Description.

The common bean is a highly variable species with a long history. Bush varieties form erect bushes tall, while pole or running varieties form vines long. All varieties bear alternate, green or purple leaves, which are divided into three oval, smooth-edged leaflets, each long and wide. The white, pink, or purple flowers are about 1 cm long, and they give way to pods long and 1–1.5 cm wide. These may be green, yellow, black, or purple in color, each containing 4–6 beans. The beans are smooth, plump, kidney-shaped, up to 1.5 cm long, range widely in color, and are often mottled in two or more colors. Raw or undercooked beans contain a toxic protein called phytohaemagglutinin.

Dry beans.

Similar to other beans, the common bean is high in starch, protein, and dietary fiber, and is an excellent source of iron, potassium, selenium, thiamine, vitamin B, and folate.  Dry beans will keep indefinitely if stored in a cool, dry place, but as time passes, their nutritive value and flavor degrade and cooking times lengthen. Dried beans are almost always cooked by boiling, often after being soaked in water for several hours. While the soaking is not strictly necessary, it shortens cooking time and results in more evenly textured beans. In addition, soaking beans removes 5 to 10% of the gas-producing sugars that can cause flatulence for some people. The methods include simple overnight soaking and the power soak method in which beans are boiled for three minutes and then set aside for 2–4 hours. Before cooking, the soaking water is drained off and discarded. Dry common beans take longer to cook than most pulses: cooking times vary from one to four hours, but are substantially reduced with pressure cooking.  In Mexico, Central America, and South America, the traditional spice used with beans is "epazote", which is also said to aid digestion. In East Asia, a type of seaweed, "kombu", is added to beans as they cook for the same purpose. Salt, sugar, and acidic foods such as tomatoes may harden uncooked beans, resulting in seasoned beans at the expense of slightly longer cooking times.  Dry beans may also be bought cooked and canned as refried beans, or whole with water, salt, and sometimes sugar.

Green beans and wax beans.

The three commonly known types of green beans are string or snap beans, which may be round or have a flat pod; stringless or French beans, which lack a tough, fibrous string running along the length of the pod; and runner beans, which belong to a separate species, "Phaseolus coccineus". Green beans may have a purple rather than green pod, which changes to green when cooked. Wax beans are "P. vulgaris" beans that have a yellow or white pod. Wax bean cultivars are commonly grown; the plants are often of the bush or dwarf form.  As the name implies, snap beans break easily when the pod is bent, giving off a distinct audible snap sound. The pods of snap beans (green, yellow and purple in colour) are harvested when they are rapidly growing, fleshy, tender (not tough and stringy), bright in colour, and the seeds are small and underdeveloped (8 to 10 days after flowering).  Compared to dry beans, green and wax beans provide less starch and protein and more vitamin A and vitamin C. Green beans and wax beans are often steamed, boiled, stir-fried, or baked in casseroles.

Shelling beans.

Shell, shelled, or shelling beans are beans removed from their pods before being cooked or dried. Common beans can be used as shell beans, but the term also refers to other species of beans whose pods are not typically eaten, such as lima beans, soybeans, peas, and fava beans. Fresh shell beans are nutritionally similar to dry beans, but are prepared more like a vegetable, often being steamed, fried, or made into soups.

Popping beans.

The "nuña" is an Andean subspecies, "P. v." subsp. "nunas" (formerly "P. vulgaris" Nuñas group), with round, multicolored seeds that resemble pigeon eggs. When cooked on high heat, the bean explodes, exposing the inner part, in the manner of popcorn and other puffed grains.

Cultivars and varieties.

Some scientists have proposed Mesoamerica as a possible origin for the common bean. Scientists disagree over whether the common bean was a product of one or multiple domestication events. Over time two diverse gene pools emerged: the Andean gene pool from Southern Peru to Northwest Argentina and the Mesoamerican gene pool between Mexico and Colombia.  Many well-known bean cultivars and varieties belong to this species, and the list below is in no way exhaustive. Both bush and running (pole) cultivars/varieties exist. The colors and shapes of pods and seeds vary over a wide range.

Production.

In 2016, world production of green beans was 23.6 million tonnes, led by China with 79% of the total (table). World dried bean production in 2016 was 26.8 million tonnes, with Myanmar, India, and Brazil as leading producers (table).

Toxicity.

The toxic compound phytohaemagglutinin, a lectin, is present in many common bean varieties, but is especially concentrated in red kidney beans. White kidney beans contain about a third as much toxin as the red variety; broad beans ("Vicia faba") contain 5 to 10% as much as red kidney beans.  Phytohaemagglutinin can be deactivated by cooking beans for ten minutes at boiling point (100 °C, 212 °F). Insufficient cooking, such as in a slow cooker at 80 °C/ 176 °F, however, is not sufficient to deactivate all toxin. To safely cook the beans, the U.S Food and Drug Administration recommends boiling for 30 minutes to ensure they reach a sufficient temperature for long enough to completely destroy the toxin. For dry beans, the FDA also recommends an initial soak of at least 5 hours in water which should then be discarded. Outbreaks of poisoning have been associated with cooking kidney beans in slow cookers.  The primary symptoms of phytohaemagglutinin poisoning are nausea, vomiting, and diarrhea. Onset is from one to three hours after consumption of improperly prepared beans, and symptoms typically resolve within a few hours. Consumption of as few as four or five raw, soaked kidney beans can cause symptoms. Canned red kidney beans, though, are safe to use immediately, as they have already been cooked.  Beans are high in purines, which are metabolized to uric acid. Uric acid is not a toxin as such, but may promote the development or exacerbation of gout. However, more recent research has questioned this association, finding that moderate intake of purine-rich foods is not associated with increased risk of gout.

Other uses.

Bean leaves have been used to trap bedbugs in houses. Microscopic hairs (trichomes) on the bean leaves entrap the insects.  From ancient times, beans were used as device in various methods of divination. Fortune-telling using beans is called favomancy.

Phaseolus vulgaris, also known as the common bean, is a herbaceous annual plant grown worldwide for its edible dry seeds or unripe fruit (both commonly called beans). The main categories of common beans, on the basis of use, are dry beans (seeds harvested at complete maturity), snap beans (tender pods with reduced fibre harvested before the seed development phase) and shell (shelled) beans (seeds harvested at physiological maturity). Its leaf is also occasionally used as a vegetable and the straw as fodder. Its botanical classification, along with other "Phaseolus" species, is as a member of the legume family Fabaceae. Like most members of this family, common beans acquire the nitrogen they require through an association with rhizobia, which are nitrogen-fixing bacteria.

Die Gartenbohne ("Phaseolus vulgaris"), auch Grüne Bohne, Schnittbohne oder österreichisch Fisole, ist eine Pflanzenart aus der Unterfamilie der Schmetterlingsblütler (Faboideae). Sie ist in Deutschland fast immer mit dem Ausdruck „Bohne“ gemeint, der sich aber auch auf viele andere Nutzpflanzenarten beziehen kann. Je nach Wuchsform wird die Art auch als Buschbohne oder Stangenbohne bezeichnet.


History.

The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying, construction, astronomy, and various crafts. The earliest known texts on geometry are the Egyptian "Rhind Papyrus" (2000–1800 BC) and "Moscow Papyrus" (c. 1890 BC), the Babylonian clay tablets such as Plimpton 322 (1900 BC). For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum. Later clay tablets (350–50 BC) demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space. These geometric procedures anticipated the Oxford Calculators, including the mean speed theorem, by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks.  In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, which is credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history. Eudoxus (408–c. 355 BC) developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures, as well as a theory of ratios that avoided the problem of incommensurable magnitudes, which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose "Elements", widely considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. Although most of the contents of the "Elements" were already known, Euclid arranged them into a single, coherent logical framework. The "Elements" was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes (c. 287–212 BC) of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave remarkably accurate approximations of Pi. He also studied the spiral bearing his name and obtained formulas for the volumes of surfaces of revolution.  Indian mathematicians also made many important contributions in geometry. The "Satapatha Brahmana" (3rd century BC) contains rules for ritual geometric constructions that are similar to the "Sulba Sutras". According to, the "Śulba Sūtras" contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians. They contain lists of Pythagorean triples, which are particular cases of Diophantine equations. In the Bakhshali manuscript, there is a handful of geometric problems (including problems about volumes of irregular solids). The Bakhshali manuscript also "employs a decimal place value system with a dot for zero." Aryabhata's "Aryabhatiya" (499) includes the computation of areas and volumes. Brahmagupta wrote his astronomical work "" in 628. Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In the latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral. Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalization of Heron's formula), as well as a complete description of rational triangles ("i.e." triangles with rational sides and rational areas).  In the Middle Ages, mathematics in medieval Islam contributed to the development of geometry, especially algebraic geometry. Al-Mahani (b. 853) conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Thābit ibn Qurra (known as Thebit in Latin) (836–901) dealt with arithmetic operations applied to ratios of geometrical quantities, and contributed to the development of analytic geometry. Omar Khayyám (1048–1131) found geometric solutions to cubic equations. The theorems of Ibn al-Haytham (Alhazen), Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals, including the Lambert quadrilateral and Saccheri quadrilateral, were early results in hyperbolic geometry, and along with their alternative postulates, such as Playfair's axiom, these works had a considerable influence on the development of non-Euclidean geometry among later European geometers, including Witelo (c. 1230–c. 1314), Gersonides (1288–1344), Alfonso, John Wallis, and Giovanni Girolamo Saccheri.  In the early 17th century, there were two important developments in geometry. The first was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665). This was a necessary precursor to the development of calculus and a precise quantitative science of physics. The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry studies properties of shapes which are unchanged under projections and sections, especially as they relate to artistic perspective.  Two developments in geometry in the 19th century changed the way it had been studied previously. These were the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss and of the formulation of symmetry as the central consideration in the Erlangen Programme of Felix Klein (which generalized the Euclidean and non-Euclidean geometries). Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis, and introducing the Riemann surface, and Henri Poincaré, the founder of algebraic topology and the geometric theory of dynamical systems. As a consequence of these major changes in the conception of geometry, the concept of "space" became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics.

