List of works designed with the golden ratio

[1] For example, claims have been made about golden ratio proportions in Egyptian, Sumerian and Greek vases, Chinese pottery, Olmec sculptures, and Cretan and Mycenaean products from the late Bronze Age.

[2] As another example, Carlos Chanfón Olmos states that the sculpture of King Gudea (c. 2350 BC) has golden proportions between all of its secondary elements repeated many times at its base.

[3][6] John F. Pile, interior design professor and historian, has claimed that Egyptian architects sought the golden proportions without mathematical techniques and that it is common to see the 1.618:1 ratio, along with many other simpler geometrical concepts, in their architectural details, art, and everyday objects found in tombs.

[15] Lothar Haselberger claims that the Temple of Apollo in Didyma (c. 334 BC), designed by Daphnis of Mileto and Paionios of Ephesus, has golden proportions.

Manuel Amabilis published his studies along with several self-explanatory images of other pre-columbian buildings made with golden ratio proportions in La Arquitectura Precolombina de Mexico.

For the builder, the most important function Fi, as we write the golden mean, is that if the uses is consistently he will find that every subdivision, no matter how accidentally it may have been derived, will fit somewhere into the series.

[24] De divina proportione, written by Luca Pacioli in Milan in 1496–1498, published in Venice in 1509,[25] features 60 drawings by Leonardo da Vinci, some of which illustrate the appearance of the golden ratio in geometric figures.

Some authors feel there is no actual evidence that Da Vinci used the golden ratio in Vitruvian Man;[27] however, Olmos[3] (1991) observes otherwise through geometrical analysis.

He also proposes Leonardo da Vinci's self portrait, Michelangelo's David (1501–1504), Albrecht Dürer's Melencolia I and the classic violin design by the masters of Cremona (Guarneri, Stradivari and several members of the Amati family) as having similar regulator lines related to the golden ratio.

Da Vinci's Mona Lisa (c. 1503–1506) "has been the subject of so many volumes of contradicting scholarly and popular speculations that it virtually impossible to reach any unambiguous conclusions" with respect to the golden ratio, according to Livio.

[11] The Tempietto chapel at the Monastery of Saint Peter in Montorio, Rome, built by Bramante, has relations to the golden ratio in its elevation and interior lines.

[28] José Villagrán García has claimed[29] that the golden ratio is an important element in the design of the Mexico City Metropolitan Cathedral (circa 1667–1813).

Olmos claims the same for the design of the cities of Coatepec (1579), Chicoaloapa (1579) and Huejutla (1580), as well as the Mérida Cathedral, the Acolman Temple, Christ Crucified by Diego Velázquez (1639) and The Immaculate Conception by Bartolomé Esteban Murillo.

Rather, they correspond to basic mathematical divisions (simple ratios that appear to approximate the golden section), as noted by Seurat with citations from the mathematician, inventor, esthetician Charles Henry.

Jean Metzinger, Juan Gris and possibly Marcel Duchamp at this time were associates of Maurice Princet, an amateur mathematician credited for introducing profound and rational scientific arguments into Cubist discussions.

[37] The name 'Section d'Or' represented simultaneously a continuity with past traditions and current trends in related fields, while leaving open future developments in the arts.

[45] The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion.

Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci number, which he described as "rhythms apparent to the eye and clear in their relations with one another.

He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's Vitruvian Man, the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture.

[47] In The Modulor: A Harmonious Measure to the Human Scale, Universally Applicable to Architecture and Mechanics Le Corbusier reveals he used his system in the Marseilles Unité d'habitation (in the general plan and section, the front elevation, plan and section of the apartment, in the woodwork, the wall, the roof and some prefabricated furniture), a small office in 35 rue de Sèvres, a factory in Saint-Die and the United Nations Headquarters building in New York City.

[51] According to the official tourism page of Buenos Aires, Argentina, the ground floor of the Palacio Barolo (1923), designed by Italian architect Mario Palanti, is built according to the golden ratio.

[53] Ernő Lendvai analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale,[54] though other music scholars reject that analysis.

[56] Leonid Sabaneyev hypothesizes that the separate time intervals of the musical pieces connected by the "culmination event", as a rule, are in the ratio of the golden section.