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Example research essay topic: 19 Th Century Art And Architecture - 5,152 words

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Architecture, the practice of building design and its resulting products; customary usage refers only to those designs and structures that are culturally significant. Architecture is to building as literature is to the printed word. Vitruvius, a 1 st-century BC Roman, wrote encyclopedically about architecture, and the English poet Sir Henry Wotton was quoting him in his charmingly phrased dictum: "Well building hath three conditions: Commodities, Firmenes, and Delight. " More prosaically, one would say today that architecture must satisfy its intended uses, must be technically sound, and must convey aesthetic meaning. But the best buildings are often so well constructed that they outlast their original use.

They then survive not only as beautiful objects, but as documents of the history of cultures, achievements in architecture that testify to the nature of the society that produced them. These achievements are never wholly the work of individuals. Architecture is a social art. Architectural form is inevitably influenced by the technologies applied, but building technology is conservative and knowledge about it is cumulative. Precast concrete, for instance, has not rendered brick obsolete. Although design and construction have become highly sophisticated and are often computer directed, this complex apparatus rests on preindustrial traditions inherited from millennia during which most structures were lived in by the people who erected them.

The technical demands on building remain the elemental ones-to exclude enemies, to circumvent gravity, and to avoid discomforts caused by an excess of heat or cold or by the intrusion of rain, wind, or vermin. This is no trivial assignment even with the best modern technology. The availability of suitable materials fostered the crafts to exploit them and influenced the shapes of buildings. Large areas of the world were once forested, and their inhabitants developed carpentry.

Although it has become relatively scarce, timber remains an important building material. Many kinds of stone lend themselves to building. Stone and marble were chosen for important monuments because they are incombustible and can be expected to endure. Stone is also a sculptural material; stone architecture was often integral with stone sculpture. The use of stone has declined, however, because a number of other materials are more amenable to industrial use and assembly. Some regions lack both timber and stone; their peoples used the earth itself, tamping certain mixtures into walls or forming them into bricks to be dried in the sun.

Later they baked these substances in kilns, producing a range of bricks and tiles with greater durability. Thus, early cultures used substances occurring in their environment and invented the tools, skills, and technologies to exploit a variety of materials, creating a legacy that continues to inform more industrialized methods. Building with stones or bricks is called masonry. The elements cohere through sheer gravity or the use of mortar, first composed of lime and sand. The Romans found a natural cement that, combined with inert substances, produced concrete. They usually faced this with materials that would give a better finish.

In the early 19 th century a truly waterproof cement was developed, the key ingredient of modern concrete. In the 19 th century also, steel suddenly became abundant; rolling mills turned out shapes that could make structural frames stronger than the traditional wooden frames. Moreover, steel rods could be positioned in wet concrete so as to greatly improve the versatility of that material, giving impetus early in the 20 th century to new forms facilitated by reinforced concrete construction. The subsequent profusion of aluminum and its anodized coatings provided cladding (surfacing) material that was lightweight and virtually maintenance free. Glass was known in prehistory and is celebrated for its contributions to Gothic architecture.

Its quality and availability have been enormously enhanced by industrial processing, which has revolutionized the exploitation of natural light and transparency. When masonry materials are stacked vertically, they are very stable; every part is undergoing compression. The real problem of construction, however, is spanning. Ways must be found to connect walls so as to provide a roof. The two basic approaches to spanning are post-and-lintel construction and arch, vault, and dome construction. In post-and-lintel construction, lintels, or beams, are laid horizontally across the tops of posts, or columns; additional horizontals span from beam to beam, forming decks that can become roofs or be occupied as floors.

In arch, vault, and dome construction, the spanning element is curved rather than straight. In the flat plane of a wall, arches may be used in rows, supported by piers or columns to form an arcade; for roofs or ceilings, a sequence of arches, one behind the other, may be used to form a half-cylinder (or barrel) vault; to span large centralized spaces, an arch may be rotated from its peak to form a hemispherical dome (see Arch and Vault; Dome). Post-and-lintel solutions can be executed in various materials, but gravity subjects the horizontal members to bending stress, in which parts of the member are in compression while others are in tension. Wood, steel, and reinforced concrete are efficient as beams, whereas masonry, because it lacks tensile components, requires much greater bulk and weight. Vaulting permits spanning without subjecting material to tension; thus, it can cover large areas with masonry or concrete. Its outward thrust, however, must be counteracted by abutment, or buttressing.