Important concepts in geometry.

The following are some of the most important concepts in geometry.

Axioms.

Euclid took an abstract approach to geometry in his Elements, one of the most influential books ever written. Euclid introduced certain axioms, or postulates, expressing primary or self-evident properties of points, lines, and planes. He proceeded to rigorously deduce other properties by mathematical reasoning. The characteristic feature of Euclid's approach to geometry was its rigor, and it has come to be known as "axiomatic" or "synthetic" geometry. At the start of the 19th century, the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky (1792–1856), János Bolyai (1802–1860), Carl Friedrich Gauss (1777–1855) and others led to a revival of interest in this discipline, and in the 20th century, David Hilbert (1862–1943) employed axiomatic reasoning in an attempt to provide a modern foundation of geometry.

Points.

Points are considered fundamental objects in Euclidean geometry. They have been defined in a variety of ways, including Euclid's definition as 'that which has no part' and through the use of algebra or nested sets. In many areas of geometry, such as analytic geometry, differential geometry, and topology, all objects are considered to be built up from points. However, there has been some study of geometry without reference to points.

Lines.

Euclid described a line as "breadthless length" which "lies equally with respect to the points on itself". In modern mathematics, given the multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry, a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation, but in a more abstract setting, such as incidence geometry, a line may be an independent object, distinct from the set of points which lie on it. In differential geometry, a geodesic is a generalization of the notion of a line to curved spaces.

Planes.

A plane is a flat, two-dimensional surface that extends infinitely far. Planes are used in every area of geometry. For instance, planes can be studied as a topological surface without reference to distances or angles; it can be studied as an affine space, where collinearity and ratios can be studied but not distances; it can be studied as the complex plane using techniques of complex analysis; and so on.

Angles.

Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. In modern terms, an angle is the figure formed by two rays, called the "sides" of the angle, sharing a common endpoint, called the "vertex" of the angle. In Euclidean geometry, angles are used to study polygons and triangles, as well as forming an object of study in their own right. The study of the angles of a triangle or of angles in a unit circle forms the basis of trigonometry.  In differential geometry and calculus, the angles between plane curves or space curves or surfaces can be calculated using the derivative.

Curves.

A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves.  In topology, a curve is defined by a function from an interval of the real numbers to another space. In differential geometry, the same definition is used, but the defining function is required to be differentiable Algebraic geometry studies algebraic curves, which are defined as algebraic varieties of dimension one.

Surfaces.

A surface is a two-dimensional object, such as a sphere or paraboloid. In differential geometry and topology, surfaces are described by two-dimensional 'patches' (or neighborhoods) that are assembled by diffeomorphisms or homeomorphisms, respectively. In algebraic geometry, surfaces are described by polynomial equations.

Manifolds.

A manifold is a generalization of the concepts of curve and surface. In topology, a manifold is a topological space where every point has a neighborhood that is homeomorphic to Euclidean space. In differential geometry, a differentiable manifold is a space where each neighborhood is diffeomorphic to Euclidean space.  Manifolds are used extensively in physics, including in general relativity and string theory.

Length, area, and volume.

Length, area, and volume describe the size or extant of an object in one dimension, two dimension, and three dimensions respectively.  In Euclidean geometry and analytic geometry, the length of a line segment can often be calculated by the Pythagorean theorem.  Area and volume can be defined as fundamental quantities separate from length, or they can be described and calculated in terms of lengths in a plane or 3-dimensional space. Mathematicians have found many explicit formulas for area and formulas for volume of various geometric objects. In calculus, area and volume can be defined in terms of integrals, such as the Riemann integral or the Lebesgue integral.

Metrics and measures.

The concept of length or distance can be generalized, leading to the idea of metrics. For instance, the Euclidean metric measures the distance between points in the Euclidean plane, while the hyperbolic metric measures the distance in the hyperbolic plane. Other important examples of metrics include the Lorentz metric of special relativity and the semi-Riemannian metrics of general relativity.  In a different direction, the concepts of length, area and volume are extended by measure theory, which studies methods of assigning a size or "measure" to sets, where the measures follow rules similar to those of classical area and volume.

Congruence and similarity.

Congruence and similarity are concepts that describe when two shapes have similar characteristics. In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape. Hilbert, in his work on creating a more rigorous foundation for geometry, treated congruence as an undefined term whose properties are defined by axioms.  Congruence and similarity are generalized in transformation geometry, which studies the properties of geometric objects that are preserved by different kinds of transformations.

Compass and straightedge constructions.

Classical geometers paid special attention to constructing geometric objects that had been described in some other way. Classically, the only instruments allowed in geometric constructions are the compass and straightedge. Also, every construction had to be complete in a finite number of steps. However, some problems turned out to be difficult or impossible to solve by these means alone, and ingenious constructions using parabolas and other curves, as well as mechanical devices, were found.

Dimension.

Where the traditional geometry allowed dimensions 1 (a line), 2 (a plane) and 3 (our ambient world conceived of as three-dimensional space), mathematicians and physicists have used higher dimensions for nearly two centuries. One example of a mathematical use for higher dimensions is the configuration space of a physical system, which has a dimension equal to the system's degrees of freedom. For instance, the configuration of a screw can be described by five coordinates.  In general topology, the concept of dimension has been extended from natural numbers, to infinite dimension (Hilbert spaces, for example) and positive real numbers (in fractal geometry). In algebraic geometry, the dimension of an algebraic variety has received a number of apparently different definitions, which are all equivalent in the most common cases.

Symmetry.

The theme of symmetry in geometry is nearly as old as the science of geometry itself. Symmetric shapes such as the circle, regular polygons and platonic solids held deep significance for many ancient philosophers and were investigated in detail before the time of Euclid. Symmetric patterns occur in nature and were artistically rendered in a multitude of forms, including the graphics of da Vinci, M.C. Escher, and others. In the second half of the 19th century, the relationship between symmetry and geometry came under intense scrutiny. Felix Klein's Erlangen program proclaimed that, in a very precise sense, symmetry, expressed via the notion of a transformation group, determines what geometry "is". Symmetry in classical Euclidean geometry is represented by congruences and rigid motions, whereas in projective geometry an analogous role is played by collineations, geometric transformations that take straight lines into straight lines. However it was in the new geometries of Bolyai and Lobachevsky, Riemann, Clifford and Klein, and Sophus Lie that Klein's idea to 'define a geometry via its symmetry group' found its inspiration. Both discrete and continuous symmetries play prominent roles in geometry, the former in topology and geometric group theory, the latter in Lie theory and Riemannian geometry.  A different type of symmetry is the principle of duality in projective geometry, among other fields. This meta-phenomenon can roughly be described as follows: in any theorem, exchange "point" with "plane", "join" with "meet", "lies in" with "contains", and the result is an equally true theorem. A similar and closely related form of duality exists between a vector space and its dual space.

Contemporary geometry.

Euclidean geometry.

Euclidean geometry is geometry in its classical sense. As it models the space of the physical world, it is used in many scientific areas, such as mechanics, astronomy, crystallography, and many technical fields, such as engineering, architecture, geodesy, aerodynamics, and navigation. The mandatory educational curriculum of the majority of nations includes the study of Euclidean concepts such as points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, and analytic geometry.

Differential geometry.

Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics, econometrics, and bioinformatics, among others.  In particular, differential geometry is of importance to mathematical physics due to Albert Einstein's general relativity postulation that the universe is curved. Differential geometry can either be "intrinsic" (meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric, which determines how distances are measured near each point) or "extrinsic" (where the object under study is a part of some ambient flat Euclidean space).

Non-Euclidean geometry.

Euclidean geometry was not the only historical form of geometry studied. Spherical geometry has long been used by astronomers, astrologers, and navigators.  Immanuel Kant argued that there is only one, "absolute", geometry, which is known to be true "a priori" by an inner faculty of mind: Euclidean geometry was synthetic a priori. This view was at first somewhat challenged by thinkers such as Saccheri, then finally overturned by the revolutionary discovery of non-Euclidean geometry in the works of Bolyai, Lobachevsky, and Gauss (who never published his theory). They demonstrated that ordinary Euclidean space is only one possibility for development of geometry. A broad vision of the subject of geometry was then expressed by Riemann in his 1867 inauguration lecture "Über die Hypothesen, welche der Geometrie zu Grunde liegen" ("On the hypotheses on which geometry is based"), published only after his death. Riemann's new idea of space proved crucial in Albert Einstein's general relativity theory. Riemannian geometry, which considers very general spaces in which the notion of length is defined, is a mainstay of modern geometry.

Topology.

Topology is the field concerned with the properties of continuous mappings, and can be considered a generalization of Euclidean geometry. In practice, topology often means dealing with large-scale properties of spaces, such as connectedness and compactness.  The field of topology, which saw massive development in the 20th century, is in a technical sense a type of transformation geometry, in which transformations are homeomorphisms. This has often been expressed in the form of the saying 'topology is rubber-sheet geometry'. Subfields of topology include geometric topology, differential topology, algebraic topology and general topology.

