PHI Ratio in Architecture (the Golden Mean, Golden Rectangle, et. al.)
So far the images in this gallery are mostly designs for religious buildings or temples. But symbology finds its way into secular architecture as well, and the phi (or Golden Ratio) comes into play a lot.
It seems to be everywhere in architecture, and nature; as well, an archetypal commentary that mathematicians cannot seem to get enough of. There's much more information about Phi in the Mathematics section of this website (or there will be soon).
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PYRAMIDS: (Mathematical structure)
FROM: WIKIPEDIA | The Golden Ratio
A pyramid in which the apothem (slant height along the bisector of a face)
is equal to φ times the semi-base (half the base width) is sometimes called
a golden pyramid. The isosceles triangle that is the face of such a
pyramid can be constructed from the two halves of a diagonally split golden
rectangle (of size semi-base by apothem), joining the medium-length edges
to make the apothem. The height of this pyramid is
times the semi-base (that is, the slope of the face is
);
the square of the height is equal to the area of a face, φ times the square
of the semi-base.
The medial
right triangle of this "golden" pyramid (see diagram), with sides
is interesting in its own right, demonstrating via the
Pythagorean theorem the relationship
or
.
This "Kepler triangle" is
the only right triangle proportion with edge lengths in
geometric progression, just as the
3–4–5 triangle is the only right triangle proportion with edge lengths in
arithmetic progression. The angle
with tangent
corresponds to the angle that the side of the pyramid makes with respect to
the ground, 51.827... degrees (51° 49' 38").
Buddhist structure
The upper terrace at Borobodur, Java, at dawn; inside each of the domes is a statue of the Buddha. Built between 750 A.D. and 850 A.D., Borobodur represents a Buddhist vision of the cosmos, peaking with Nirvana at its center.
Indigenous - Stonehenge
Stonehenge is a Neolithic and Bronze Age monument located near Amesbury in the English county of Wiltshire, about 8 miles (13 km) northwest of Salisbury. It is composed of earthworks surrounding a circular setting of large standing stones, known as megaliths. There is some debate about the age of the stone circle, but most archaeologists think that it was mainly constructed between 2500 BC and 2000 BC. The older circular earth bank and ditch, which constitute the earliest phase of the monument, have been dated to about 3100 BC. It is located at 51° 10′ 43.9″ N, 1° 49′ 31.6″ W.
Many early historians were influenced by supernatural folktales in their explanations. Some legends held that Merlin the wizard had a giant build the structure for him, while others held the Devil responsible.
In the 1600’s it was argued that Stonehenge was a Roman temple, dedicated to Cnelus, a pagan god, and built following the Tuscan order. Later commentators maintained that the Danes erected it. Up until the late nineteenth century, the site was commonly attributed to the Saxons or other relatively recent societies. The first academic effort to survey and understand the monument was made around 1740 by William Stukeley, who attributed the site to the Druids. Druids - In Celtic Polytheism, the word Druid denotes the priestly class in ancient Celtic societies, which existed through much of Western Europe north of the Alps and in the British Isles. Druidic practices were part of the culture of all the tribal peoples called "Keltoi" and "Galatai" by Greeks and "Celtae" and "Galli" by Romans, which evolved into modern English "Celtic" and "Gaulish".
Stukeley did the requisite research, and contributed measured drawings of the site; which permitted greater analysis of its form and significance. From this work he was able to demonstrate an astronomical or calendrical role in the stones' placement.
Hindu temple - Mandir
One of the numerous temples at Khajurah, Madhya Pradesh in India, Kadariya Mahadev is decorated with 872 carved figures which, like many others around; are depicted in erotic postures. The temple was constructed between 1025 and 1050.
Shinto Temple:
Built at the ends of noisy gravel paths, the Shinto temple tends to still everyday conversation. There is a special silence, broken only by ritual hand-claps, or the sound of crows and seasonal insects.
Shinto ritual, including music (gakaku) and dance (kagura), is characterized by a special slow, measure pace, appropriate to the timeless kami and different from daily life outside.
On special occasions (matsuri) a mass of local people will crowd together in noisy festivity, letting themselves go in front of the kami in ways they would never dream of doing outside the shrine.
Shinto Gate:
The outer gate to the Tobakushi Okusha shrine in winter, Nagaho, Japan. Such gates are known as Torii and form the ceremonial boundary between the spiritual and secular world. There may be several buildings within a shrine complex, including the priest's house and office.
Zen Gardens:
a Zen garden in Kyoto, Japan. Zen gardens are designed to facilitate quiet reflection, and mirror the whole cosmos in miniature scale.
The Parthenon:
Artists's rendering of the remains of the Parthenon on the Acropolis in Athens. The Acropolis is the greatest relic of the ancient Greek city-states. The Parthenon is a temple to the goddess Athene and encapsulates the classical ideals of beauty and proportion (RE: phi proportion).
Islam - Mamluk
The fourteenth-century Mamluk, Sultan Hasan Mosque in Cairo. The mihrab or concavity; indicates the direction of prayer toward Makkah. The stepped mimbar is the podium from which the Friday address is given.
Islam - the Dome of the Rock
also called the Al-Aqsa Mosque in Jerusalem. The golden dome screens the rock from which the Prophet ascended to the Divine presence. It is the third holiest mosque of Islam.
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