The Golden Number

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  • Format: Hardcover
  • Copyright: 8/29/2016
  • Publisher: Inner Traditions

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The first English translation of Ghyka’s masterwork on sacred geometry

• Reveals how the Golden Number Phi underlies the spiritual nature of beauty and the hidden harmonies that connect the whole of creation

• Explains how the spiritual mysteries of the Golden Number were passed down in an unbroken line of transmission from the Pythagorean brotherhoods through the medieval builders’ guilds to the secret societies of 18th-century Europe

The Golden Number, or Phi (Φ), is a geometric ratio found throughout nature, often underlying the dimensions of objects considered especially beautiful. Simplified as 1.618 and symbolized by the Fibonacci sequence, the Golden Number represents the unique relationship within an object where the ratio of a larger part to a smaller part is the same as the ratio of the whole to the larger part. It appears in the proportions of the human face and body as well as in the proportions of animals, plants, and celestial bodies.

Called the divine proportion by the monk Fra Luca Pacioli, whose book on the subject was illustrated by Leonardo da Vinci, Phi’s use in art and architecture goes back at least to the mystical mathematics of Pythagoras and his followers in the sixth century BCE. The perfect synthesis of spiritual and material, it can be found in the measurements of the sacred temples of Egypt, Ancient Greece, and Medieval and Renaissance Europe. The asymptotic series of integers that define Phi represent the macrocosm and microcosm as portrayed in Plato’s concept of the world soul.

Presenting Matila Ghyka’s classic treatise on the Golden Number for the first time in English, this book reveals the many ways this ratio can be found not only in the organic forms of nature--such as in the spirals of shells or the number of petals on a flower--but also in the most beautiful and highest creations of humanity. One of the most important concepts of sacred geometry, its mysteries were passed down in an unbroken line of transmission from the Pythagorean brotherhoods through the medieval builders’ guilds to the secret societies of 18th-century Europe. Ghyka shows how the secrets of this divine proportion were not sought merely for their value in architecture, painting, and music, but also as a portal to a deeper understanding of the spiritual nature of beauty and the hidden harmonies that connect the whole of creation.

Author Biography

Prince Matila Costiesco Ghyka (1881-1965) was a Romanian mathematician, historian, philosopher, and diplomat, who served as the Plenipotentiary Minister in the United Kingdom during the late 1930s. He was also a visiting professor of aesthetics at the University of Southern California and at the Mary Washington College in Virginia. His previous books in English include The Geometry of Art and Life and an autobiography, The World Mine Oyster. Though his prolific literary output includes fiction, poetry, and philosophy, the overarching concern of his work was a synthesis of higher mathematics and the arts.

Table of Contents

Publisher's Preface

Foreword by Paul Valéry


Part 1     RHYTHMS

Chapter   1  
  From Number to Harmony

Chapter   2    The Divine Proportion

Chapter   3    The Geometric Canons of Mediterranean Architecture

Chapter   4    The Orchestration of Volumes and Architectural Harmony

Chapter   5    From Rhythm to Incantation

Chapter   6    From Incantation to Love

Part 2     Rites

Chapter   7    Pythagoras

Chapter   8    The Lamp under the Bushel

Chapter   9    Esotericism and Politics:From Plato’s Cave to the Masonic Lodges

Chapter   10    Modern Science and the Return to Pythagoras

Chapter   11    Life Force, Rhythm, and Duration

Chapter  12    The Phoenix of Metapontum and the Duel of the Magicians




1.    Polygonal figurate numbers and gnomons

2.    Golden section, pentagon, pentagram, phi rectangle

3.    The five regular polyhedrons (Platonic solids)

4.    The five Platonic solids inscribed inside one another

5.    Star dodecahedron with twenty vertices

6.    Star dodecahedron with twelve vertices

7.    Icosahedron and dodecahedron by Leonardo da Vinci for Pacioli’s Divina Proportione

8.    Semi-regular polyhedrons by Leonardo da Vinci

9.    Star dodecahedron and stella octangula by Leonardo da Vinci

10.    Pentagonal symmetries: Φ rectangle and spiral of harmonious growth

11.    Three growth patterns governed by the golden section

12.    Hexagonal symmetries (crystals)

13.    Pentamerous flowers

14.    Pentamerous calyx (Symphytum officinale)

15.    Cardium pseudolima and Solarium perspectivum

16.    Nautilus pompilius and Triton tritonis (X-rays)

17.    Man-Microcosm according to Agrippa von Nettesheim and the directing icosahedron in the choreography manual by R. von Laban

18.    Miss Helen Wills (Mrs. F. Moody)

19.    Harmonic analysis of the previous photograph

20.    Explanation of the diagram in plate

21.    Isabella d’Este, by Leonardo da Vinci

22.    Male nude, harmonic analysis (square and golden section)

23.    The “Microcosm”

24.    Hellenistic bas-relief

25.    Harmonic rectangles (Φ and 5) based on Hambidge

26.    Harmonic decomposition of drawings according to Hambidge’s method

27.    Egyptian harmonic drawings

28.    Harmonic decomposition of the Φ rectangle

29.    Systems of proportion obtained by the polar segmentation of the circle

30.    Plans of an Egyptian temple and the rock temple of Mira

31.    Typical Greek temple designs

32.    Mössel’s typical diagrams for an early Christian basilica and Gothic church

33.    Typical Gothic designs according to Mössel

34.    Establishing the transverse proportion of Gothic naves

35.    Canon of Pythagoras

36.    Relationship between the Pythagorean scale and the columns of Greek temples

37.    Milan cathedral; plan reproduced by Caesariano in his commentary on Virtruvius

38.    Milan cathedral (elevation and vertical section by Caesar Caesariano, 1521)

39.    Explanatory diagram for plate

40.    Small temple of Minerva in Rome, harmonic analysis

41.    Pantheon of Rome, harmonic analysis

42.    San Stefano Rotunda in Rome, harmonic analysis

   Explanatory diagram for the San Stefano plan

44.    The Great Pyramid, meridian section

45.    Miloutine Borissavlievitch’s optico-physiological perspectivism

46.    Projected analogies by Miloutine Borissavlievitch’s perspectivism

47.    Hieronymus Bosch, The Garden of Earthly Delights

48.    Maat, goddess of truth

49.    Rose window of Amiens, magical pentacles, cinquefoil from the Saint-Chapelle

50.    Masons’ marks

51.    Gothic masons’ marks

52.    Gothic symphony (Burgos cathedral)

53.    Baroque catharsis (Melk Abbey)

54.    Baroque catharsis (Melk Abbey)

55.    Baroque catharsis, monstrance

56.    The mystic handshake

57.    Square and plumb line on a funerary mosaic in Pompeii

58.    Christ the “Initiate,” Saint Stephen’s Cathedral, Vienna

59.    Le Corbusier and Pierre Jeanneret, regulating drawings

60.    Le Corbusier and Pierre Jeanneret, regulating drawing

61.    Harmonic variations on the dodecahedron

62.    Harmonic variations on the icosahedron

63.    Lilies

64.    Ancient nude: Bronze in the style of Polykleitos

65.    Another view of plate

66.    The new Nordic naturism

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