Trussing is an important structural device used to achieve spans with less weighty construction. Obviously, a frame composed of three end-connected members cannot change its shape, even if its joints could act as hinges. Fortunately, however, the principle of triangulation-attaching a horizontal tie beam to the bottom ends of two peaked rafters-can be extended indefinitely. Spanning systems of almost any shape can be subdivided into triangles, the sides of which can be made of any appropriate material-wood, rolled steel, or tubing-and assembled using suitable end connections. Each separate part is then subject only to either compressive or tensile stress.

In the 18 th century, mathematicians learned to apply their science to the behavior of structures, thus making it possible to determine the amounts of these stresses. This led to the development of space frames, which are simply trusses or other elements arrayed three-dimensionally. Advances in the art of analyzing structural behavior resulted from the demand in the 19 th century for great civil engineering structures: dams, bridges, and tunnels. It is now possible to enclose space with suspension structures-the obverse of vaulting, in that materials are in tension-or pneumatic structures, the skins of which are held in place by air pressure. Sophisticated analysis is particularly necessary in very tall structures, because wind loads and stresses that could be induced by earthquakes then become more important than gravity.

Architecture must also take into account the internal functional equipment of modern buildings. In recent decades, elaborate systems for vertical transportation, the control of temperature and humidity, forced ventilation, artificial lighting, sanitation, control of fire, and the distribution of electricity and other services have been developed. This has added to the cost of construction and has increased expectations of comfort and convenience. In modern architectural terminology the word program denotes the purposes for which buildings are constructed. Certain broad purposes have always been discernible. The noblest works-temples, churches, mosques-celebrate the mysteries of religion and provide assembly places where gods can be propitiated or where the multitudes can be instructed in interpretations of belief and can participate in symbolic rituals.

Another important purpose has been to provide physical security: Many of the world's most permanent structures were built with defense in mind. Related to defense is the desire to create buildings that serve as status symbols. Kings and emperors insisted on palaces proclaiming power and wealth. People of privilege have always been the best clients of designers, artists, and artisans, and in their projects the best work of a given period is often represented. Today large corporations, governments, and universities play the role of patron in a less personal way. A proliferation of building types reflects the complexity of modern life.

More people live in mass housing and go to work in large office buildings; they spend their incomes in large shopping centers, send their children to many different kinds of schools, and when sick go to specialized hospitals and clinics. They linger in airports on the way to distant hotels and resorts. Each class of facility has accumulated experiences that contribute to the expertise needed by its designers. The attention of clients, architects, and users is more and more focused on the overall qualities manifested by aggregates of buildings and parts of cities as being more significant than individual structures.

As the total building stock grows, conserving buildings and adapting them for changes in use becomes more important. See City Planning. The aesthetic response to architecture is complex. It involves all the issues already discussed, as well as other, more abstract qualities. An experience of architectural space is personal and psychological; it differs from that of sculpture or painting because the observer is in it. It is affected by associations the observer may have with the materials used and the way they have been assembled, and by the lighting conditions.

Structural logic may or may not have been dramatized. Elements such as windows, and their scale and rhythm, affect the observer, as do the interplay of geometrical form and the way space is articulated. Movement through a sequence of spaces has narrative force; no single point of view is adequately descriptive. The recurrence of thematic forms, appearing in varied guises and contexts, contributes to unity and creates feelings-relaxation and protection or stimulation and awe.

Perhaps the key element is proportion-the relation of various dimensions to one another and their relation to human scale. During the mid- 19 th century, architecture became institutionalized as a profession requiring formal preparation and subject to codes of performance. During this period connoisseurship-full academic training in the history of architecture and its aesthetics-was the designer's most important qualification. In every Western country the cole des Beaux-Arts in Paris was accepted as the model for architectural education.

Architecture was easily separated from engineering, which had pragmatic rather than aesthetic goals. Yet today the profession delivers not only aesthetic guidance but also a bewildering array of technical services requiring many specialized contributors. The architect strives to maintain the position of generalist, one who can take the long view while orchestrating the resolution of complex interrelated issues. For the convenience of Western readers, the architecture of the ancient world, of the Orient, and of the pre-Columbian Americas may be divided into two groups: indigenous architecture, or ways of building that appear to have developed independently in isolated, local cultural conditions; and classical architecture, the systems and building methods of Greece and Rome, which directly determined the course of Western architecture. The oldest designed environments stable enough to have left traces date from the first development of cities. This region, the greater part of modern Iraq, comprises the lower valleys of the Tigris and Euphrates rivers.