Algebraic geometry.

The field of algebraic geometry developed from the Cartesian geometry of co-ordinates. It underwent periodic periods of growth, accompanied by the creation and study of projective geometry, birational geometry, algebraic varieties, and commutative algebra, among other topics. From the late 1950s through the mid-1970s it had undergone major foundational development, largely due to work of Jean-Pierre Serre and Alexander Grothendieck. This led to the introduction of schemes and greater emphasis on topological methods, including various cohomology theories. One of seven Millennium Prize problems, the Hodge conjecture, is a question in algebraic geometry. Wiles' proof of Fermat's Last Theorem uses advanced methods of algebraic geometry for solving a long-standing problem of number theory.  In general, algebraic geometry studies geometry through the use of concepts in commutative algebra such as multivariate polynomials. It has applications in many areas, including cryptography and string theory.

Complex geometry.

Complex geometry studies the nature of geometric structures modelled on, or arising out of, the complex plane. Complex geometry lies at the intersection of differential geometry, algebraic geometry, and analysis of several complex variables, and has found applications to string theory and mirror symmetry.  Complex geometry first appeared as a distinct area of study in the work of Bernhard Riemann in his study of Riemann surfaces. Work in the spirit of Riemann was carried out by the Italian school of algebraic geometry in the early 1900s. Contemporary treatment of complex geometry began with the work of Jean-Pierre Serre, who introduced the concept of sheaves to the subject, and illuminated the relations between complex geometry and algebraic geometry. The primary objects of study in complex geometry are complex manifolds, complex algebraic varieties, and complex analytic varieties, and holomorphic vector bundles and coherent sheaves over these spaces. Special examples of spaces studied in complex geometry include Riemann surfaces, and Calabi-Yau manifolds, and these spaces find uses in string theory. In particular, worldsheets of strings are modelled by Riemann surfaces, and superstring theory predicts that the extra 6 dimensions of 10 dimensional spacetime may be modelled by Calabi-Yau manifolds.

Discrete geometry.

Discrete geometry is a subject that has close connections with convex geometry. It is concerned mainly with questions of relative position of simple geometric objects, such as points, lines and circles. Examples include the study of sphere packings, triangulations, the Kneser-Poulsen conjecture, etc. It shares many methods and principles with combinatorics.

Computational geometry.

Computational geometry deals with algorithms and their implementations for manipulating geometrical objects. Important problems historically have included the travelling salesman problem, minimum spanning trees, hidden-line removal, and linear programming.  Although being a young area of geometry, it has many applications in computer vision, image processing, computer-aided design, medical imaging, etc.

Geometric group theory.

Geometric group theory uses large-scale geometric techniques to study finitely generated groups. It is closely connected to low-dimensional topology, such as in Grigori Perelman's proof of the Geometrization conjecture, which included the proof of the Poincaré conjecture, a Millennium Prize Problem.  Geometric group theory often revolves around the Cayley graph, which is a geometric representation of a group. Other important topics include quasi-isometries, Gromov-hyperbolic groups, and right angled Artin groups.

Convex geometry.

Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues, often using techniques of real analysis and discrete mathematics. It has close connections to convex analysis, optimization and functional analysis and important applications in number theory.  Convex geometry dates back to antiquity. Archimedes gave the first known precise definition of convexity. The isoperimetric problem, a recurring concept in convex geometry, was studied by the Greeks as well, including Zenodorus. Archimedes, Plato, Euclid, and later Kepler and Coxeter all studied convex polytopes and their properties. From the 19th century on, mathematicians have studied other areas of convex mathematics, including higher-dimensional polytopes, volume and surface area of convex bodies, Gaussian curvature, algorithms, tilings and lattices.

Applications.

Geometry has found applications in many fields, some of which are described below.

Art.

Mathematics and art are related in a variety of ways. For instance, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry.  Artists have long used concepts of proportion in design. Vitruvius developed a complicated theory of "ideal proportions" for the human figure. These concepts have been used and adapted by artists from Michelangelo to modern comic book artists.  The golden ratio is a particular proportion that has had a controversial role in art. Often claimed to be the most aesthetically pleasing ratio of lengths, it is frequently stated to be incorporated into famous works of art, though the most reliable and unambiguous examples were made deliberately by artists aware of this legend.  Tilings, or tessellations, have been used in art throughout history. Islamic art makes frequent use of tessellations, as did the art of Escher. Escher's work also made use of hyperbolic geometry.  Cézanne advanced the theory that all images can be built up from the sphere, the cone, and the cylinder. This is still used in art theory today, although the exact list of shapes varies from author to author.

Architecture.

Geometry has many applications in architecture. In fact, it has been said that geometry lies at the core of architectural design. Applications of geometry to architecture include the use of projective geometry to create forced perspective, the use of conic sections in constructing domes and similar objects, the use of tessellations, and the use of symmetry.

Physics.

The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, have served as an important source of geometric problems throughout history.  Riemannian geometry and pseudo-Riemannian geometry are used in general relativity. String theory makes use of several variants of geometry, as does quantum information theory.

Other fields of mathematics.

Calculus was strongly influenced by geometry. For instance, the introduction of coordinates by René Descartes and the concurrent developments of algebra marked a new stage for geometry, since geometric figures such as plane curves could now be represented analytically in the form of functions and equations. This played a key role in the emergence of infinitesimal calculus in the 17th century. Analytic geometry continues to be a mainstay of pre-calculus and calculus curriculum.  Another important area of application is number theory. In ancient Greece the Pythagoreans considered the role of numbers in geometry. However, the discovery of incommensurable lengths contradicted their philosophical views. Since the 19th century, geometry has been used for solving problems in number theory, for example through the geometry of numbers or, more recently, scheme theory, which is used in Wiles's proof of Fermat's Last Theorem.

Geometry (from the ; "geo-" "earth", "-metron" "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer.

Die Geometrie (, ionisch, ‚Erdmaße‘, ‚Erdmessung‘, ‚Landmessung‘) ist ein Teilgebiet der Mathematik. Einerseits versteht man unter "Geometrie" die zwei- und dreidimensionale euklidische Geometrie, die Elementargeometrie, die auch im Mathematikunterricht – früher unter dem Begriff "Raumlehre" – gelehrt wird und die sich mit Punkten, Geraden, Ebenen, Abständen, Winkeln usw. beschäftigt, sowie diejenigen Begriffsbildungen und Methoden, die im Zuge einer systematischen und mathematischen Behandlung dieses Themas entwickelt wurden.


Symbol.

The symbol can be annotated to denote various sets, with varying usage amongst different authors:, or for the positive integers, for non-negative integers, for non-zero integers. Some authors use for non-zero integers, others use it for non-negative integers, or for. Additionally, is used to denote either the set of integers modulo, i.e., a set of congruence classes of integers, or the set of -adic integers.

Algebraic properties.

Like the natural numbers, is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly,, (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring.  The following table lists some of the basic properties of addition and multiplication for any integers, and. In the language of abstract algebra, the first five properties listed above for addition say that under addition is an abelian group. It is also a cyclic group, since every non-zero integer can be written as a finite sum or. In fact, under addition is the "only" infinite cyclic group, in the sense that any infinite cyclic group is isomorphic to.  The first four properties listed above for multiplication say that under multiplication is a commutative monoid. However, not every integer has a multiplicative inverse; e.g., there is no integer such that. This means that under multiplication is not a group.  All the rules from the above property table, except for the last, taken together say that together with addition and multiplication is a commutative ring with unity. It is the prototype of all objects of such algebraic structure. Only those equalities of expressions are true in for all values of variables, which are true in any unital commutative ring. Certain non-zero integers map to zero in certain rings.  The lack of zero divisors in the integers (last property in the table) means that the commutative ring is an integral domain.  The lack of multiplicative inverses, which is equivalent to the fact that is not closed under division, means that is "not" a field. The smallest field containing the integers as a subring is the field of rational numbers. The process of constructing the rationals from the integers can be mimicked to form the field of fractions of any integral domain. And back, starting from an algebraic number field (an extension of rational numbers), its ring of integers can be extracted, which includes as its subring.  Although ordinary division is not defined on, the division "with remainder" is defined on them. It is called Euclidean division and possesses the following important property: that is, given two integers and with, there exist unique integers and such that and, where denotes the absolute value of. The integer is called the "quotient" and is called the "remainder" of the division of by. The Euclidean algorithm for computing greatest common divisors works by a sequence of Euclidean divisions.  Again, in the language of abstract algebra, the above says that Z is a Euclidean domain. This implies that is a principal ideal domain and any positive integer can be written as the products of primes in an essentially unique way. This is the fundamental theorem of arithmetic.

Order-theoretic properties.

is a totally ordered set without upper or lower bound. The ordering of is given by:  An integer is "positive" if it is greater than zero and "negative" if it is less than zero. Zero is defined as neither negative nor positive.  The ordering of integers is compatible with the algebraic operations in the following way:  It follows that together with the above ordering is an ordered ring.  The integers are the only nontrivial totally ordered abelian group whose positive elements are well-ordered. This is equivalent to the statement that any Noetherian valuation ring is either a field or a discrete valuation ring.

Construction.

