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

Front Matter....Pages i-xix
Relationships Between Architecture and Mathematics....Pages 1-21
Front Matter....Pages 23-23
Can There Be Any Relationships Between Mathematics and Architecture?....Pages 25-29
Mathematics in , of and for Architecture: A Framework of Types....Pages 31-57
Relationships Between History of Mathematics and History of Art....Pages 59-66
Art and Mathematics Before the Quattrocento: A Context for Understanding Renaissance Architecture....Pages 67-80
The Influence of Mathematics on the Development of Structural Form....Pages 81-93
Front Matter....Pages 95-95
Old Shoes, New Feet, and the Puzzle of the First Square in Ancient Egyptian Architecture....Pages 97-111
Geometric and Complex Analyses of Maya Architecture: Some Examples....Pages 113-125
A New Geometric Analysis of the Teotihuacan Complex....Pages 127-147
Geometry of Vedic Altars....Pages 149-162
Inauguration: Ritual Planning in Ancient Greece and Italy....Pages 163-175
The Geometry of the Master Plan of Roman Florence and Its Surroundings....Pages 177-188
Architecture and Mathematics in Roman Amphitheatres....Pages 189-199
The Square and the Roman House: Architecture and Decoration at Pompeii and Herculaneum....Pages 201-213
The “Quadrivium” in the Pantheon of Rome....Pages 215-227
“Systems of Monads” in the Hagia Sophia Hagia Sophia (Istanbul) : Neo-Platonic Mathematics in the Architecture of Late Antiquity....Pages 229-242
Front Matter....Pages 243-243
Measure, Metre, Irony: Reuniting Pure Mathematics with Architecture....Pages 245-259
Façade Measurement by Trigonometry....Pages 261-269
Ancient Architecture and Mathematics: Methodology and the Doric Temple....Pages 271-295
Calculation of Arches and Domes in Fifteenth-Century Samarkand....Pages 297-307
Front Matter....Pages 243-243
Curves of Clay: Mexican Brick Vaults and Domes....Pages 309-324
Mathematics and Structural Repair of Gothic Structures....Pages 325-332
Mathematics of Carpentry in Historic Japanese Architecture....Pages 333-347
On Some Geometrical and Architectural Ideas from African Art and Craft....Pages 349-360
Design, Construction, and Measurement in the Inka Empire....Pages 361-372
Front Matter....Pages 373-373
Vastu Geometry: Beyond Building Codes....Pages 375-388
Algorithmic Architecture in Twelfth-Century China: The Yingzao Fashi ....Pages 389-397
The Celestial Key: Heaven Projected on Earth....Pages 399-422
Friedrich II and the Love of Geometry....Pages 423-436
Metrology and Proportion in the Ecclesiastical Architecture of Medieval Ireland....Pages 437-451
The Cloisters of Hauterive Hauterive, Cistercian Monastery of ....Pages 453-466
The Use of Cubic Equations in Islamic Art and Architecture....Pages 467-481
Explicit and Implicit Geometric Orders in Mamluk Floors: Secrets of the Sultan Hassan Floor in Cairo....Pages 483-496
The Fibonacci Sequence and the Palazzo della Signoria Palazzo della Signoria (Florence) in Florence....Pages 497-507
What Geometries in Milan Cathedral Milan Cathedral ?....Pages 509-534
The Symmetries of the Baptistery and the Leaning Tower of Pisa Leaning Tower of Pisa ....Pages 535-546
Front Matter....Pages 547-547
Musical Proportions at the Basis of Systems of Architectural Proportion both Ancient and Modern....Pages 549-565
From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture....Pages 567-584
Quasi-Periodicity in Islamic Geometric Design....Pages 585-602
The Universality of the Symmetry Concept....Pages 603-618
Front Matter....Pages 547-547
Contra Divinam Proportionem....Pages 619-626
Front Matter....Pages 627-627
Alberti Alberti, Leon Battista ’s Sant’Andrea and the Etruscan Proportion....Pages 629-644
The Numberable Architecture of Leon Battista Alberti Alberti, Leon Battista as a Universal Sign of Order and Harmony....Pages 645-661
Leon Battista Alberti Alberti, Leon Battista and the Art of Building....Pages 663-673
Verrocchio Verrocchio (Andrea del Verrocchio) ’s Tombslab for Cosimo de’ Medici Tombslab for Cosimo de’ Medici : Designing with a Mathematical Vocabulary....Pages 675-685
A New Geometric Analysis of the Pazzi Chapel Pazzi Chapel (Florence) in Santa Croce, Florence....Pages 687-707
Muqarnas: Construction and Reconstruction....Pages 709-719
Back Matter....Pages 721-735