application to the Analysis of Structures
    (pp. 265-300)

    At around the time that Bernini was putting the finishing touches to St. Peter’s square in Rome and Wren was beginning to build the new St. Paul’s Cathedral, Newton and Leibniz developed calculus, a powerful and widely applicable new mathematics. The circumstances surrounding these two geniuses could not have been more different.

    Isaac Newton (1642–1727), an English university student in his early twenties, went back to the family farm when the black plague closed Cambridge University. With extraordinary insights and great powers of concentration he worked there on his own in the years 1665 and 1666. In this short...

  12. Glossary of Architectural Terms
    (pp. 301-306)
  13. References
    (pp. 307-310)
  14. Index
    (pp. 311-317)
  15. Photo Sources
    (pp. 318-318)