Complex geometryIn mathematics, complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions such as holomorphic vector bundles and coherent sheaves. Application of transcendental methods to algebraic geometry falls in this category, together with more geometric aspects of complex analysis.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Riemannian geometryRiemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). This gives, in particular, local notions of angle, length of curves, surface area and volume. From those, some other global quantities can be derived by integrating local contributions.
Medieval artThe medieval art of the Western world covers a vast scope of time and place, with over 1000 years of art in Europe, and at certain periods in Western Asia and Northern Africa. It includes major art movements and periods, national and regional art, genres, revivals, the artists' crafts, and the artists themselves. Art historians attempt to classify medieval art into major periods and styles, often with some difficulty.
Renaissance Revival architectureRenaissance Revival architecture (sometimes referred to as "Neo-Renaissance") is a group of 19th century architectural revival styles which were neither Greek Revival nor Gothic Revival but which instead drew inspiration from a wide range of classicizing Italian modes. Under the broad designation Renaissance architecture nineteenth-century architects and critics went beyond the architectural style which began in Florence and Central Italy in the early 15th century as an expression of Renaissance humanism; they also included styles that can be identified as Mannerist or Baroque.
Gothic architectureGothic architecture is an architectural style that was prevalent in Europe from the late 12th to the 16th century, during the High and Late Middle Ages, surviving into the 17th and 18th centuries in some areas. It evolved from Romanesque architecture and was succeeded by Renaissance architecture. It originated in the Île-de-France and Picardy regions of northern France. The style at the time was sometimes known as opus Francigenum (French work); the term Gothic was first applied contemptuously during the later Renaissance, by those ambitious to revive the architecture of classical antiquity.
Symplectic geometrySymplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. The term "symplectic", introduced by Weyl, is a calque of "complex"; previously, the "symplectic group" had been called the "line complex group".
MuqarnasMuqarnas (مقرنص; مقرنس, or آهوپای), also known in Iberian architecture as Mocárabe, is a form of ornamented vaulting in Islamic architecture. It is the archetypal form of Islamic architecture, integral to the vernacular of Islamic buildings. It was most likely first developed in eleventh-century Iraq, though the earliest preserved examples are also found outside this region. The muqarnas structure originated from the squinch.
ArtArt is a diverse range of human activity, and resulting product, that involves creative or imaginative talent expressive of technical proficiency, beauty, emotional power, or conceptual ideas. There is no generally agreed definition of what constitutes art, and its interpretation has varied greatly throughout history and across cultures. In the Western tradition, the three classical branches of visual art are painting, sculpture, and architecture.
Conformal geometryIn mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale.
OctagonIn geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square, t{4}, which alternates two types of edges. A truncated octagon, t{8} is a hexadecagon, {16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be a truncated square. The sum of all the internal angles of any octagon is 1080°.
Regular polygonIn Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex, star or skew. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. These properties apply to all regular polygons, whether convex or star.
Islamic geometric patternsIslamic geometric patterns are one of the major forms of Islamic ornament, which tends to avoid using figurative images, as it is forbidden to create a representation of an important Islamic figure according to many holy scriptures. The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques (with which they are often combined), to form intricate and complex patterns, including a wide variety of tessellations.
Polar coordinate systemIn mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth.
Architecture of the medieval cathedrals of EnglandThe medieval cathedrals of England, which date from between approximately 1040 and 1540, are a group of twenty-six buildings that constitute a major aspect of the country's artistic heritage and are among the most significant material symbols of Christianity. Though diverse in style, they are united by a common function. As cathedrals, each of these buildings serves as central church for an administrative region (or diocese) and houses the throne of a bishop (Late Latin ecclēsia cathedrālis, from the Greek, καθέδρα).
Wood carvingWood carving is a form of woodworking by means of a cutting tool (knife) in one hand or a chisel by two hands or with one hand on a chisel and one hand on a mallet, resulting in a wooden figure or figurine, or in the sculptural ornamentation of a wooden object. The phrase may also refer to the finished product, from individual sculptures to hand-worked mouldings composing part of a tracery. The making of sculpture in wood has been extremely widely practised, but doesn't survive undamaged as well as the other main materials like stone and bronze, as it is vulnerable to decay, insect damage, and fire.
Distinctive featureIn linguistics, a distinctive feature is the most basic unit of phonological structure that distinguishes one sound from another within a language. For example, the feature [voice] distinguishes the two bilabial plosives: [p] and [b]. There are many different ways of defining and arranging features into feature systems: some deal with only one language while others are developed to apply to all languages. Distinctive features are grouped into categories according to the natural classes of segments they describe: major class features, laryngeal features, manner features, and place features.
Sistine Chapel ceilingThe Sistine Chapel ceiling (Soffitto della Cappella Sistina), painted in fresco by Michelangelo between 1508 and 1512, is a cornerstone work of High Renaissance art. The Sistine Chapel is the large papal chapel built within the Vatican between 1477 and 1480 by Pope Sixtus IV, for whom the chapel is named. The ceiling was painted at the commission of Pope Julius II. The ceiling's various painted elements form part of a larger scheme of decoration within the chapel.
ManifoldIn mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane.
Art of EuropeThe art of Europe, also known as Western art, encompasses the history of visual art in Europe. European prehistoric art started as mobile Upper Paleolithic rock and cave painting and petroglyph art and was characteristic of the period between the Paleolithic and the Iron Age. Written histories of European art often begin with the Aegean civilizations, dating from the 3rd millennium BC. However a consistent pattern of artistic development within Europe becomes clear only with Ancient Greek art, which was adopted and transformed by Rome and carried; with the Roman Empire, across much of Europe, North Africa and Western Asia.
