Architecture and Mathematics from Antiquity to the Future : Volume II: The 1500s to the Future

"Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals. Volume I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices. Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume's content includes works in the United States of America and Australia, in addition to those in Europe and Asia."--Back covers. Front Matter....Pages i-xix The Revolutionary, The Reactionary and The Revivalist: Architecture and Mathematics After 1500....Pages 1-27 Front Matter....Pages 29-29 Architecture, Mathematics and Theology in Raphael’s Paintings....Pages 31-42 Raphael and the Pantheon’s Interior: A Pivotal Moment in Architectural Representation....Pages 43-56 Design and Perspective Construction: Why Is the Chalice the Shape It Is?....Pages 57-71 Perspective in António Rodrigues’s Tratado de Arquitectura ....Pages 73-91 Front Matter....Pages 93-93 Ottoman Architecture: Relationships between Architectural Design and Mathematics in Sinan’s Works....Pages 95-106 The Mathematics of Palladio’s Villas....Pages 107-120 Golden Proportions in a Great House: Palladio’s Villa Emo....Pages 121-138 The Hidden Pavement Designs of the Laurentian Library....Pages 139-149 Measuring up to Michelangelo: A Methodology....Pages 151-164 António Rodrigues, a Portuguese Architect with a Scientific Inclination....Pages 165-181 Villalpando’s Sacred Architecture in the Light of Isaac Newton’s Commentary....Pages 183-196 Coelum Britannicum : Inigo Jones and Symbolic Geometry....Pages 197-216 The Science Behind Francesco Borromini’s Divine Geometry....Pages 217-229 Transformational Geometry and the Central European Baroque Church....Pages 231-242 Are There Connections Between the Mathematical Thought and Architecture of Sir Christopher Wren?....Pages 243-255 Robert Hooke’s Fire Monument: Architecture as a Scientific Instrument....Pages 257-267 Practical and Theoretical Applications of Geometry at Claude Perrault’s Observatoire de Paris (1667–1672)....Pages 269-285 Front Matter....Pages 287-287 Geomantic (Re)Creation: Magic Squares and Claude Bragdon’s Theosophic Architecture....Pages 289-303 Mathematics and Music in the Art Glass Windows of Frank Lloyd Wright....Pages 305-323 Front Matter....Pages 287-287 Fractal Geometry in the Late Work of Frank Lloyd Wright: The Palmer House....Pages 325-337 Characteristic Visual Complexity: Fractal Dimensions in the Architecture of Frank Lloyd Wright and Le Corbusier....Pages 339-354 From Cosmic City to Esoteric Cinema: Pythagorean Mathematics and Design in Australia....Pages 355-366 The Ruled Geometries of Marcel Breuer....Pages 367-375 Conoids and Hyperbolic Paraboloids in Le Corbusier’s Philips Pavilion....Pages 377-387 Oscar Niemeyer Curved Lines: Few Words Many Sentences....Pages 389-405 Dom Hans van der Laan and the Plastic Number....Pages 407-419 Louis Kahn’s Platonic Approach to Number and Geometry....Pages 421-434 The Salk: A Geometrical Analysis Supported by Historical Evidence....Pages 435-446 Front Matter....Pages 447-447 Architecture and Mathematics: Soap Bubbles and Soap Films....Pages 449-458 Aperiodic Tiling, Penrose Tiling and the Generation of Architectural Forms....Pages 459-471 Paving the Alexanderplatz Efficiently with a Quasi-Periodic Tiling....Pages 473-481 Generation of Architectural Forms Through Linear Algebra....Pages 483-496 The Praxis of Roman Geometrical Ordering in the Design of a New American Prairie House....Pages 497-512 Exploring Architectural Form in Perspective: A Fractal Hypercube-Building....Pages 513-524 The Compass, the Ruler and the Computer: An Analysis of the Design of the Amphitheatre of Pompeii....Pages 525-540 Correlation of Laser-Scan Surveys of Irish Classical Architecture with Historic Documentation from Architectural Pattern Books....Pages 541-550 Front Matter....Pages 551-551 Mathematics and Architecture Since 1960....Pages 553-578 BiOrganic Design: A New Method for Architecture and the City....Pages 579-591 Formal Mutations: Variation, Constraint, Selection....Pages 593-608 Front Matter....Pages 551-551 The Role of Mathematics in the Design Process Under the Influence of Computational and Information Technologies....Pages 609-617 Generative Design Grammars: An Intelligent Approach Towards Dynamic and Autonomous Design....Pages 619-631 Ethics and Geometry: Computational Transformations and the Curved Surface in Architecture....Pages 633-647 Equiangular Numbers....Pages 649-659 Architecture as Verb and the Ethics of Making....Pages 661-673 Back Matter....Pages 675-690 The goal of this collection of essays is to present a broad portrait of the ways in which two seemingly different disciplines are interconnected. The diversity and varied texture of the essays richly illustrate the affinity between architecture and mathematics. As the nearly 100 articles presented in this two-volume publication show, every era and every culture has relied on mathematical principles incorporated into their works of architecture to imbue their built environment with meaning and order. Included are discussions of geometry, proportional systems, linear algebra, periodic and aperiodic mosaics, fractals, perspective, computer science, and mechanics. Western architecture from each period is examined: Egyptian, Roman, Medieval, Renaissance, Baroque, Enlightenment, 20th century and beyond, as well as the architecture of Turkey, China, India, Japan, Australia and Islam. The mathematical nature of the architecture of Leon Battista Alberti, Andrea Palladio and Frank Lloyd Wright is examined, and the philosophical background behind Renaissance architecture is explored. Contributors come from a wide range of disciplines and cultural backgrounds: architects, mathematicians, historians, theorists, scientists and educators from around the world. Architecture can be seen and understood from a new perspective, by both professionals and non-professionals The aim of this collection of essays is to present a broad portrait of the ways in which two seemingly different disciplines are interconnected. The diversity and varied texture of the essays richly illustrates the affinity between architecture and mathematics. As the almost 100 papers presented in this two-volume publication show, every age and every culture has relied on principles of mathematics incorporated in their works of architecture to imbue their built environment with meaning and order. Included are discussions of geometry, proportional systems, linear algebra, periodic and aperiodic tilings, fractals, perspective, computer science and mechanics. Western architecture of every period is examined: Egyptian, Roman, Medieval, Renaissance, Baroque, Enlightenment, twentieth-century and beyond, as is the architecture of Turkey, China, India, Japan, Australia and Islam. The mathematical nature of the architecture of Leon Battista Alberti, Andrea Palladio and Frank Lloyd Wright is examined, and the philosophical background behind Renaissance architecture is explored. Contributors come from a wide range of disciplines and cultural backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators from the world over. Architecture may be seen and understood in a new light, by professionals as well as non-professionals