Algebraic varietyAlgebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.
Rational varietyIn mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set of indeterminates, where d is the dimension of the variety. Let V be an affine algebraic variety of dimension d defined by a prime ideal I = ⟨f1, ..., fk⟩ in . If V is rational, then there are n + 1 polynomials g0, ..., gn in such that In order words, we have a of the variety.
Power toolA power tool is a tool that is actuated by an additional power source and mechanism other than the solely manual labor used with hand tools. The most common types of power tools use electric motors. Internal combustion engines and compressed air are also commonly used. Tools directly driven by animal power are not generally considered power tools. Power tools are used in industry, in construction, in the garden, for housework tasks such as cooking, cleaning, and around the house for purposes of driving (fasteners), drilling, cutting, shaping, sanding, grinding, routing, polishing, painting, heating and more.
ToolA tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.
Television showA television show – or simply TV show – is the general reference to any content produced for viewing on a television set which is broadcast via over-the-air, satellite, or cable. This includes content made by television broadcasters and content made for broadcasting by film production companies. It excludes breaking news, advertisements, or trailers that are typically placed between shows. Television shows are most often scheduled for broadcast well ahead of time and appear on electronic guides or other TV listings, but streaming services often make them available for viewing anytime.
Production companyA production company, production house, production studio, or a production team is a studio that creates works in the fields of performing arts, new media art, film, television, radio, comics, interactive arts, video games, websites, music, and video. These groups consist of technical staff to produce the media, and are often incorporated as a commercial publisher. Generally the term refers to all individuals responsible for the technical aspects of creating a particular product, regardless of where in the process their expertise is required, or how long they are involved in the project.
Aspect ratio (image)The aspect ratio of an image is the ratio of its width to its height, and is expressed with two numbers separated by a colon, such as 16:9, sixteen-to-nine. For the x:y aspect ratio, the image is x units wide and y units high. Common aspect ratios are 1.85:1 and 2.39:1 in cinematography, 4:3 and 16:9 in television photography, and 3:2 in still photography. The common film aspect ratios used in cinemas are 1.85:1 and 2.39:1. Two common videographic aspect ratios are 4:3 (1.:1), the universal video format of the 20th century, and 16:9 (1.
16 mm film16 mm film is a historically popular and economical gauge of film. 16 mm refers to the width of the film (about inch); other common film gauges include 8 and 35 mm. It is generally used for non-theatrical (e.g., industrial, educational, televisual) film-making, or for low-budget motion pictures. It also existed as a popular amateur or home movie-making format for several decades, alongside 8 mm film and later Super 8 film. Eastman Kodak released the first 16 mm "outfit" in 1923, consisting of a camera, projector, tripod, screen and splicer, for US$335 ().
Complete varietyIn mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the morphism is a closed map (i.e. maps closed sets onto closed sets). This can be seen as an analogue of compactness in algebraic geometry: a topological space X is compact if and only if the above projection map is closed with respect to topological products. The image of a complete variety is closed and is a complete variety. A closed subvariety of a complete variety is complete.