In elementary school teaching, integers are often intuitively defined as the (positive) natural numbers, zero, and the negations of the natural numbers. However, this style of definition leads to many different cases (each arithmetic operation needs to be defined on each combination of types of integer) and makes it tedious to prove that these operations obey the laws of arithmetic. Therefore, in modern set-theoretic mathematics a more abstract construction, which allows one to define the arithmetical operations without any case distinction, is often used instead. The integers can thus be formally constructed as the equivalence classes of ordered pairs of natural numbers.  The intuition is that stands for the result of subtracting from. To confirm our expectation that and denote the same number, we define an equivalence relation on these pairs with the following rule: precisely when  Addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers; denoting by the equivalence class having as a member, one has:  The negation (or additive inverse) of an integer is obtained by reversing the order of the pair:  Hence subtraction can be defined as the addition of the additive inverse:  The standard ordering on the integers is given by:  It is easily verified that these definitions are independent of the choice of representatives of the equivalence classes.  Every equivalence class has a unique member that is of the form or (or both at once). The natural number is identified with the class (in other words the natural numbers are embedded into the integers by map sending to ), and the class is denoted (this covers all remaining classes, and gives the class a second time since  Thus, is denoted by  If the natural numbers are identified with the corresponding integers (using the embedding mentioned above), this convention creates no ambiguity.  This notation recovers the familiar representation of the integers as }.  Some examples are:  In theoretical computer science, other approaches for the construction of integers are used by automated theorem provers and term rewrite engines. Integers are represented as algebraic terms built using a few basic operations (such as zero, succ, pred, etc.) and, possibly, using natural numbers, which are assumed to be already constructed (e.g., using the Peano approach).  There exist at least ten such constructions of signed integers. These constructions differ in several ways: the number of basic operations used for the construction, the number (usually, between 0 and 2) and the types of arguments accepted by these operations; the presence or absence of natural numbers as arguments of some of these operations, and the fact that these operations are free constructors or not, i.e., that the same integer can be represented using only one or many algebraic terms.  The technique for the construction of integers presented above in this section corresponds to the particular case where there is a single basic operation pairformula_12 that takes as arguments two natural numbers formula_13 and formula_14, and returns an integer (equal to formula_15). This operation is not free since the integer 0 can be written pair(0,0), or pair(1,1), or pair(2,2), etc. This technique of construction is used by the proof assistant Isabelle; however, many other tools use alternative construction techniques, notable those based upon free constructors, which are simpler and can be implemented more efficiently in computers.

Computer science.

An integer is often a primitive data type in computer languages. However, integer data types can only represent a subset of all integers, since practical computers are of finite capacity. Also, in the common two's complement representation, the inherent definition of sign distinguishes between "negative" and "non-negative" rather than "negative, positive, and 0". (It is, however, certainly possible for a computer to determine whether an integer value is truly positive.) Fixed length integer approximation data types (or subsets) are denoted "int" or Integer in several programming languages (such as Algol68, C, Java, Delphi, etc.).  Variable-length representations of integers, such as bignums, can store any integer that fits in the computer's memory. Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10).

Cardinality.

The cardinality of the set of integers is equal to (aleph-null). This is readily demonstrated by the construction of a bijection, that is, a function that is injective and surjective from to. If then consider the function: If then consider the function: If the domain is restricted to then each and every member of has one and only one corresponding member of N and by the definition of cardinal equality the two sets have equal cardinality.

An integer (from the Latin "integer" meaning "whole") is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75,, and are not.

Die ganzen Zahlen (auch "Ganzzahlen", lat. "numeri integri") sind eine Erweiterung der natürlichen Zahlen. Die ganzen Zahlen umfassen alle Zahlen


Life.

Childhood and youth.

Gerhart Hauptmann was born in 1862 in Obersalzbrunn, now known as Szczawno-Zdrój, in Lower Silesia (then a part of the Kingdom of Prussia, now a part of Poland). His parents were Robert and Marie Hauptmann, who ran a hotel in the area. As a youth, Hauptmann had a reputation of being loose with the truth.  Beginning in 1868, he attended the village school and then, in 1874, the Realschule in Breslau for which he had only barely passed the qualifying exam. Hauptmann had difficulties adjusting himself to his new surroundings in the city. He lived, along with his brother Carl, in a somewhat run-down student boarding house before finding lodging with a pastor.  He ran into problems with the Prussian-influenced school. Above all the strictness of the teachers and the better treatment of his noble classmates. His dislike and numerous illness which kept him from attending class, led to his having to repeat his first year. Over time, he came to appreciate Breslau because of the opportunity to visit the theater.  In the spring of 1878, Hauptmann left the Realschule to learn agriculture on his uncle's farm in Lohnig (today Łagiewniki Średzkie in Gmina Udanin, Poland). After a year and a half, however, he had to break off his training. He was not physically prepared for the work and he had a contracted a life-threatening lung ailment that troubled him for the next twenty months.

Studies and life as a sculptor.

After he failed to pass an officer entry exam for the Prussian Army, Hauptmann entered the sculpture school at the Royal Art and Vocational School in Breslau in 1880. There he met Josef Block who became a lifelong friend. He was temporarily expelled for "poor behavior and insufficient diligence," but quickly reinstated on the recommendation of the sculptor and Professor Robert Härtel. Hauptmann left the school in 1882.  For his brother's wedding, he wrote a short play, "Liebesfrühling", which was performed on the night before. Also at the wedding, he met the bride's sister, Marie Thienemann. They became secretly engaged and she began supporting him financially, which enabled him to begin a semester of philosophy and literary history at the University of Jena, which he soon quit.  After he left Jena, Marie financed a Mediterranean trip, which he undertook with his brother Carl. There he decided to settle in Rome as a sculptor, but with little success. His attempt to establish himself as part of Rome's German expatriate community also failed and his large clay sculpture of a German warrior collapsed. Hauptmann returned disappointed to Germany, where he began a brief stint at the Royal Academy in Dresden before beginning to study history at the University of Berlin. While there, he devoted his interests to the theater rather than to his studies. In 1891 he moved to Schreiberhau in Silesia.

Marriage and beginning as a writer.

Hauptmann married Marie Theienemann in Radebeul on 5 May 1885. In July, they took their honeymoon to Rügen along with Carl and his wife, Marie's sister, Martha. They visited the island of Hiddensee, which would become a favorite retreat of Hauptmann's. Because the city air bothered Gerhart's lungs, the couple spent the first four years of their marriage in the town of Erkner, where their three sons were born. In 1889, they moved to Charlottenburg in Berlin. There he joined the naturalist literary club "Durch", which included among others Karl Bleibtreu and Wilhelm Bölsche.  During this period he began to write. His first work was a "novelistic study" "Signalman Thiel" in 1888. His first play, "Before Sunrise", was first staged in 1889, directed by Otto Brahm. It inaugurated the naturalistic movement in modern German literature. It was followed by "The Reconciliation" (1890), "Lonely People" (1891) and "The Weavers" (1892), a powerful drama depicting the rising of the Silesian weavers in 1844, for which he is best known outside of Germany. His work also included comedies, including "Colleague Crampton" (1891) and "The Beaver Coat" (1893).  In 1893, he also took actress Margarete Marschalk as his lover. In order to get some distance, Marie moved to the US with their sons. Hauptmann prepared the first French performance of his play "The Assumption of Hannele" and then went after Marie, without even staying for the premiere. The rift, however, was not to be bridged. After several years of separation, the marriage was ended in July, 1904. However, Marie continued to live in the villa Hauptmann had built in Dresden.

Recognition and World War I.

From 1901, Hauptmann lived with Margarete Marschalk in Agnetendorf (today Jagniątków in Poland). He called it ""the mystical protective sheathing of my soul"". In the preceding year, Margarete had born him a son, Benvenuto. In September 1904, they were married; this second marriage lasted until his death, though it was thrown into a serious crisis in 1905 and 1906 by his affair with a 16-year-old actress, Ida Orloff.  In 1910, Hauptmann's first novel was published, "The Fool in Christ, Emanuel Quint", which told the story of a wandering preacher who mixed sun worship and Christianity together. His 1912 novel, "Atlantis", became the basis for a Danish silent film of the same name. The novel was written one month before the RMS "Titanic" disaster, and the film's 1913 release was less than one year after the event.  The storyline for both involved a romance aboard a doomed ocean liner, and the similarity to the disaster became obvious. This coincidental untimeliness caused the film to be banned in Norway, due to perceived insensitivity. Nevertheless, excited by the possibilities of this new medium, Hauptmann wrote several screenplays (e.g. Appolonius of Tyre), none of which was ever filmed.  Around the turn of the century, Hauptmann began to receive official recognition. Three times he was awarded the Austrian Franz-Grillparzer-Preis. He also received honorary doctorates from Worcester College at Oxford in 1905 and from the University of Leipzig in 1909. In 1912, he was awarded the Nobel Prize for Literature "primarily in recognition of his fruitful, varied and outstanding production in the realm of dramatic art", after he had been nominated in that year by Erich Schmidt, member of the Prussian Academy of Science.  Kaiser Wilhelm II, however, did not care for the "social democratic" poet. He vetoed the awarding of the 1896 Schiller Preis (for "The Assumption of Hannele") and at the instigation of his son, Crown Prince Wilhelm, in 1913, a Breslau production of Hauptmann's play "Commemoration Masque" ("Festspiel in deutschen Reimen") was canceled, because in it the hundredth anniversary of the Liberation of Germany from Napoleon was depicted with a pacifistic rather than patriotic tone. However, the very same Hauptmann who had criticized militarism in the "Masque", the very next year was among those who supported the war.  Hauptmann signed the Manifesto of the Ninety-Three, a manifesto signed by 93 German scientists, scholars and artists, declaring their unequivocal support of German military actions at the beginning of World War I. He published supportive poems (many of which read as unintentional satires and which he later crossed out in the manuscript).  In 1915, Wilhelm II awarded him the Order of the Red Eagle, Fourth Class. After Germany's military defeat and the fall of the monarchy, Hauptmann fled to the pacifist colony Monte Verità in near Locarno, Switzerland. Several years later, he wrote "Till Eulenspiegel", a poetic memorial to Hans Paasche, the pacifist and reformer who was assassinated by ultra-nationalists.

