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.
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.
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.
Renaissance in PolandThe Renaissance in Poland (Renesans, Odrodzenie; literally: the Rebirth) lasted from the late 15th to the late 16th century and is widely considered to have been the Golden Age of Polish culture. Ruled by the Jagiellonian dynasty, the Crown of the Kingdom of Poland (from 1569 part of the Polish–Lithuanian Commonwealth) actively participated in the broad European Renaissance. The multinational Polish state experienced a period of cultural growth thanks in part to a century without major wars, aside from conflicts in the sparsely-populated eastern and southern borderlands.
Parametric modelIn statistics, a parametric model or parametric family or finite-dimensional model is a particular class of statistical models. Specifically, a parametric model is a family of probability distributions that has a finite number of parameters. A statistical model is a collection of probability distributions on some sample space. We assume that the collection, P, is indexed by some set Θ. The set Θ is called the parameter set or, more commonly, the parameter space.
Projective spaceIn mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines. This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs.
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.
Parametric statisticsParametric statistics is a branch of statistics which assumes that sample data comes from a population that can be adequately modeled by a probability distribution that has a fixed set of parameters. Conversely a non-parametric model does not assume an explicit (finite-parametric) mathematical form for the distribution when modeling the data. However, it may make some assumptions about that distribution, such as continuity or symmetry. Most well-known statistical methods are parametric.
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.
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.
Nonparametric statisticsNonparametric statistics is the type of statistics that is not restricted by assumptions concerning the nature of the population from which a sample is drawn. This is opposed to parametric statistics, for which a problem is restricted a priori by assumptions concerning the specific distribution of the population (such as the normal distribution) and parameters (such the mean or variance).
High RenaissanceIn art history, the High Renaissance was a short period of the most exceptional artistic production in the Italian states, particularly Rome, capital of the Papal States, and in Florence, during the Italian Renaissance. Most art historians state that the High Renaissance started around 1495 or 1500 and ended in 1520 with the death of Raphael, although some say the High Renaissance ended about 1525, or in 1527 with the Sack of Rome by the army of Charles V, Holy Roman Emperor, or about 1530.
Correlation (projective geometry)In projective geometry, a correlation is a transformation of a d-dimensional projective space that maps subspaces of dimension k to subspaces of dimension d − k − 1, reversing inclusion and preserving incidence. Correlations are also called reciprocities or reciprocal transformations. In the real projective plane, points and lines are dual to each other. As expressed by Coxeter, A correlation is a point-to-line and a line-to-point transformation that preserves the relation of incidence in accordance with the principle of duality.
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
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.
Projective harmonic conjugateIn projective geometry, the harmonic conjugate point of a point on the real projective line with respect to two other points is defined by the following construction: Given three collinear points A, B, C, let L be a point not lying on their join and let any line through C meet LA, LB at M, N respectively. If AN and BM meet at K, and LK meets AB at D, then D is called the harmonic conjugate of C with respect to A and B. The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N.
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.
Global Positioning SystemThe Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radio navigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite systems (GNSS) that provides geolocation and time information to a GPS receiver anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites.
