EuclidEuclid (ˈjuːklɪd; Εὐκλείδης; 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus.
Portrait paintingPortrait painting is a genre in painting, where the intent is to represent a specific human subject. The term 'portrait painting' can also describe the actual painted portrait. Portraitists may create their work by commission, for public and private persons, or they may be inspired by admiration or affection for the subject. Portraits often serve as important state and family records, as well as remembrances. Historically, portrait paintings have primarily memorialized the rich and powerful.
PaintPaint is a liquid pigment that, after application to a solid material, and allowed to dry, adds a film-like layer to protect, add color, or provide texture. Paint can be made in many colors—and in many different types. Most paints are either oil-based or water-based, and each has distinct characteristics. For one, it is illegal in most municipalities to discard oil-based paint down household drains or sewers. Clean-up solvents are also different for water-based paint than oil-based paint.
PortraitA portrait is a painting, photograph, sculpture, or other artistic representation of a person, in which the face and its expressions are predominant. The intent is to display the likeness, personality, and even the mood of the person. For this reason, in photography a portrait is generally not a snapshot, but a composed image of a person in a still position. A portrait often shows a person looking directly at the painter or photographer, in order to most successfully engage the subject with the viewer.
GeometryGeometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts.
Self-portraitA self-portrait is a portrait of an artist made by that artist. Although self-portraits have been made since the earliest times, it is not until the Early Renaissance in the mid-15th century that artists can be frequently identified depicting themselves as either the main subject, or as important characters in their work. With better and cheaper mirrors, and the advent of the panel portrait, many painters, sculptors and printmakers tried some form of self-portraiture.
Spent nuclear fuelSpent nuclear fuel, occasionally called used nuclear fuel, is nuclear fuel that has been irradiated in a nuclear reactor (usually at a nuclear power plant). It is no longer useful in sustaining a nuclear reaction in an ordinary thermal reactor and, depending on its point along the nuclear fuel cycle, it will have different isotopic constituents than when it started. Nuclear fuel rods become progressively more radioactive (and less thermally useful) due to neutron activation as they are fissioned, or "burnt" in the reactor.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Oil paintOil paint is a type of slow-drying paint that consists of particles of pigment suspended in a drying oil, commonly linseed oil. The viscosity of the paint may be modified by the addition of a solvent such as turpentine or white spirit, and varnish may be added to increase the glossiness of the dried oil paint film. The addition of oil or alkyd medium can also be used to modify the viscosity and drying time of oil paint. Oil paints were first used in Asia as early as the 7th century AD and can be seen in examples of Buddhist paintings in Afghanistan.
Euclidean geometryEuclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
Non-Euclidean geometryIn mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries.
Spent fuel poolSpent fuel pools (SFP) are storage pools (or "ponds" in the United Kingdom) for spent fuel from nuclear reactors. They are typically 40 or more feet (12 m) deep, with the bottom 14 feet (4.3 m) equipped with storage racks designed to hold fuel assemblies removed from reactors. A reactor's local pool is specially designed for the reactor in which the fuel was used and is situated at the reactor site. Such pools are used for short-term cooling of the fuel rods.
Elliptic geometryElliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry.
Hyperbolic geometryIn mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in the plane containing both line R and point P there are at least two distinct lines through P that do not intersect R. (Compare the above with Playfair's axiom, the modern version of Euclid's parallel postulate.) The hyperbolic plane is a plane where every point is a saddle point.
Projective geometryIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa.
Synthetic geometrySynthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is geometry without the use of coordinates. It relies on the axiomatic method for proving all results from a few basic properties initially called postulate, and at present called axioms. The term "synthetic geometry" has been coined only after the 17th century, and the introduction by René Descartes of the coordinate method, which was called analytic geometry.
Acrylic paintAcrylic paint is a fast-drying paint made of pigment suspended in acrylic polymer emulsion and plasticizers, silicone oils, defoamers, stabilizers, or metal soaps. Most acrylic paints are water-based, but become water-resistant when dry. Depending on how much the paint is diluted with water, or modified with acrylic gels, mediums, or pastes, the finished acrylic painting can resemble a watercolor, a gouache, or an oil painting, or have its own unique characteristics not attainable with other media.
Nuclear flaskA nuclear flask is a shipping container that is used to transport active nuclear materials between nuclear power station and spent fuel reprocessing facilities. Each shipping container is designed to maintain its integrity under normal transportation conditions and during hypothetical accident conditions. They must protect their contents against damage from the outside world, such as impact or fire. They must also contain their contents from leakage, both for physical leakage and for radiological shielding.
Euclid's ElementsEuclid's Elements (Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.
Algebraic geometryAlgebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.
