An order in architecture is a certain assemblage of parts subject to uniform established proportions, regulated by the office that each part has to perform. Coming down to the present from Ancient Greek and Ancient Roman civilization, the architectural orders are the styles of classical architecture, each distinguished by its proportions and characteristic profiles and details, and most readily recognizable by the type of column employed. The three orders of architecture—the Doric, Ionic, and Corinthian—originated in Greece. To these the Romans added, in practice if not in name, the Tuscan, which they made simpler than Doric, and the Composite, which was more ornamental than the Corinthian. The architectural order of a classical building is akin to the mode or key of classical music; the grammar or rhetoric of a written composition. It is established by certain modules like the intervals of music, and it raises certain expectations in an audience attuned to its language.
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities and with ,
Vitruvius was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled De architectura. He originated the idea that all buildings should have three attributes: firmitas, utilitas, and venustas. These principles were later widely adopted in Roman architecture. His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing of the Vitruvian Man by Leonardo da Vinci.
The Corinthian order is the last developed of the three principal classical orders of Ancient Greek architecture and Roman architecture. The other two are the Doric order which was the earliest, followed by the Ionic order. In Ancient Greek architecture, the Corinthian order follows the Ionic in almost all respects other than the capitals of the columns.
The Doric order was one of the three orders of ancient Greek and later Roman architecture; the other two canonical orders were the Ionic and the Corinthian. The Doric is most easily recognized by the simple circular capitals at the top of columns. Originating in the western Doric region of Greece, it is the earliest and, in its essence, the simplest of the orders, though still with complex details in the entablature above.
Polykleitos was an ancient Greek sculptor in bronze of the 5th century BCE. Alongside the Athenian sculptors Pheidias, Myron and Praxiteles, he is considered one of the most important sculptors of classical antiquity. The 4th century BCE catalogue attributed to Xenocrates, which was Pliny's guide in matters of art, ranked him between Pheidias and Myron. He is particularly known for his lost treatise, the Canon of Polykleitos, setting out his mathematical basis of an idealised male body shape.
Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings.
The Vitruvian Man is a drawing by the Italian Renaissance artist and scientist Leonardo da Vinci, dated to c. 1490. Inspired by the writings by the ancient Roman architect Vitruvius, the drawing depicts a nude man in two superimposed positions with his arms and legs apart and inscribed in both a circle and square. Described by the art historian Carmen C. Bambach as "justly ranked among the all-time iconic images of Western civilization," the work is a unique synthesis of artistic and scientific ideals and often considered an archetypal representation of the High Renaissance.
Palladian architecture is a European architectural style derived from the work of the Venetian architect Andrea Palladio (1508–1580). What is today recognised as Palladian architecture evolved from his concepts of symmetry, perspective and the principles of formal classical architecture from ancient Greek and Roman traditions. In the 17th and 18th centuries, Palladio's interpretation of this classical architecture developed into the style known as Palladianism.
Interest in Hermogenes of Priene, the Hellenistic architect of a temple of Artemis Leukophryene (Artemision) at Magnesia in Lydia, an Ionian colony on the banks of the Maeander river in Anatolia, has been sparked by references to his esthetic made by the 1st-century Roman architect Vitruvius.
The Modulor is an anthropometric scale of proportions devised by the Swiss-born French architect Le Corbusier (1887–1965).
A module is a term that was in use among Roman architects, corresponding to the semidiameter of the column at its base. The term was first set forth by Vitruvius, and was employed by architects in the Italian Renaissance to determine the relative proportions of the various parts of the Classical orders. The module was divided by the 16th century theorists into thirty parts, called minutes, allowing for much greater precision than was thought necessary by Vitruvius, whose subdivision was usually six parts.
While there is significant variation in anatomical proportions between people, certain body proportions have become canonical in figurative art. The study of body proportions, as part of the study of artistic anatomy, explores the relation of the elements of the human body to each other and to the whole. These ratios are used in depictions of the human figure and may become part of an artistic canon of body proportion within a culture. Academic art of the nineteenth century demanded close adherence to these reference metrics and some artists in the early twentieth century rejected those constraints and consciously mutated them.
The Doryphoros of Polykleitos is one of the best known Greek sculptures of Classical antiquity, depicting a solidly built, muscular, standing warrior, originally bearing a spear balanced on his left shoulder. Rendered somewhat above life-size, the lost bronze original of the work would have been cast circa 440 BC, but it is today known only from later marble copies. The work nonetheless forms an important early example of both Classical Greek contrapposto and classical realism; as such, the iconic Doryphoros proved highly influential elsewhere in ancient art.
De architectura is a treatise on architecture written by the Roman architect and military engineer Marcus Vitruvius Pollio and dedicated to his patron, the emperor Caesar Augustus, as a guide for building projects. As the only treatise on architecture to survive from antiquity, it has been regarded since the Renaissance as the first book on architectural theory, as well as a major source on the canon of classical architecture. It contains a variety of information on Greek and Roman buildings, as well as prescriptions for the planning and design of military camps, cities, and structures both large and small. Since Vitruvius published before the development of cross vaulting, domes, concrete, and other innovations associated with Imperial Roman architecture, his ten books give no information on these hallmarks of Roman building design and technology.
An artistic canon of body proportions, in the sphere of visual arts, is a formally codified set of criteria deemed mandatory for a particular artistic style of figurative art. The word canon was first used for this type of rule in Classical Greece, where it set a reference standard for body proportions, so as to produce a harmoniously formed figure appropriate to depict gods or kings. Other art styles have similar rules that apply particularly to the representation of royal or divine personalities.
A dynamic rectangle is a right-angled, four-sided figure with dynamic symmetry which, in this case, means that aspect ratio is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge's books. These dynamic rectangles begin with a square, which is extended to form the desired figure, which can be the golden rectangle, the 2:3 rectangle, the double square (1:2), or a root rectangle.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Mark Roland Wilson Jones is an architect and prominent architectural historian whose research covers varied aspects of classical architecture while concentrating on that of ancient Greece and Rome. He is best known for his work on the design of monumental buildings, especially the Pantheon, Rome, and that of the Architectural orders in both Roman and Greek contexts. He is the author of two important books of classical architecture, and is currently a senior lecturer at the University of Bath.