The Assyrian city of Khorsabad, built of clay and brick in the reign of Sargon II (reigned 722 - 705 BC), was excavated as early as 1842, and much of its general plan is known. It became the basis for the study of Mesopotamian architecture, because the far older cities of Babylon and Ur were not discovered and excavated until the late 19 th and 20 th centuries. See Mesopotamian Art and Architecture. Early Persian architecture-influenced by the Greeks, with whom the Persians were at war in the 5 th century BC-left the great royal compound of Persepolis (518 - 460 BC), created by Darius the Great, and several nearby rock-cut tombs, all north of Sarah in Iran. See Iranian Art and Architecture. The urban culture of Egypt also developed very early.

Its political history was more stable, however, with strong continuity in the development and conservation of tradition. Also, granite, sandstone, and limestone were available in abundance. These circumstances, in a cultural system conferring enormous power on rulers and priests, made possible the erection, over a long period, of the most awesome of the world's ancient monuments. Each Egyptian ruler was obsessed with constructing a tomb for himself more impressive and longer lasting than that of his predecessors.

Before the 4 th Dynasty (begins c. 2680 BC) Egyptian royal burial took the form of the mastaba, an archetypal rectangular mass of masonry. This evolved into the stepped pyramid and finally into the fully refined pyramid, of which the largest and best preserved are those of Khufu (built c. 2570 BC) and Khafre (circa 2530 BC) at Giza near Cairo. These immense monuments testify to the pharaohs' vast social control and also to the fascination of their architects with abstract, perfect geometrical forms, a concern that reappears frequently throughout history. Egyptians built temples to dignify the ritual observances of those in power and to exclude others.

Thus, they were built within walled enclosures, their great columned halls (hypostyle's) turning inward, visible from a distance only as a sheer mass of masonry. A hierarchical linear sequence of spaces led to successively more privileged precincts. In this way was born the concept of the axis, which in the Egyptian temples was greatly extended by avenues of sphinxes in order to intensify the climactic experience of the approaching participants. The temples also introduce the monumental use of post-and-lintel construction in stone, in which massive columns are closely spaced and bear deep lintels. The best-known Egyptian temples are in the mid-Nile area in the vicinity of the old capital, Thebes. Here are found the great temples of Luxor, Karnak, and Deir al Bar (15 th- 12 th century BC) and If (3 rd century BC).

See Egyptian Art and Architecture; Temple. Hindu traditions are rich in visual symbols; the early stone architecture of India was elaborately carved, more like sculpture than building, especially as the designers did not emphasize structural systems and rarely faced the task of enclosing large spaces. The Indian commemorative monument takes the form of large hemispherical mounds called stupas, like the one built from the 3 rd century BC to the 1 st century AD, during Buddhist ascendancy, at Sanchi, near Bhopal in central India. In the early period of monastery and temple building, shrines were sculpted out of the solid rock of cliffs.

At sites such as Ellora and Ajanta, northeast of Bombay, are great series of these artificial caves carved over many centuries. As the art of temple building developed, construction by subtraction gave way to the more conventional method of adding stones to form a structure, always, however, with more concern for sculptural mass than for enclosed volume. Hindu temples are found throughout India, especially in the south and east, which were less dominated by the Mughal rulers. Jainism, still a very successful cult, has its own temple tradition and continues to build on it. See Indian Art and Architecture. In Southeast Asia a Buddhist temple is called a wat.

The most famous of these, and perhaps also the largest known, is Angkor Wat in central Cambodia, built in the early 12 th century under the long-dominant Khmer dynasty. A richly sculptured stone complex, it rises 61 m (200 ft) and is approached by a ceremonial bridge 183 m (600 ft) long that spans the surrounding moat. Buddhist architectural traditions, sometimes coming via China, are strongly evident in Myanmar (formerly known as Burma), Thailand, Malaysia, Java, and Sri Lanka. The rich temples and shrines of the Royal Palace compound in Bangkok are less than 200 years old, testifying to that culture's continuing vitality. The cultures of China and Japan have shared many features, but each has used them according to its national temperament. The resultant architectures are quite different from each other in both form and purpose.