Representative poet of Germany.

In 1918, he joined a declaration, signed by a number of German intellectuals and published in the "Berliner Tageblatt" newspaper, showing solidarity with the Republic. During the early years of the republic, he was considered as a candidate for the Reichspräsident and offered the position of Reichskanzler, which he turned down.  In the following years, he was the first recipient of the Adlerschild des Deutschen Reiches (The Eagle Shield of the German Reich) an award for scholarly or artistic achievement. During this period, the demand for Hauptmann's work had declined, to the point where, in order to maintain his lifestyle, he had begun to do films and serializations. Despite this, he continued to enjoy popularity. He was seen abroad as the representative of German Literature. In 1932, in honor of the centenary of Goethe's death, he went on a lecture tour of the United States and was awarded and honorary doctorate from Columbia University. In addition he was awarded the Goethe Prize of the city of Frankfurt am Main.  On his 70th birthday, he was awarded several honorary citizenships. There were countless exhibitions and performances of his work, many with well-known performers. Max Reinhardt played the lead in the premiere of Hauptmann's new play "Before Sunset." From 1926-43, Hauptmann summered with his family in Hiddensee.

The Nazi era.

After the Nazis came to power in Germany in 1933, Hauptmann signed a loyalty oath of the German Academy of Literature, a section of the Prussian Academy of Arts. In the summer of the same year, according to writer and historian Ernst Klee, he applied for membership in the Nazi party but his application was denied by the regional party office.  Hauptmann's copy of "Mein Kampf", which can now be found in the Hauptmann collection at the Berlin State Library, was also heavily annotated. He regarded himself as being fundamentally a poet, above the political fray; and certainly nothing from the Nazi ideology was incorporated into his works. However, he had earlier been a founding member of the eugenics organization the German Society for Racial Hygiene, in Berlin in 1905, and his play "Before Sunrise" is deeply concerned with hereditary alcoholism, a popular idea with eugenicists, and the main character rejects his fiancée due to concerns about his potential children's genetics.  Because Hauptmann remained highly regarded by the German people, the Nazis did everything to keep him from leaving the country, despite the emigration of many of his colleagues. At times he suffered from official disapproval. The censors of the Propaganda Minister Goebbels kept an eye on Hauptmann's work and even banned a new edition of his novella "The Shot in the Park" because it featured a black character. Hauptmann was told that reprinting was impossible because of a paper shortage. The film versions of "The Beaver Coat" and "Before Sunrise" were censored, and the film adaptation of "Schluck and Jau" was banned. For Hauptmann's 80th birthday, in 1942, representatives of the Nazi regime cooperated with honors, celebrations, and celebratory performances. Hauptmann was presented by his publisher with the first copy of his 17-volume Complete Works. Hauptmann lived through the end of World War II at his house, Wiesenstein. In 1944, he published his Atreus Tetralogy, which he had been working on for four years. It comprises "Iphigenia in Delphi", "Iphigenia in Aulis", "Agamemnon's Death", and "Electra". In 1944, Hauptmann's name was included in the Gottbegnadeten list (the "God-gifted list"), a list of artists considered crucial to the German culture, who were therefore exempt from mobilization in the war effort. He was one of the six most important writers in the special list of the "irreplaceable artists.".  During the bombing of Dresden, Hauptmann was staying at a Dresden sanatorium due to severe pneumonia. He said of the inferno, "Whoever had forgotten how to cry learned again at the destruction of Dresden. I stand at the end of my life and envy my dead comrades, who were spared this experience."  After the war, Silesia, where Hauptmann was living, became part of Poland, but Hauptmann was temporarily allowed to stay due to a letter of protection. Then, on April 7, 1946, he was informed by the Soviet military authorities that the Polish government was insisting on his resettlement. Before his expulsion, he became very ill.

Death.

At the beginning of May 1946, Hauptmann learned that the Polish government was insisting on the expulsion of all Germans without exception. On 6 June, he died of bronchitis in Agnieszków (present-day Jagniątków, a part of "Hirschberg im Riesengebirge", now Jelenia Góra). His last words were reported to be, "Am I still in my house?" Despite his final wishes, as expressed in his last will, Hauptmann was not buried at his home.  An official letter from the Soviet Administration in favor of the writer, who was highly regarded in the Soviet Union, proved ineffective, though the family was permitted to take its belongings. Only an hour after his death, the local militia had gathered outside the window directly under his deathbed and banging pots and pans and blowing whistles and trumpets.

Funeral.

At a funeral service held in Stralsund, near Hauptmann's summer home on Hiddensee island, Wilhelm Pieck, then co-chairman of the Socialist Unity Party of Germany in the Soviet occupation zone of Germany spoke, along with poet Johannes R. Becher, and Soviet official Sergei Ivanovich Tiulpanov all spoke.  On the morning of 28 July, 52 days after his death, he was buried before sunrise at the cemetery in Hiddensee. His widow mixed a small sack earth from the Riesengebirge/Karkonosze Mountains (Krkonoše) in Silesia with the sandy soil of the Baltic coast where he was buried. In 1951, a granite block was unveiled as the grave stone. It bore, as per Hauptmann's wish, only his name. In 1983, his wife Margarete's remains were moved to lie beside her husband's, though she had died in 1957.

Work.

Influences.

Hauptmann first encountered the various representatives of the naturalist movement through the avant-garde society "Durch" in 1885, which was an important influence. The society hearkened back to historical examples from the Sturm und Drang movement, especially the circle centered on the Hart Brothers up until the Vormärz period before the revolutions of 1848.  At their meetings, aesthetic questions about idealism, Realism and the naturalist movement were discussed. Hauptmann gave a lecture about the theretofore largely forgotten poet and dramatist Georg Büchner. With that, he also established his naturalistic orientation.  At the end of the 1880s, he was confronted with the incipient anti-socialist movement. The first of the Anti-Socialist Laws was passed in 1878 and strengthened in 1887. Hauptmann was in 1887 as called before the court in Breslau, because he had been a follower of the "Icharians," whose ideas hearkened back to the ideas of French communist Etienne Cabet.  He sought refuge in his brother's house in Zurich in order to avoid prosecution. While there he encountered psychiatrist August Forel and the preacher Johannes Guttzeit, whose ideas influenced "Before Sunrise". Hauptmann's early dream of a utopian-socialist community were further fed by his encounter with the poet Gusto Gräser, whose communal colony Hauptmann would visit several times in 1919. The story "The Heretic of Soana", the novel "The Fool in Christ Emmanuel Quint", and the final chapter of "Till Eulenspiegel" deal with his experience of a Dionysian-Jesuanic itinerant prophet.

Naturalism.

Hauptmann began producing naturalistic works in Zurich. From there, he sent the manuscript of "Bahnwärter Thiel," his first naturalistic work, to Munich to be read by the critic Michael Georg Conrad. Hauptmann's 1889 play "Before Sunrise" caused one of the largest scandals in German theater history. The bourgeois audience was shocked by the frank depictions of alcoholism and sexuality.  According to Franz-Josef Payrhuber, "Before Sunrise" was an epoch-making work, but it is not the representative example of naturalistic drama, that label would go to Die Familie Selicke by Arno Holz and Johannes Schlaf. Hauptmann however did have an important role, with the support of Otto Brahm, in establishing naturalistic drama on the German stage. Theaters under Brahm's leadership premiered 17 of Hauptmann's plays. Those plays, and the numerous performances across Germany, gave Naturalism its first broad exposure and social impact.  With his most important play, "The Weavers", which he had already been contemplating during his stay in Zurich, Hauptmann achieved world renown and reached the high point of his Naturalistic phase.

Critical reception.

Hauptmann's early work received differing reviews. Conservative circles and also the government were not excited about his socially critical dramas, which made itself felt through censorship. His position in the opposition raised his profile in progressive, intellectual circles, which appreciated these aspects of his work. After many naturalistic-influenced works, Hauptmann's style changed and he grew increasingly well-received among the educated and upper classes.  Nevertheless, he was still in demand as a writer and was regarded abroad as the representative poet of Germany. The Hungarian philosopher and literature critic, Georg Lukacs later called Hauptmann the "representative poet of bourgeois Germany," by which he did not mean to underscore Hauptmann's prominent position. Rather, he expressed displeasure with Hauptmann's fickleness and lack of attachment to his "revolutionary beginnings." Despite his preeminence, the sale of his works steadily declined as other poets and playwrights took the spotlight.  Hauptmann had taken up a lavish lifestyle, lived in expensive hotels, often received guests, and took trips to Italy. He summered in his large house on the Hiddensee, that Günter Kunert called a "do-it-yourself Olympia." Thomas Mann referred to this lavish lifestyle when he called him in 1922 the "King of the Republic." Mann met Hauptmann at an Alpine resort and wrote to his brother, "I hobnob every evening with Hauptmann, who is a really good fellow." In addition Mann adapted some of Hauptmann's traits for his character Mynheer Peeperkorn in his book "The Magic Mountain".  When Hauptmann continued to live in Germany after the Nazis came to power, they attempted to use Hauptmann for their own purposes. Various works that displeased the party leaders were banned but others continued to be performed. At his 80th birthday, in 1942 he was honored by the government with a festival and tributes, which he accepted. Hauptmann's ebb-and-flow character was highlighted in William L. Shirer's "The Rise and Fall of the Third Reich". Shirer offered in a first-person account:  After his death, the fame he had enjoyed in life began to fade. His reputation was further diminished by his uncritical attitude toward the Nazis. Nevertheless, centenary celebrations were held in many German cities in 1962, and his works continued to be performed on West German stages into the 1970s, especially "Der Biberpelz" and "Die Ratten".

