Architecture and Mathematics from Antiquity to the Future

1. Relationships Between Architecture and Mathematics
Michael J. Ostwald, Kim Williams

Part I. Mathematics in Architecture

2. Can There Be Any Relationships Between Mathematics and Architecture?
Mario Salvadori

3. Mathematics in, of and for Architecture: A Framework of Types
Michael J. Ostwald, Kim Williams

4. Relationships Between History of Mathematics and History of Art
Clara Silvia Roero

5. Art and Mathematics Before the Quattrocento: A Context for Understanding Renaissance Architecture
Stephen R. Wassell

6. The Influence of Mathematics on the Development of Structural Form
Holger Falter

Part II. From 2000 B.C. to 1000 A.D.

7. Old Shoes, New Feet, and the Puzzle of the First Square in Ancient Egyptian Architecture
Peter Schneider

8. Geometric and Complex Analyses of Maya Architecture: Some Examples
Gerardo Burkle-Elizondo, Nicoletta Sala, Ricardo David Valdez-Cepeda

9. A New Geometric Analysis of the Teotihuacan Complex
Mark A. Reynolds

10. Geometry of Vedic Altars
George Gheverghese Joseph

11. Inauguration: Ritual Planning in Ancient Greece and Italy
Graham Pont

12. The Geometry of the Master Plan of Roman Florence and Its Surroundings
Carol Martin Watts

13. Architecture and Mathematics in Roman Amphitheatres
Sylvie Duvernoy

14. The Square and the Roman House: Architecture and Decoration at Pompeii and Herculaneum
Carol Martin Watts

15. The “Quadrivium” in the Pantheon of Rome
Gert Sperling

16. “Systems of Monads” in the Hagia Sophia
Hagia Sophia (Istanbul)
: Neo-Platonic Mathematics in the Architecture of Late Antiquity
Helge Svenshon, Rudolf H. W. Stichel

Part III. Theories of Measurement and Structure

17. Measure, Metre, Irony: Reuniting Pure Mathematics with Architecture
Robert Tavernor

18. Façade Measurement by Trigonometry
Paul A. Calter

19. Ancient Architecture and Mathematics: Methodology and the Doric Temple
Mark Wilson Jones

20. Calculation of Arches and Domes in Fifteenth-Century Samarkand
Yvonne Dold-Samplonius

21. Curves of Clay: Mexican Brick Vaults and Domes
Alfonso Ramírez Ponce, Rafael Ramírez Melendez

22. Mathematics and Structural Repair of Gothic Structures
Javier Barrallo, Santiago Sanchez-Beitia

23. Mathematics of Carpentry in Historic Japanese Architecture
Izumi Kuroishi

24. On Some Geometrical and Architectural Ideas from African Art and Craft
Paulus Gerdes

25. Design, Construction, and Measurement in the Inka Empire
William D. Sapp

Part IV. From 1100 A.D.–1400 A.D.

26. Vastu Geometry: Beyond Building Codes
Vini Nathan

27. Algorithmic Architecture in Twelfth-Century China: The Yingzao Fashi

Andrew I-kang Li

28. The Celestial Key: Heaven Projected on Earth
Niels Bandholm

29. Friedrich II and the Love of Geometry
Heinz Götze

30. Metrology and Proportion in the Ecclesiastical Architecture of Medieval Ireland
Avril Behan, Rachel Moss

31. The Cloisters of Hauterive
Hauterive, Cistercian Monastery of

Benno Artmann

32. The Use of Cubic Equations in Islamic Art and Architecture
Alpay Özdural

33. Explicit and Implicit Geometric Orders in Mamluk Floors: Secrets of the Sultan Hassan Floor in Cairo
Gulzar Haider, Muhammad Moussa

34. The Fibonacci Sequence and the Palazzo della Signoria

Palazzo della Signoria (Florence)

in Florence
Maria Teresa Bartoli

35. What Geometries in Milan Cathedral

Milan Cathedral

?
Elena Marchetti, Luisa Rossi Costa

36. The Symmetries of the Baptistery and the Leaning Tower of Pisa
Leaning Tower of Pisa

David Speiser

Part V. Theories of Proportion, Symmetry, Periodicity

37. Musical Proportions at the Basis of Systems of Architectural Proportion both Ancient and Modern
Jay Kappraff

38. From Renaissance Musical Proportions to Polytonality in Twentieth Century Architecture
Radoslav Zuk

39. Quasi-Periodicity in Islamic Geometric Design
Peter Saltzman

40. The Universality of the Symmetry Concept
István Hargittai, Magdolna Hargittai

41. Contra Divinam Proportionem
Marco Frascari, Livio G. Volpi Ghirardini

Part VI. From 1400 A.D.–1500 A.D.

42. Alberti

Alberti, Leon Battista

’s Sant’Andrea and the Etruscan Proportion
Michael R. Ytterberg

43. The Numberable Architecture of Leon Battista Alberti
Alberti, Leon Battista
as a Universal Sign of Order and Harmony
Livio G. Volpi Ghirardini

44. Leon Battista Alberti
Alberti, Leon Battista
and the Art of Building
Salvatore Pasquale

45. Verrocchio
Verrocchio (Andrea del Verrocchio)
’s Tombslab for Cosimo de’ Medici
Tombslab for Cosimo de’ Medici
: Designing with a Mathematical Vocabulary
Kim Williams

46. A New Geometric Analysis of the Pazzi Chapel
Pazzi Chapel (Florence)
in Santa Croce, Florence
Mark A. Reynolds

47. Muqarnas: Construction and Reconstruction
Yvonne Dold-Samplonius, Silvia L. Harmsen

Keywords: Mathematics, Mathematics in Art and Architecture, History of Mathematical Sciences