China has a traditional reverence toward ancestors; the stable and hierarchical life of the Chinese extended family is proverbial. It is reflected in the formality of the Chinese house, built in rectangular form, preferably at the northern end of a walled courtyard entered from the south, with auxiliary elements disposed in a symmetrical fashion on either side of the north-south axis. This pattern was the point of departure for more lavish programs for mansions, monasteries, palaces, and, eventually, whole cities. The city of Beijing took form over a very long time, under various rulers.

Two contiguous rectangles, the Inner City and the newer Outer City, each embrace several square kilometers. The Inner City contains the Imperial City, which in turn contains the Forbidden City, which sheltered the imperial court and the imperial family. The entire development adheres to symmetry along a strong north-south avenue-the apotheosis, on a grand urban scale, of the Chinese house. Stone, brick, tile, and timber are available in both China and Japan. The most characteristic architectural forms in both countries are based on timber framing. In China, the wooden post carried on its top an openwork timber structure, a kind of inverted pyramid formed of layers of horizontal beams connected and supported by brackets and short posts to support the rafters and beams of a steep and heavy tile roof.

The eaves extended well beyond column lines on cantilevers. The resulting archetype is rectangular in plan, usually one story high, with a prominent roof. See Chinese Art and Architecture. The Japanese house developed differently. The Japanese express a deep poetic response to nature, and their houses are more concerned with achieving a satisfying relationship with earth, water, rocks, and trees than with establishing a social order. This approach is epitomized in the Katsura Detached Palace (1 st half of the 17 th century), designed and built by a master of the tea ceremony.

Its constructions ramble in a seemingly casual way, but in reality constitute a carefully considered sequence always integrated with vistas to or from outdoor features. Japan had already perfected timber prototypes early in its history. The Ise Shrine, on the coast southwest of Tokyo, dates from the 5 th or 6 th century; it is scrupulously rebuilt every 20 years. Its principal building, within a rectangular compound containing auxiliary structures, is a timber treasure house elevated on wooden posts buried in the ground and crowned by a massive roof of thatch. Lacking both bracketing and trussing, the ridge is supported by a beam or ridgepole held up by fat posts at the middle of each gabled end; the forked rafters, joining atop the ridgepole, exert no outward thrust. This tiny but beautifully proportioned and crafted monument is an excellent example of the understated subtlety of the art of Japan.

See Japanese Art and Architecture. The nomadic North American tribes left little permanent building, but the Pueblos of Sonora, Mexico, and of Arizona and New Mexico did build in stone and adobe. These cultures were already in decline by AD 1300; a number of impressive cliff dwellings and other villages remain as significant monuments. See Native Americans. The Spanish conquistador Here Cort's encountered the Aztecs in 1519 and within two years had destroyed their capital city, Tenochtitln, where Mexico City now stands. But he passed over the nearby center of the older Teotihuacn culture (100 BC-AD 700), which has now been extensively restored and excavated.

Teotihuacn contains two immense pyramids-of the sun and of the moon-that recall those of Egypt. They are arranged, along with other monuments and plazas, on a north-south axis at least 3 km (2 mi) in length, and the complex is embedded in what was a vast city, laid out accurately in blocks. Monte All, near Oaxaca de June, was the center of the Zapotec culture that flourished about the same time. Its imposing stone structures are set around a spacious plaza created by leveling the top of a mountain.

The Mayan civilization had existed for 2700 years when first confronted by the Spanish in the 17 th century, but its greatest building periods fall within the 4 th to the 11 th century. The Maya occupied every part of the Yucatan Peninsula, the principal sites, in roughly the order of their development, being Can (Honduras), Tikal (Guatemala), Palenque, Uxmal, Chicken Itz, and Tulum (Mexico). The important ceremonial monuments found in these centers are of stone; although the enclosure of space has more emphasis than in other pre-Columbian cultures, the Mayans never mastered the true vault. Nevertheless, they created impressive structures through extensive earth moving and bold architectural sculpture either integral with the stone or as added stucco ornamentation. The so-called Governors' Palace at Uxmal, sited on a great artificial terrace, is a long, horizontal building, the proportions and ornamentation of which suggest the eye and hand of a master designer. The Incas' thriving empire was centered high in the Andes of east-central Peru at Cuzco, which flourished from about 1200 to 1533, with other cities at nearby Sacsahuaman and Machu Picchu.

Inca architecture lacks the sculptural genius of the Maya, but the masonry craftsmanship is unexcelled; enormous pieces of stone were transported over mountain terrain and fitted together with precision, in what is called cyclopean masonry. See Pre. Columbian Art and Architecture. The building systems and forms of ancient Greece and Rome are called classical architecture.

