Pyramid of Cheops

(about 2550 b.C., Giza Necropolis, Egypt)

In the Cheops pyramid it is possible to obtain golden number φ from the ratio between the apothem a of the pyramid (hypotenuse of the triangle) and half the length of the side of the base square of the pyramid, indicated in the figure with the letter b:

a/b ~ φ

Karnak Temple

(19th - 4th century b.C., Luxor, Egypt)

Golden rectangles are present in the plan of the Great Temple of Amun of Thebes or Temple of Karnak:

Karnak Temple entrance, 1st pylon. The access road is dotted with cryocephalic sphinxes, that is to say ram's head.

One of the ram-headed sphinxes at the entrance to the Great Temple of Amun.

Parthenon

(5th century b.C., Athens, Greece)

The facade of the Greek temple of Athena, built by the architects Ictinus and Callicrates, under the supervision of Phidias, can be perfectly inscribed in a golden rectangle. Furthermore, the golden ratio is repeated several times between different elements of the front:

The golden proportions are also respected in the facade of the Erechtheion temple, positioned on the top of the hill of the Acropolis of Athens and in the structure of the caryatids, which form its famous loggia. In particular, the caryatids can be inscribed in a series of golden rectangles.

The Acropolis of Athens, Greece. View from Philopappos Hill. Photo taken in 2006.

The Caryatids of the Erechtheion exhibited at the Acropolis Museum in Athens. These are the original statues, moved from their natural location to avoid further damage by the smog of the Greek capital.

Arch of Constantine

(official inauguration in 315 A.D., Rome, Italy)

The Arch of Constantine, located in Via dei Fori imperiali, is one of the three triumphal arches of classical Rome, the other two arches are: the Arch of Titus (about 81 - 90 A.D.) and the Arch of Septimius Severus ( 202 - 203 A.D.).

The Arch of Constantine was erected to commemorate the victory of Constantine I against Maxentius in the battle of Ponte Milvio (October 28, 312 A.D.) and it was officially inaugurated in 315 A.D., on the occasion of the ten-year anniversary of the emperor's power.

The central height of this arch divides the total height according to the golden section, while in the two minor arches the golden section is involved in the distance between the base and the lower strip:

Notre Dame de Paris

(1163 - 1345, Paris, France)

The main facade of the Notre-Dame cathedral, one of the most famous Gothic buildings in the world, was designed following the golden ratio. In particular, the ratio between the height of the cathedral and its width is 1.61; furthermore, the total height is approximately 1.61 times the height of the first two floors and the total width is approximately 1.61 the width of a tower plus the central section.

The following image highlights the golden section of the segments that can be identified on the facade of the cathedral:

University of Salamanca

(founded 1218, Salamanca, Spain)

The Gothic facade of the University of Salamanca, founded by King Alfonso IX of León, is defined by a large golden rectangle:

Facade of the University of Salamanca by Juan Laurent, 1878, Department of Image Collections, National Gallery of Art Library, Washington, DC.

Cologne Cathedral

(began construction 1248; completed 1880, Cologne, Germany)

The golden ratio φ, in the Cologne Cathedral, is found with such frequency that the archaeologist Peter Wilhelm Lund considers it, among all the cathedrals of the Middle Ages, the closest to the Parthenon:

The Cathedral in 1880.

Portal of Castel del Monte

(1240, Andria, Italy)

The portal of Castel del Monte, an example of Gothic architecture in Puglia, springs from the starry pentagon and its decomposition according to the golden number φ.

Castel del Monte is a thirteenth century fortress which, Frederick II of Swabia, Emperor of the Holy Roman Empire and King of Sicily, built on the top of a hill 540 meters high in the western Murge plateau in Puglia:

Castel del Monte in an 1890 print.

Old Palace

(founded 1299, Florence, Italy)

Palazzo Vecchio, headquarters of the Municipality, in Piazza della Signoria in Florence, is an example of fourteenth-century civil architecture of the city and is one of the best-known civic buildings in the world. Observing the building and drawing an imaginary line passing through the center of its tower, it can be noticed the presence of 8 windows to the right of the imaginary line and 5 windows to the left; in total there are 13 windows under the facade of the building. These numbers belong to the Fibonacci sequence. Furthermore, setting the width of the facade of the building equal to 1, the distance between the center of the tower and the extreme is equal to 0.604, that is a number that approximates the reciprocal of the golden number φ:

It should still be emphasized that the side facade of the building can be divided into two golden rectangles.

Mole Antonelliana

(1863 - 1889, Turin, Italy)

The Mole Antonelliana, with its height of 167.5 meters, represented the tallest masonry building in the world, starting from 1889 until 1908.

The particularity of this monumental building is given by the presence of a permanent work of art, entitled "The Flight of Numbers" and located on the curve of the dome. Its creation took place on the occasion of the "Luci d'Artista" event, which started in 1998 from a public lighting project for the Christmas holidays.

The artwork consists in the reproduction, with red neon, of the first terms of the Fibonacci sequence, arranged vertically in ascending order from bottom to top. It was put into practice by the Italian painter and sculptor Mario Merz (1925 – 2003), a leading exponent of the Arte Povera movement and always attracted by the numbers of the Fibonacci sequence. With this installation, the artist wanted to represent the growth process inherent in many natural phenomena belonging to the animal and vegetable world.

Tāj Maḥal

(1632, Agra, India)

The Tāj Maḥal is a mausoleum located in Agra, in northern India, it was built by the Mughal emperor Shāh Jahān in memory of his wife Arjumand Banu Begum. The whole structure of the mausoleum is modulated by the golden ratios:

Taj Mahal and outlying buildings seen from across the Yamuna River (north view).

Glass building of the UN

(built 1947 and completed 1952, New York, USA)

The glass building of the United Nations Secretariat is a 39-storey office skyscraper with a height of 154 m. The building was designed by the Brazilian architect Oscar Niemeyer and the Swiss-French architect Le Corbusier.

In this building the golden proportions can be found in the facade, which is composed of golden rectangles, but olso in the width and height of the floors and furthermore in the dimensions of the windows:

CN Tower

(1973 - 1976, Toronto, Canada)

The CN Tower (Canadian National Tower) is a telecommunications tower and, of its kind, is the fourth tallest structure in the world, as well as being the third tallest free-standing structure in the world.

The tower respects the golden ratio; in fact, the ratio between its overall height of 553.33 meters and the height of the observation deck at 342 meters is equal to 1.618: