Glossary of chess

This page explains commonly used terms in chess in alphabetical order. Some of these have their own pages, like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of chess-related games, see Chess variants.

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[adjective: prophylactic] Prophylactic techniques include the blockade, overprotection, and the mysterious rook move.

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References

Bibliography

Space (mathematics)

In mathematics, a space is a set (sometimes called a universe) with some added structure.

Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space. For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space such that:

where the norm is indicated by enclosing in double vertical lines, and the inner product is indicated enclosing in by angle brackets.

Modern mathematics treats "space" quite differently compared to classical mathematics.

History

Before the golden age of geometry

In the ancient mathematics, "space" was a geometric abstraction of the three-dimensional space observed in the everyday life. Axiomatic method had been the main research tool since Euclid (about 300 BC). The method of coordinates (analytic geometry) was adopted by René Descartes in 1637. At that time, geometric theorems were treated as an absolute objective truth knowable through intuition and reason, similar to objects of natural science; and axioms were treated as obvious implications of definitions.

Five-dimensional space

A five-dimensional space is a space with five dimensions. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativitistic physics. It is an abstraction which occurs frequently in mathematics, where it is a legitimate construct. In physics and mathematics, a sequence of N numbers can be understood to represent a location in an N-dimensional space. Whether or not the actual universe in which we live is five-dimensional is a topic of debate.

Physics

Much of the early work on five dimensional space was in an attempt to develop a theory that unifies the four fundamental forces in nature: strong and weak nuclear forces, gravity and electromagnetism. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.

Lotna

Lotna is a Polish war film released in 1959 and directed by Andrzej Wajda.

Overview

This highly symbolic movie is both the director's tribute to the long and glorious history of the Polish cavalry, as well as a more ambiguous portrait of the passing of an era. Wajda was the son of a Polish Cavalry officer who was murdered by the Soviets during the Katyn massacre.

The horse Lotna represents the entire Romantic tradition in culture, a tradition that had a huge influence in the course of Polish history and the formation of Polish literature. Lotna is Wajda's meditation on the historical breaking point that was 1939, as well as a reflection on the ending of an entire era for literature and culture in Poland and in Europe as a whole. Writing of the film, Wajda states that it "held great hopes for him, perhaps more than any other." Sadly, Wajda came to think of Lotna "a failure as a film."

The film remains highly controversial, as Wajda includes a mythical scene in which Polish horsemen suicidally charge a unit of German tanks, an event that never actually happened.

Speed (South Korean band)

Speed (Korean: 스피드; commonly stylized as SPEED) is a South Korean boy group formed by MBK Entertainment (formerly known as Core Contents Media) in 2012. The group was also formerly known as the "Male Unit" of Coed School until their agency announced that they were an independent group in 2013.

Speed was originally a six-member group composed of Kwanghaeng, Noori, Jungwoo, Taewoon, Sungmin, and Jongkook. In January 2012, they released their first song "Lovey-Dovey Plus." A few days after their first song release, Sejun joined the group. Following Kwanghaeng and Noori's withdrawal from the group in September 2012, Yuhwan and Taeha were added in October 2012. Speed officially debuted as a seven-member group with the release of their first single "It's Over" in January 2013. In March 2015, leader Taewoon left Speed to pursue a solo career. Yuhwan replaced Taewoon as Speed's leader and a new member, KI-O, was added in May 2015.

History

2011–2012: Co-Ed School Sub-Units, Formation, and Pre-debut Projects

Four-velocity

In physics, in particular in special relativity and general relativity, a four-velocity is a four-vector in four-dimensional spacetime that represents the relativistic counterpart of velocity, which is a three-dimensional vector in space.

Physical events correspond to mathematical points in time and space, the set of all of them together forming a mathematical model of physical four-dimensional spacetime. The history of an object traces a curve in spacetime, called its world line. If the object is massive, so that its speed is less than the speed of light, the world line may be parametrized by the proper time of the object. The four-velocity is the rate of change of four-position with respect to the proper time along the curve. The velocity, in contrast, is the rate of change of the position in (three-dimensional) space of the object, as seen by an observer, with respect to the observer's time.

The value of the magnitude of an object's four-velocity, i. e. the quantity obtained by applying the metric tensor g to the four-velocity u, that is ||u||² = u ⋅ u = g_μνu^νu^μ, is always equal to ±c², where c is the speed of light. Whether the plus or minus sign applies depends on the choice of metric signature. For an object at rest its four-velocity is parallel to the direction of the time coordinate with u⁰ = c. A four-velocity is thus the normalized future-directed timelike tangent vector to a world line, and is a contravariant vector. Though it is a vector, addition of two four-velocities does not yield a four-velocity: The space of four-velocities is not itself a vector space.

Sanctuary (season 1)

The first season of the Canadian science fiction–fantasy television series Sanctuary premiered on the Sci Fi Channel in the United States on October 3, 2008, and concluded on ITV4 in the United Kingdom on January 5, 2009, after 13 episodes. It follows the actions of a secret organization known as the Sanctuary, who track down a series of creatures known as abnormals, and then bring them to the Sanctuary for refuge. The main story arc of the season involves the Sanctuary working against the Cabal, an organization who seek to control all abnormals for their own gain. Amanda Tapping, Robin Dunne, Emilie Ullerup, and Christopher Heyerdahl are billed in the opening credits as the main cast.

Initially an eight-part web series, Sanctuary was successful enough for Sci Fi to commission a television series. Series creator and head writer Damian Kindler hired Sam Egan, and the two wrote all the episodes and composed the season-long storyline. Many episodes had been written throughout the 2007 Christmas season before the season was green-lit. Principal photography started in May 2008. It was the first instance in North American television where RED cameras were used. Most of the season was filmed using green screen in a warehouse in Burnaby, British Columbia, though there are instances throughout that were filmed on location, including the Riverview Hospital in Coquitlam and the North Shore Mountains outside Vancouver. Anthem Visual Effects produced the season's visual effects. The virtual sets meant that they produced around 400 visual effects per episode. Other forms of special effects, including prosthetics, were used to present the abnormals. The first season was budgeted at an estimated $21 million.