Greek contributions in architecture, as in so much else, defy summarization. The architecture of the Roman Empire has pervaded Western architecture for more than two millennia. The architecture that developed on mainland Greece (Helladic) and in the basin of the Aegean Sea (Minoan) belongs to the Greek cultures that preceded the arrival in about 1000 BC of the Ionians and the Dorians. The Minoan culture (3000 - 1200 BC) flourished on the island of Crete; its principal site is the multi chambered Palace of Minos at Knossos, near present-day Irklion.

On the Pelopnnisos near Argos are the fortress-palaces of Mycenae and Tiryns, and in Asia Minor the city of Troy-all of them excavated by the German archaeologist Heinrich Schliemann in the last quarter of the 19 th century. Mycenae and Tiryns are believed to represent the Achaean culture, the subject of Homer's epic Iliad and Odyssey. See Aegean Civilization. The Greek temple emerged as the archetypal shrine of all time.

Unlike the Egyptians, the Greeks put their walls inside to protect the cella and their columns on the outside, where they could articulate exterior space. Perhaps for the first time, the overriding concern is for the building seen as a beautiful object externally, while at the same time containing precious and sacred inner space. Greek architects have been praised for not crushing the viewer with over monumentality; yet they found it appropriate to build temples on basically the same theme ranging in size from the tiny Temple of Nike Apteros (427 - 424 BC) of about 6 by 9 m (about 20 by 30 ft) on the Athens Acropolis to the gigantic Temple of Zeus (circa 500 BC) at Agrigento in Sicily, which covered more than 1 hectare (more than 2 acres). The Greeks seldom arranged their monuments hierarchically along an axis, preferring to site their temples to be seen from several viewpoints in order to display the relation of ends to sides. In successive efforts during many centuries the Greeks modified their earlier models. Concern for the profile of the building in space spurred designers toward perfection in the articulation of parts, and these parts became intellectualized as stylobate, base, shaft, capital, architrave, frieze, cornice, and pediment, each representing metaphorically its structural purpose.

Two orders developed more or less concurrently. The Doric order predominated on the mainland and in the western colonies. The acknowledged Doric masterpiece is the Parthenon (448 - 432 BC) crowning the Athens Acropolis (see Parthenon). The Ionic order originated in the cities on the islands and coasts of Asia Minor, which were more exposed to Asian and Egyptian influences; it featured capitals with spiral volutes, a more slender shaft with quite different fluting, and an elaborate and curvilinear base.

Most of the early examples are gone, but Ionic was used inside the Propylaea (begun 437 BC) and in the Erechtheum (begun 421 BC), both on the Athens Acropolis. The Corinthian order, a later development, introduced Ionic capitals elaborated with acanthus leaves. It has the advantage of facing equally in four directions and is therefore more adaptable than Ionic for corners. City planning was stimulated by the need to rebuild Dorian cities after the end (466 BC) of the Persian Wars and again by the challenge of new cities established (beginning 333 BC) by Alexander the Great.

The plan of Miletus in Asia Minor is an early example of the gridiron block, and it provides a prototype for the disposition of the central public areas, with the significant municipal buildings related to the major civic open spaces. A typical Greek agora included a temple, a council house (bouleuterion), a theater, and gymnasiums, as well as porticoes giving shape to the edges of the open space. Greek domestic architecture transformed the Mycenaean megaron (hearth room) into the house with rooms disposed about a small open court, or atrium, a theme later elaborated in Italy, Spain, and North Africa. See Greek Art and Architecture; House. Roman architecture continued the development now referred to as classical, but with quite different results. Unlike the tenuously allied Greek city-states, Rome became a powerful, well-organized empire that planted its constructions throughout the Mediterranean world, northward into Britain, and eastward into Asia Minor.

Romans built great engineering works-roads, canals, bridges, and aqueducts. Their masonry was more varied; they used bricks and concrete freely, as well as stone, marble, and mosaic. Use of the arch and vault introduced curved forms; curved walls produced a semicircular space, or apse, for terminating an axis. Cylindrical and spherical spaces became elements of design, well suited to the grandiose rooms appropriate to the Roman imperial scale. Barrel or tunnel vaults are inherently limited in span, and they exert lateral thrust.

