Mathematics and architecture have always enjoyed a close association with each other, not only in the sense that the latter is informed by the former, but also in that both share the search for order and beauty, the former in nature and the latter in buildings. Mathematics is indispensable to the understanding of structural concepts and calculations. It is also employed as visual ordering element or as a means to achieve harmony with the universe. Here geometry becomes the guiding principle. Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. ...

Golden rectangle

In Greek architecture, the Golden mean or the Golden rectangle served as a canon for planning. However, its use was intuitive. The rational construction of the Golden mean has been taken only in the 20th century. This corresponds to a proportion of 1: 1.618, considered in Western architectural theory to be very pleasing. This number is also known as Phi. In Islamic architecture, a proportion of 1: √2 was often used—the plan would be a square and the elevation would be obtained by projecting from the diagonal of the plan. The dimensions of the various horizontal components of the elevation such as mouldings and cornices too were obtained from the diagonals of the various projections and recesses in plan. This is a simple image of the golden rectangle, created by myself. ... This is a simple image of the golden rectangle, created by myself. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... The large rectangle BA is a golden rectangle. ... The term Western world or the West can have multiple meanings depending on its context. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Islamic architecture is the entire range of architecture that has evolved within Muslim culture in the course of the history of Islam. ...

The optical illusions of the Parthenon at the Acropolis, Athens, could not have been done without a thorough knowledge of geometry. The Parthenon seen from the hill of the Pnyx to the west The Parthenon (Greek: Παρθενώνας) is the best-known surviving building of Ancient Greece and is regarded as one of the worlds greatest cultural monuments. ... Acropolis in Athens. ... Athens (Greek: Αθήνα Athína IPA ) is the capital of Greece and one of the most famous cities in the world. ...

Ancient architecture such as that of the Egyptians and Indians employed planning principles and proportions that rooted the buildings to the cosmos, considering the movements of sun, stars, and other heavenly bodies. Vaastu Shastra, the ancient Indian canons of architecture and town planning employs mathematical drawings called mandalas. Extremely complex calculations are used to arrive at the dimensions of a building and its components. Some of these calculations form part of astrology and astronomy whereas others are based on considerations of aesthetics such as rhythm. Vaastu Shastra (Vaastu- physical environment and Shastra- knowledge/ text/ principles. ... Mandala (Sanskrit circle) is of Hindu origin, but is also used in Buddhist context, to refer to various tangible objects. ... Astrology refers to any of several systems, traditions or beliefs in which knowledge of the apparent positions of celestial bodies is held to be useful in understanding, interpreting, and organizing knowledge about human affairs and events on earth. ... Lunar astronomy: the large crater is Daedalus, photographed by the crew of Apollo 11 as they circled the Moon in 1969. ...

Renaissance architecture used symmetry as a guiding principle. The works of Andrea Palladio serve as good examples. Later High Renaissance or Baroque used curved and dramatically twisted shapes in as varied contexts such as rooms, columns, staircases and squares. St. Peter's Square in Rome, fronting the St. Peter's Basilica, is an approximately keyhole-shaped (albeit with non-parallel sides) exterior space bounded by columns giving a very dynamic visual experience. The Renaissance was a social, cultural and economic revolution which began a period of scientific revolution, religious reform, artistic and architectural development, and philosophical openness, and marks the beginning of modern European history. ... Square with symmetry group D4 Symmetry is a characteristic of geometrical shapes, equations, and other objects; we say that such an object is symmetric with respect to a given operation if this operation, when applied to the object, does not appear to change it. ... Andrea Palladio Andrea Palladio (November 30, 1508 - August 19, 1580), or Andrea di Pietro della Gondola, was an architect born in Padua, Italy. ... By Region: Italian Renaissance Northern Renaissance -French Renaissance -German Renaissance -English Renaissance The Renaissance was a great cultural movement which brought about a period of scientific revolution and artistic transformation, at the dawn of modern European history. ... Adoration, by Peter Paul Rubens: dynamic figures spiral down around a void: draperies blow: a whirl of movement lit in a shaft of light, rendered in a free bravura handling of paint In the arts, Baroque (or baroque) is both a period and the artistic style that dominated it. ... Berninis piazza was extended by the Via della Conciliazione, Mussolinis grand avenue of approach. ... City motto: Senatus Populusque Romanus – SPQR (The Senate and the People of Rome) Founded 21 April 753 BC mythical, 1st millennium BC Region Latium Mayor Walter Veltroni (Left-Wing Democrats) Area  - City Proper  1285 km² Population  - City (2004)  - Metropolitan  - Density (city proper) 2,553,873 almost 4,300,000 1. ... The Basilica of Saint Peter from Castel SantAngelo. ...

The term Cartesian planning given to the planning of cities using a grid plan, shows the close association between architecture and geometry. Ancient Greek cities such as Olynthus had such a pattern superimposed on rugged terrain giving rise to dramatic visual qualities, though proving difficult to negotiate heights. Modern town planning used the grid pattern extensively, and according to some, resulting in monotony and traffic problems. Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... A simple grid plan road map (Windermere, Florida). ... Olynthus, an ancient city of Chalcidice, situated in a fertile plain at the head of the Gulf of Torone, near the neck of the peninsula of Pallene, at some little distance from the sea, and about 60 stadia (7 or 8 miles) from Potidaea. ...

The beginning of the twentieth century saw the heightened use of Euclidean or Cartesian rectilinear geometry in Modern Architecture. In the De Stijl movement specifically,the horizontal and the vertical were seen as constituting the universal. The architectural form therefore is constituted from the juxtaposition of these two directional tendencies, employing elements such as roof planes,wall planes and balconies, either sliding past or intersecting each other. The Rietveld Schröder House by Gerrit Rietveld is a good example of this approach. (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s As a means of recording the passage of time, the 20th century was that century which lasted from 1901–2000 in the sense of the Gregorian calendar (1900–1999 in the... In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... Modern architecture is a broad term given to a number of building styles with similar characteristics, primarily the simplification of form and the elimination of ornament, that first arose around 1900. ... Composition with Red, Yellow and Blue 1921. ... The Rietveld Schröder House was built in 1924 by Dutch architect Gerrit Rietveld for Mrs. ... Red and Blue chair Lamp, designed by Rietveld Rietveld-Schröder house Gerrit Rietveld (Utrecht June 24, 1888 – Utrecht June 26, 1964), was a Dutch designer, architect and cabinet maker. ...

Virupaksha Temple, Hampi, India

The most recent movement-Deconstructivism-employs non-Euclidean geometry to achieve its complex objectives resulting in a chaotic order. Non-parallel walls, superimposed grids and complex 2-D surfaces are some external manifestations of this approach which is exemplified by the works of Peter Eisenman, Zaha Hadid, and Frank Gehry. Topology has been a fascinating influence. Hampi- Virupaksha Temple Photograph taken by me (KRS) in December 2003 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Hampi- Virupaksha Temple Photograph taken by me (KRS) in December 2003 File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... The aluminium clad east face of Daniel Libeskinds Imperial War Museum North. ... Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Peter Eisenman (born August 11, 1932 in Newark, New Jersey) is one of the foremost practitioners of deconstructivism in American architecture. ... Zaha Hadid (Arabic: زها حديد) (born October 31, 1950) is a notable British deconstructivist architect. ... Gehrys most famous work, the Guggenheim Museum in Bilbao, Spain Frank Owen Gehry, CC (born Ephraim Goldberg, February 28, 1929) is an architect known for his sculptural approach to building design. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ...

In recent times, the concept of fractals has been used to analyse many historical or interesting buildings and demonstrate that such buildings have universal appeal and are visually satisfying because they are able to provide the viewer a sense of scale at different levels/ distances of viewing. Fractals have been used to study Hindu temples where the part and the whole have the same character. A fractal is a geometric object which can be divided into parts, each of which is similar to the original object. ... A Hindu (archaic Hindoo), as per modern definition is an adherent of philosophies and scriptures of Hinduism, the predominant religious, philosophical and cultural system of the Indian subcontinent and the island of Bali. ...

As is apparent, architecture has always tried to achieve ends that not only relate to function, but also to aesthetics, philosophy and meaning. And in many a case, the means has been the beauty and structure of mathematics.

See also

• Vitruvian Man

The Vitruvian Man is a famous drawing with accompanying notes by Leonardo da Vinci made around the year 1490 in one of his journals. ...

External links

• Nexusjournal
• Isama.org
• Architectural history topics
• http://www.math.nus.edu.sg/aslaksen/teaching/math-art-arch.shtml
• http://www.dartmouth.edu/~matc/math5.geometry/unit1/INTRO.html

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