Publications.

Novels  Short novels  Verse novels  Plays  In English translation

References.

General references

Gerhart Johann Robert Hauptmann (; 15 November 1862 – 6 June 1946) was a German dramatist and novelist. He is counted among the most important promoters of literary naturalism, though he integrated other styles into his work as well. He received the Nobel Prize in Literature in 1912.

Gerhart Johann Robert Hauptmann (* 15. November 1862 in Ober Salzbrunn in Schlesien; † 6. Juni 1946 in Agnieszków, deutsch: Agnetendorf in Niederschlesien) war ein deutscher Dramatiker und Schriftsteller. Er gilt als der bedeutendste deutsche Vertreter des Naturalismus, hat aber auch andere Stilrichtungen in sein Schaffen integriert. 1912 erhielt er den Nobelpreis für Literatur.


Definition.

The inductance of an electric circuit is one henry when an electric current that is changing at one ampere per second results in an electromotive force of one volt across the inductor: where "V"("t") denotes the resulting voltage across the circuit, "I"("t") is the current through the circuit, and "L" is the inductance of the circuit.  The henry is a derived unit based on four of the seven base units of the International System of Units: kilogram (kg), metre (m), second (s), and ampere (A). Expressed in combinations of SI units, the henry is: where:,,,,,,,,,,,, Hz = hertz

Use.

The International System of Units (SI) specifies to write the symbol of a unit named for a person with an initial capital letter, while the name is not capitalized in sentence text, except when any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.  The United States National Institute of Standards and Technology recommends users writing in English to use the plural as "henries".

Applications.

The inductance of a coil depends on its size, the number of turns, and the permeability of the material within and surrounding the coil. Formulas can be used to calculate the inductance of many common arrangements of conductors, such as parallel wires, or a solenoid. A small air-core coil used for broadcast AM radio tuning might have an inductance of a few tens of microhenries. A large motor winding with many turns around an iron core may have an inductance of scores or hundreds of henries. The physical size of an inductance is also related to its current carrying and voltage withstand ratings.

The henry (symbol: H) is the SI derived unit of electrical inductance. If a current of 1 ampere flowing through the coil produces flux linkage of 1 weber turn, the coil has a self inductance of 1 henry. The unit is named after Joseph Henry (1797–1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791–1867) in England.

Henry ist im SI-Einheitensystem die Einheit der Induktivität und ist nach Joseph Henry benannt. Sie ist für jede Leiterspule spezifisch und wird meistens auf ihr angegeben.


Early life.

He was born on 28 July 1954 in his paternal grandmother Rosa Inéz Chávez's home, a modest three-room house located in the rural village Sabaneta, Barinas State. The Chávez family were of Amerindian, Afro-Venezuelan and Spanish descent. His parents, Hugo de los Reyes Chávez – described as a proud COPEI member– and Elena Frías de Chávez, were schoolteachers who lived in the small village of Los Rastrojos.  Hugo was born the second of seven children. Hugo described his childhood as "poor... [but] very happy", though his childhood of supposed

Military career.

Military academy.

Aged 17, Chávez studied at the Venezuelan Academy of Military Sciences in Caracas, following a curriculum known as the Andrés Bello Plan, instituted by a group of progressive, nationalistic military officers. This new curriculum encouraged students to learn not only military routines and tactics but also a wide variety of other topics, and to do so civilian professors were brought in from other universities to give lectures to the military cadets.  Living in Caracas, he saw more of the endemic poverty faced by working class Venezuelans, and said that this experience only made him further committed to achieving social justice. He also began to get involved in activities outside of the military school, playing baseball and softball with the "Criollitos de Venezuela" team, progressing with them to the Venezuelan National Baseball Championships. He also wrote poetry, fiction, and drama, and painted, and he researched the life and political thought of 19th-century South American revolutionary Simón Bolívar. He also became interested in the Marxist revolutionary

Early military career.

Following his graduation, Chávez was stationed as a communications officer at a counterinsurgency unit in Barinas, although the Marxist–Leninist insurgency which the army was sent to combat had already been eradicated from that state. At one point he found a stash of Marxist literature that apparently had belonged to insurgents many years before. He went on to read these books, which included titles by Karl Marx, Vladimir Lenin, and Mao Zedong, but his favorite was a work entitled "The Times of Ezequiel Zamora", written about the 19th-century federalist general whom Chávez had admired as a child. These books further convinced Chávez of the need for a leftist government in Venezuela: "By the time I was 21 or 22, I made myself a man of the left".  In 1977, Chávez's unit was transferred to Anzoátegui, where they were involved in battling the Red Flag Party, a

Bolivarian Revolutionary Army-200.

Five years after his creation of the ELPV, Chávez went on to form a new secretive cell within the military, the Bolivarian Revolutionary Army-200 (EBR-200), later redesignated the Revolutionary Bolivarian Movement-200 (MBR-200). He was inspired by Ezequiel Zamora (1817–1860), Simón Bolívar (1783–1830) and Simón Rodríguez (1769–1854), who became known as the "three roots of the tree" of the MBR-200. Later, Chávez said that "the Bolivarian movement that was being born did not propose political objectives... Its goals were imminently internal. Its efforts were directed in the first place to studying the military history of Venezuela as a source of a military doctrine of our own, which up to then didn't exist". However, he always hoped for the Bolivarian Movement to become a politically dominant party that would "accept all kinds of ideas, from the right, from the left, from the ideological ruins of those old capitalist and communist systems". Indeed, Irish political analyst Barry Cannon noted that the MBR's early ideology "was a doctrine in construction, a heterogeneous amalgam of thoughts and ideologies, from universal thought, capitalism, Marxism, but rejecting the neoliberal models currently being imposed in Latin America and

Political rise.

While Chávez and the other senior members of the MBR-200 were in prison, his relationship with Herma Marksman broke up in July 1993. In 1994, Rafael Caldera (1916–2009) of the centrist National Convergence Party who allegedly had knowledge of the coup was elected president and soon afterward he freed Chávez and the other imprisoned MBR-200 members, though Caldera banned them from returning to the military. Chávez went on a 100-day tour of the country, promoting his Bolivarian cause of social revolution. On his tours around the country he met Marisabel Rodríguez, who would give birth to their daughter shortly before becoming his second wife in 1997.  Travelling around Latin America in search of foreign support for his Bolivarian movement, he visited Argentina, Uruguay, Chile, Colombia, and finally Cuba, where he met Castro and became friends with him. During his stay in Colombia, he spent six months receiving guerilla training and establishing contacts with the FARC and ELN terrorist groups, and even adopted a "nom de guerre", Comandante Centeno. After his return to Venezuela, Chávez was critical of President Caldera and his liberal economic policies. A drop in per capita income, coupled with increases in poverty and crime, "led to gaps emerging between rulers and ruled which favored the emergence of a populist leader".  By now Chávez was a supporter of taking military action, believing that the "oligarchy" would never allow him and his supporters to win an election, while Francisco Arias Cárdenas insisted that they take part in the representative democratic process. Indeed, Cárdenas soon joined the Radical Cause socialist party and won the December 1995 election to become governor of the oil-rich Zulia State. As a result, Chávez and his supporters founded a political party, the Fifth Republic Movement (MVR – "Movimiento Quinta República") in July 1997 in order to support Chávez's candidacy in the 1998 presidential election.

1998 election.

At the start of the election run-up, front runner Irene Sáez was backed by one of Venezuela's two primary political parties, Copei. Chávez's revolutionary rhetoric gained him support from "Patria Para Todos" (Homeland for All), the "Partido Comunista Venezolano" (Venezeuelan Communist Party) and the "Movimiento al Socialismo" (Movement for Socialism). Chávez's promises of widespread social and economic reforms won the trust and favor of the primarily poor and working class. By May 1998, Chávez's

Presidency (1999–2013).

First presidential term: 2 February 1999 – 10 January 2001.

Chávez's presidential inauguration took place 2 February 1999. He deviated from the usual words of the presidential oath when he took it, proclaiming: "I swear before God and my people that upon this "moribund" constitution I will drive forth the necessary democratic transformations so that the new republic will have a Magna Carta befitting these new times." Freedom in Venezuela suffered following "the decision of President Hugo Chávez, ratified in a national referendum, to abolish congress and the judiciary, and by his creation of a parallel government of military cronies". Soon after being established into office, Chávez spent much of his time attempting to abolish existing checks and balances in Venezuela. He appointed new figures to government posts, adding leftist allies to key positions and "army colleagues were given a far bigger say in the day-to-day running of the country". For instance, he put Revolutionary Bolivarian Movement-200 founder in charge of the National Directorate of Intelligence and Prevention Services and made, one of the 1992 coup leaders, governor of the Federal District of Caracas.  Chávez appointed conservative, centrist and centre-right figures to government positions as well. He reappointed Caldera's economy minister, Maritza Izaquirre, to her previous position and appointed businessman Roberto Mandini president of the state-run oil company Petroleos de Venezuela. His critics referred to these government officials as the "Boliburguesía" or "Bolivarian bourgeoisie", and highlighted that it "included

Second presidential term: 10 January 2001 – 10 January 2007.

