RenaissanceThe Renaissance (UKrᵻˈneɪsəns , USˈrɛnəsɑːns ) is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas and achievements of classical antiquity. It occurred after the Crisis of the Late Middle Ages and was associated with great social change. In addition to the standard periodization, proponents of a "long Renaissance" may put its beginning in the 14th century and its end in the 17th century.
Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
Italian RenaissanceThe Italian Renaissance (Rinascimento rinaʃʃiˈmento) was a period in Italian history covering the 15th and 16th centuries. The period is known for the initial development of the broader Renaissance culture that spread across Western Europe and marked the transition from the Middle Ages to modernity. Proponents of a "long Renaissance" argue that it started around the year 1300 and lasted until about 1600. In some fields, a Proto-Renaissance, beginning around 1250, is typically accepted.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Perspective (graphical)Linear or point-projection perspective () is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper.
Renaissance humanismRenaissance humanism was a worldview centered on the nature and importance of humanity, that emerged from the study of Classical antiquity. This first began in Italy and then spread across Western Europe in the 14th, 15th, and 16th centuries. During the period, the term humanist (umanista) referred to teachers and students of the humanities, known as the studia humanitatis, which included the study of Latin and Ancient Greek literatures, grammar, rhetoric, history, poetry, and moral philosophy.
Renaissance artRenaissance art (1350 – 1620 AD) is the painting, sculpture, and decorative arts of the period of European history known as the Renaissance, which emerged as a distinct style in Italy in about AD 1400, in parallel with developments which occurred in philosophy, literature, music, science, and technology. Renaissance art took as its foundation the art of Classical antiquity, perceived as the noblest of ancient traditions, but transformed that tradition by absorbing recent developments in the art of Northern Europe and by applying contemporary scientific knowledge.
GeometryGeometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
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.
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.
English RenaissanceThe English Renaissance was a cultural and artistic movement in England during the late 15th, 16th and early 17th centuries. It is associated with the pan-European Renaissance that is usually regarded as beginning in Italy in the late 14th century. As in most of the rest of northern Europe, England saw little of these developments until more than a century later within the Northern Renaissance. Renaissance style and ideas were slow to penetrate England, and the Elizabethan era in the second half of the 16th century is usually regarded as the height of the English Renaissance.
Duality (projective geometry)In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language () and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration.
Non-Euclidean geometryIn mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Renaissance literatureRenaissance literature refers to European literature which was influenced by the intellectual and cultural tendencies associated with the Renaissance. The literature of the Renaissance was written within the general movement of the Renaissance, which arose in 14th-century Italy and continued until the mid-17th century in England while being diffused into the rest of the western world. It is characterized by the adoption of a humanist philosophy and the recovery of the classical Antiquity.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Renaissance architectureRenaissance architecture is the European architecture of the period between the early 15th and early 16th centuries in different regions, demonstrating a conscious revival and development of certain elements of ancient Greek and Roman thought and material culture. Stylistically, Renaissance architecture followed Gothic architecture and was succeeded by Baroque architecture. Developed first in Florence, with Filippo Brunelleschi as one of its innovators, the Renaissance style quickly spread to other Italian cities.