Two Roman inventions of enormous importance overcame this. First was the dome, inherently more stable than the barrel vault because it is doubly curved, but also limited because it thrusts outward circumferential ly. It was possible for Hadrian to rebuild (AD 118 - 28) the Pantheon in Rome with a dome 43 m (142 ft) above the floor, but only by encircling it with a massive hollow ring wall 6 m (20 ft) thick that encloses eight segments of curved units. Thus, a dome provides for a one-room building but cannot easily be combined with other domes to make a larger space.

The second important invention was the groin vault, formed by the intersection of two identical barrel vaults over a square plan. They intersect along ellipses that go diagonally to the corners of the square. Because the curvature is in more than one direction, each barrel tends to reinforce the other. The great advantage of the groin vault is that it can be placed on four piers (built to receive 45 thrust), leaving the sides of the square for windows or for continuity with adjoining spaces. In the great Roman there (baths) and basilicas (law courts and markets), rows of square groin-vaulted bays (or units) provided vast rooms lighted by clerestory windows high on the long sides under the vaults. The Romans introduced the commemorative or triumphal arch and the colosseum or stadium.

They further developed the Greek theater and the Greek house; many excellent examples of houses were unearthed in the excavations of Pompeii and Herculaneum, towns that were buried in the violent eruption of Mount Vesuvius in AD 79. The Roman genius for grandiose urban design is seen in the plan of Rome, where each emperor left a new forum, complete with basilica, temple, and other features. Their plans are axially organized, but with greater complexity than heretofore seen. The most remarkable among the great complexes is Hadrian's Villa (AD 125 - 32) near Tivoli, which abounds in richly inventive plan forms.

The Greek orders (Doric, Ionic, Corinthian) were widely adopted and further elaborated. But the Romans ultimately trivialized them by applying them indiscriminately, usually in the form of engaged columns or pilasters with accompanying cornices, to both interior and exterior walls as a form of ornamentation. They lost in the process the orders' capacity to evoke a sense of the loads being sustained in post-and-lintel construction. See Roman Art and Architecture. Two major architectural developments were initiated by historic religious events. The first occurred in 312, when the Roman emperor Constantine the Great conferred recognition on Christianity, which led to the development of Christian architecture.

The second, the promulgation of Islam in about 610 by the Prophet Muhammad, spawned Islamic architecture. Constantine the Great's removal in 330 of the imperial capital to Byzantium, which became Constantinople (modern Istanbul), separated the Christian church into East and West and set in motion two divergent architectural developments-Early Christian and Byzantine-each taking as its point of departure a different Roman prototype. The term Early Christian is given to the basilican architecture of the church prior to the re introduction of vaulting about the year 1000. The surviving churches in Rome that most clearly evoke the Early Christian character are San Clemente (with its 4 th-century choir furnishings), Sant' Agree Fuori le Mura (rebuilt 630 and later), and Santa Sabina (422 - 32).

While Byzantine architecture developed on the concept called the central church, assembled around a central dome like the Pantheon, the Western or Roman church-more concerned with congregational participation in the Mass-preferred the Roman basilica. Early models resembled large barns, with stone walls and timber roofs. The central part (nave) of this rectangular structure was supported on columns opening toward single or double flanking aisles of lower height. The difference in roof height permitted high windows, called clerestory windows, in the nave walls; at the end of the nave, opposite the entrance, was placed the altar, backed by a large apse (also borrowed from Rome), in which the officiating clergy were seated. The Eastern emperor Justinian I was in control of Ravenna during his reign (527 - 65). Some of the constructions there can be considered Byzantine, as they featured mosaic mural compositions in Byzantine style.

Two of Ravenna's great churches, however-Sant' Apollinare Nuovo (circa 520) and Sant' Apollinare in Classe (circa 530 - 49) -are basilican in plan. See Early Christian Art and Architecture. Byzantine architecture has its early prototypes in San Vitale (526 - 47) in Ravenna and in Saint Sergius and Saint Bacchus (527) in Constantinople, both domed churches on an octagonal plan with surrounding aisles. But it was Justinian's great church at Constantinople, Asia Sophia, or the Church of the Holy Wisdom (532 - 37), that demonstrated how to place a vast dome over a square plan. The solution was to place the dome on pendentive's, or spherical triangles, that make a circle out of the square by rounding its corners.

The pendentive can be understood by visualizing its geometry. A square drawn on the ground has two circles, one circumscribed around it, the other inscribed within it. A he...


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