Under the new constitution, it was legally required that new elections be held in order to re-legitimize the government and president. This presidential election in July 2000 would be a part of a greater "megaelection", the first time in the country's history that the president, governors, national and regional congressmen, mayors and councilmen would be voted for on the same day. Going into the elections, Chávez had control of all three branches of government. For the position of president, Chávez's closest challenger proved to be his former friend and co-conspirator in the 1992 coup, Francisco Arias Cárdenas, who since becoming governor of Zulia state had turned towards the political centre and begun to denounce Chávez as autocratic. Although some of his supporters feared that he had alienated those in the middle class and the Roman Catholic Church hierarchy who had formerly supported him, Chávez was re-elected with 60% of the vote (the equivalent of 3,757,000 people), a larger majority than his 1998 electoral victory, again primarily receiving his support from the poorer sectors of Venezuelan society.  That year, Chávez helped to further cement his geopolitical and ideological ties with the Cuban government of Fidel Castro by signing an agreement under which Venezuela would supply Cuba with 53,000 barrels of oil per day at preferential rates, in return receiving 20,000 trained Cuban medics and educators. In the ensuing decade, this would be increased to 90,000 barrels a day (in exchange for 40,000 Cuban medics and

Third presidential term: 10 January 2007 – 10 January 2013.

In the presidential election of December 2006, which saw a 74% voter turnout, Chávez was once more elected, this time with 63% of the vote, beating his closest challenger Manuel Rosales, who conceded his loss. The election was certified as being free and legitimate by the Organization of American States (OAS) and the Carter Center. After this victory, Chávez promised an "expansion of the revolution".

United Socialist Party of Venezuela and domestic policy.

On 15 December 2006, Chávez publicly announced that those leftist political parties who had continually supported him in the Patriotic Pole would unite into one single, much larger party, the United Socialist Party of Venezuela ("Partido Socialista Unido de Venezuela", PSUV). In the speech which he gave announcing the PSUV's creation, Chávez declared that the old parties must "forget their own structures, party colours and slogans, because they are not the most important thing for the fatherland". According to political analyst Barry Cannon, the purpose of creating the PSUV was to "forge unity amongst the disparate elements [of the Bolivarian movement], providing grassroots input into policy and leadership formation, [and] uniting the grassroots and leadership into one single body". It was hoped that by doing so, it would decrease the problems of clientelism and corruption and also leave the movement less dependent on its leadership: as Chávez himself declared, "In this new party, the bases will elect the leaders. This will allow real leaders to emerge."  Chávez had initially proclaimed that those leftist parties which chose to not dissolve into the PSUV would have to leave the government; however, after several of those parties supporting him refused to do so, he ceased to issue such threats. There was initially much grassroots enthusiasm for the creation of the PSUV, with membership having risen to 5.7 million people by 2007, making it the largest political group in Venezuela. The United Nations' International Labour Organization however expressed concern over some voters' being pressured to join the party.  On 28 December 2006, President Chávez announced that the government would not renew RCTV's broadcast license which expired on 27 May 2007, thereby forcing the channel to cease operations on that day. On 17 May 2007, the government rejected a plea made by RCTV to stop the TV station's forced shutdown. Thousands of protesters marching both against and in support of the government's decision remained on the streets in Caracas. Other marches took place in Maracaibo and Valencia. On 21 May 2007, hundreds of journalists and students marched in Caracas carrying a banner reading "S.O.S. Freedom of Expression." A few days later, on 25 May 2007, university students from the Universidad Católica Andrés Bello, the Universidad Simón Bolívar and the Universidad Central de Venezuela protested against the government's

Fourth presidential term: 10 January 2013 – 5 March 2013.

On 7 October 2012, Chávez won election as president for a fourth time, his third six-year term. He defeated Henrique Capriles with 54% of the votes versus 45% for Capriles, which was a lower victory margin than in his previous presidential wins, in the 2012 Venezuelan presidential election. Turnout in the election was 80%, with a hotly contested election between the two candidates. There was significant support for Chávez amongst the Venezuelan lower class. Chávez's opposition blamed him for unfairly using state funds to spread largesse before the election to bolster Chavez's support among his primary electoral base, the lower class. The inauguration of Chávez's new term was scheduled for 10 January 2013, but as he was undergoing medical treatment at the time in Cuba, he

Political ideology.

Chávez propagated what he called "socialism for the 21st century", but according to the pro-Chavez academic Gregory Wilpert, "Chávez has not clearly defined twenty-first century socialism, other than to say that it is about establishing liberty, equality, social justice, and solidarity. He has also indicated that it is distinctly different from state socialism", as implemented by the governments of the Soviet Union and the People's Republic of China. As a part of his socialist ideas, he emphasised the role of so-called "participatory democracy", which he claimed increased democratic participation, and was implemented through the foundation of the Venezuelan Communal Councils and Bolivarian Circles which he cited as examples of grassroots and participatory democracy.

Bolivarianism.

Hugo Chávez defined his political position as Bolivarianism, an ideology he developed from that of Simón Bolívar (1783–1830) and others. Bolívar was a 19th-century general who led the fight against the colonialist Spanish authorities and who is widely revered across Latin America today. Along with Bolívar, the other two primary influences upon Bolivarianism are Simón Rodríguez (1769–1854), a philosopher who was Bolívar's tutor and mentor, and Ezequiel Zamora, (1817–1860), the Venezuelan Federalist general. Political analyst and Chávez supporter Gregory Wilpert, in his study of Chávez's politics, noted that "The key ingredients for Chávez's revolutionary

Marxism.

Chávez's connection to Marxism was a complex one, though he had described himself as a Marxist on some occasions. In May 1996, he gave an interview with Agustín Blanco Muñoz in which he remarked, "I am not a Marxist, but I am not anti-Marxist. I am not communist, but I am not anti-communist." In a 2009 speech to the national assembly, he said: "I am a Marxist to the same degree as the followers of the ideas of Jesus Christ and

Other influences.

Chávez's early heroes were nationalist military dictators that included former Peruvian president Juan Velasco Alvarado and former Panamanian "Maximum Leader" Omar Torrijos. One dictator Chávez admired was Marcos Pérez Jiménez, a former president of Venezuela that he praised for the public works he performed. Chávez praised Pérez Jiménez in order to vilify preceding democratic governments, stating that "General Pérez Jiménez was the best president Venezuela had in a long time... He was much better than Rómulo Betancourt, much better than all of those others. They hated him because he was a soldier."  Chávez was also well acquainted with the various traditions of Latin American socialism, espoused by such figures as Colombian politician Jorge Eliécer Gaitán and former Chilean president Salvador Allende. Early in his presidency, Chávez was advised and influenced by the Argentine Peronist Norberto Ceresole. Cuban Communist revolutionaries Che Guevara and Fidel Castro also influenced Chávez, especially with Castro's government assistance with the Bolivarian Missions. Other indirect influences on Chávez's political philosophy are the writings of American linguist Noam Chomsky and the Gospel teachings of Jesus Christ. Other inspirations of Chávez's political view are Giuseppe Garibaldi, Antonio Gramsci and Antonio Negri.

Conspiracy theories.

In September 2006, Chávez said 9/11 conspiracy theories were "not absurd" and that "A building never collapses like that, unless it's with an implosion." Chávez also told Christopher Hitchens that he did not believe that the footage of the Apollo 11 moon landings was genuine.

Policy overview.

Economic and social policy.

From his election in 1998 until his death in March 2013, Chávez's administration proposed and enacted populist economic policies. Domestic policies included redistribution of wealth, land reform, and democratization of economic activity via workplace self-management and creation of worker-owned cooperatives. The social programs were designed to be short-term, though after seeing political success as their result, Chávez made the efforts central to his administration and often overspent outside of Venezuela's budget.  With increasing oil prices in the early 2000s and funds not seen in Venezuela since the 1980s, Chávez created the Bolivarian Missions, aimed at providing public services to improve economic, cultural, and social conditions, using these populist policies in order to maintain political power. According to Corrales and Penfold, "aid was disbursed to "some" of the poor, and more gravely, in a way that ended up helping the president and his allies and cronies more than anyone else". The Missions, which were directly overseen by Chávez and often linked to his political campaigns, entailed the construction of thousands of free medical clinics for the poor, and the enactment of food and housing subsidies. A 2010 OAS report indicated achievements in addressing illiteracy, healthcare and poverty, and economic and social advances. The quality of life for Venezuelans had also improved temporarily according to a UN Index. Teresa A. Meade wrote that Chávez's popularity strongly depended "on the lower classes who have benefited from these health initiatives and similar policies". Following elections, social programs saw less attention from the government and their overall effectiveness decreased.  The Gini coefficient, a measure of income inequality, dropped from.495 in 1998 to.39 in 2011, putting Venezuela behind only Canada in the Western Hemisphere. Venezuelans aged 15 and older, 95% could also read and write, with Venezuela having one of the highest literacy rates in the region, though some scholars have disputed that literacy improvements during Chavez's presidency resulted from his administration's policies. The poverty rate fell from 48.6% in 1999 to 32.1% in 2013, according to

Crime and punishment.

During the 1980s and 1990s there was a steady increase in crime in Latin America. The countries of Colombia, El Salvador, Venezuela, and Brazil all had homicide rates above the regional average. During his terms as president, hundreds of thousands of Venezuelans were murdered due to violent crimes occurring in the country. Gareth A. Jones and Dennis Rodgers stated in their book "Youth violence in Latin America: Gangs and Juvenile Justice in Perspective" that, "With the change of political regime in 1999 and the initiation of the Bolivarian Revolution, a period of transformation and political conflict began, marked by a further increase in the number and rate of violent deaths" showing that in four years, the murder rate had increased to 44 per 100,000 people. Kidnappings also rose tremendously during Chavez's tenure, with the number of kidnappings over 20 times higher in 2011 than when Chavez was elected. Documentary filmmaker James Brabazon, stated "kidnapping crimes had skyrocketed... after late Venezuelan President Hugo Chavez freed thousands of violent prisoners as part of controversial criminal justice system reforms" while kidnappings and murders also increased due to Colombian organized crime activity as well. He further explained that common criminals felt that the Venezuelan government did not care for the problems of the higher and middle classes, which in turn gave them a sense of impunity that created a large business of kidnapping-for-ransom.  Under Chávez's administration, crimes were so prevalent

Elections under Chávez.

The electoral processes surrounding Venezuela's democracy under Chávez were often observed controversially. According to "Bloomberg", he changed Venezuela from a democracy to "a largely authoritarian system".  Given the protests and strikes, some of which were quite big, like in 10 December 2001, then the largest in the history of Venezuela, some confidential cables published on WikiLeaks tried to explain the discrepancy between Chávez's relatively low popularity and his overwhelming electoral victory.  According to the cables, Hugo Chávez used "practically unlimited state resources" for propaganda activities, and high oil prices facilitated his success. The opposition, on the contrary, was divided into different parties, which ran for the same office, and the limited financial resources were badly invested. During his re-election campaigns, Chávez, through food, health, and

Corruption.

In December 1998, Hugo Chávez declared three goals for the new government; "convening a constituent assembly to write a new constitution, eliminating government corruption, and fighting against social exclusion and poverty". However, during Hugo Chávez's time in power, corruption has become widespread throughout the government due to impunity towards members of the government, bribes and the lack of transparency. In 2004, Hugo Chávez and his allies took over the Supreme Court, filling it with supporters of Chávez and made new measures so the government could dismiss justices from the court. According to the libertarian "Cato Institute", the National Electoral Council of Venezuela was under control of Chávez where he tried to "push a constitutional reform that would have allowed him unlimited opportunities for reelection". The Corruption Perceptions Index, produced annually by the Berlin-based NGO

Aiding FARC.

According to the International Institute for Strategic Studies (IISS), "Chavez's government funded FARC's office in Caracas and gave it access to Venezuela's intelligence services" and said that during the 2002 coup attempt that "FARC also responded to requests from [Venezuela's intelligence service] to provide training in urban terrorism involving targeted killings and the use of explosives". The IISS continued saying that "the archive offers tantalizing but ultimately unproven suggestions that FARC may have undertaken assassinations of Chavez's political opponents on behalf of the Venezuelan state". Venezuelan diplomats denounced the IISS' findings saying that they had "basic inaccuracies".  In 2007,

Human rights.

1999 Venezuelan Constitution.

In the 1999 Venezuelan constitution, 116 of the 350 articles were concerned with human rights; these included increased protections for indigenous peoples and women, and established the rights of the public to education, housing, healthcare, and food. It called

Criticisms.

Shortly after Hugo Chávez's election, ratings for freedom in Venezuela dropped according to political and human rights group Freedom House and Venezuela was rated "partly free". In 2004, Amnesty International criticized Chavez's administration of not handling the 2002 coup in a proper manner, saying that violent incidents "have not been investigated effectively and have gone unpunished" and that "impunity enjoyed by the perpetrators encourages further human rights violations in a particularly volatile political climate". Amnesty International also criticized the Venezuelan National Guard and the Direccion de Inteligencia Seguridad y Prevención (DISIP) stating that they "allegedly used excessive force to control the situation on a number of occasions" during protests involving the 2004 Venezuela recall. It was also noted that many of the protesters detained seemed to not be "brought before a judge within the legal time limit".  In 2008, Human Rights Watch released a report reviewing Chávez's human rights record over his first decade in power. The report praises Chávez's 1999 amendments to the constitution which significantly expanded human rights guarantees, as well as mentioning improvements in women's rights and indigenous rights, but noted a "wide range of government policies that have undercut the human rights protections established" by the revised constitution. In particular, the report accused Chávez and his administration of engaging in discrimination on political grounds, eroding the independence of the judiciary, and of engaging in "policies that have undercut journalists' freedom of expression, workers' freedom of association, and civil society's ability to promote human rights in Venezuela". The Venezuelan government retaliated for the report by expelling members of Human Rights Watch from the country. Subsequently, over a hundred Latin American scholars signed a joint letter with the Council on Hemispheric Affairs, a leftist NGO that would defend Chávez and his movement, with the individuals criticizing

Media and the press.

Under Chávez, press freedom declined while censorship in Venezuela increased. He used state-run bodies to silence the media and to disseminate Bolivarian propaganda. Other actions included pressuring media organizations to sell to those related to his government or to face closure.  Human Rights Watch criticized Chávez for engaging in "often discriminatory policies that have undercut journalists' freedom of expression". Reporters Without Borders criticized the Chávez administration for "steadily silencing its critics".  In 2004, Chávez used the National Commission of Telecommunications and the Social Responsibility in Radio, Television and Electronic Media law to officially censor media organizations.  Chávez inaugurated TeleSUR in July 2005,

Foreign policy.

Though Chávez inspired other movements in Latin America to follow his model of "chavismo" in an attempt to reshape South America, it was later seen as being erratic and his influence internationally became exaggerated. He refocused Venezuelan foreign policy on Latin American economic and social integration by enacting bilateral trade and reciprocal aid agreements, including his so-called "oil diplomacy" making Venezuela more dependent on using oil, its main commodity, and increasing its longterm vulnerability. Chávez also aligned himself with authoritarian nations and radical movements that were seen as being anti-Western, with relations with Cuba and Iran becoming a particular

Personal life.

Chávez married twice. He first wed Nancy Colmenares, a woman from a poor family in Chávez's hometown of Sabaneta. Chávez and Colmenares remained married for 18 years, during which time they had three children: Rosa Virginia, María Gabriela, and Hugo Rafael, the latter of whom suffers from behavioural problems. The couple separated soon after Chávez's 1992 coup attempt. During his first marriage, Chávez had an affair with historian Herma Marksman; their relationship lasted nine years. Chávez's second wife was journalist Marisabel Rodríguez de Chávez, with whom he separated in 2002 and divorced in 2004. Through that marriage, Chávez had another daughter, Rosinés. Both María and Rosa had children. When Chávez was released from prison, he initiated affairs with women that had been his followers. Allegations were also made that Chávez was a womanizer throughout both his marriages, having encounters with actresses, journalists, ministers, and ministers' daughters. The allegations remained unproven and are contradicted by statements provided by other figures close to him, though one retired aide shared that while Chávez was married to Marisabel and afterward, he participated in liaisons with women and gave them gifts, with some rumors among his aides stating that some of

Illness.

In June 2011, Chávez revealed in a televised address from Havana, Cuba, that he was recovering from an operation to remove an abscessed tumor with cancerous cells. Vice President Elías Jaua declared that the president remained in "full exercise" of power and that there was no need to transfer power due to his absence from the country. On 3 July, the Venezuelan government denied, however, that Chávez's tumor had been completely removed, further stating that he was heading for "complete recovery". On 17 July 2011, television news reported that Chávez had returned to Cuba for further cancer treatments.  Chávez gave a public appearance on 28 July 2011, his 57th birthday, in which he stated that his health troubles had led him to radically reorient his life towards a "more diverse, more reflective and multi-faceted" outlook, and he went on to call on the middle classes and the private sector to get more involved in his Bolivarian Revolution, something he saw as "vital" to its success. Soon after this speech, in August Chávez announced

Death.

On 5 March 2013, Vice President Nicolás Maduro announced on state television that Chávez had died in a military hospital in Caracas at 16:25 VET (20:55 UTC). The Vice President said Chávez died "after battling a tough illness for nearly two years". According to the head of Venezuela's presidential guard, Chávez died from a massive heart attack, and his cancer of the pelvic region was very advanced when he died. Gen. Jose Ornella said that near the end of his life Chávez "couldn’t speak but he said it with his lips... ‘I don’t want to die. Please don’t let me die,’ because he loved his country, he sacrificed himself for his country". Chávez is survived by four children and

Honors and awards.

Recognition.

The United States-based "Time" magazine included Chávez among their list of the world's 100 most influential people in 2005 and 2006, noting the spreading of his anti-globalization efforts and anti-US sentiment throughout Latin America. In a 2006 list compiled by the left wing British magazine "New Statesman", he was voted 11th in the list of "Heroes of our time". In 2010 the magazine included Chávez in its annual "The World's

Honorary degrees.

Chávez was awarded

References.

Bibliography.

Books Academic articles News articles,

Hugo Rafael Chávez Frías (, ; 28 July 1954 – 5 March 2013) was a Venezuelan politician who was president of Venezuela from 1999 until his death in 2013. Chávez was also leader of the Fifth Republic Movement political party from its foundation in 1997 until 2007, when it merged with several other parties to form the United Socialist Party of Venezuela (PSUV), which he led until 2012.

Hugo Rafael Chávez Frías [] (* 28. Juli 1954 in Sabaneta; † 5. März 2013 in Caracas) war ein venezolanischer Offizier und Politiker. Von 1999 bis zu seinem Tod 2013 war er der 62. Staatspräsident Venezuelas.