Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted .

In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted.

Types of triangle

By lengths of sides

Triangles can be classified according to the lengths of their sides:

Wye (rail)

A wye or triangular junction, in rail terminology, is a triangular shaped arrangement of rail tracks with a switch or set of points at each corner. In mainline railroads, this can be used at a rail junction, where two rail lines join, in order to allow trains to pass from one line to the other line.

Wyes can also be used for turning railway equipment. By performing the railway equivalent of a three-point turn, the direction of travel and the relative orientation of a locomotive or railway vehicle can be reversed, resulting in it facing in the direction from which it came. Where a wye is built specifically for reversing purposes, one or more of the tracks making up the junction will typically be a stub siding.

Tram or streetcar tracks also make use of triangular junctions and sometimes have a short triangle or wye stubs to turn the car at the end of the line.

Considerations

At junctions

The use of triangular junctions allows flexibility in routing trains from any line to any other line, without the need to reverse the train. For this reason they are common across most rail networks. Slower bi-directional trains may enter a wye, letting a faster one pass, and continue on the same direction providing service to nearby freight transport or a passenger station.

Triangle (The X-Files)

"Triangle" is the third episode of the sixth season of the American science fiction television series The X-Files and premiered on the Fox network on November 22, 1998. Written and directed by series creator Chris Carter, "Triangle" is a "Monster-of-the-Week" episode, a stand-alone plot which is unconnected to the overarching mythology of The X-Files. "Triangle" earned a Nielsen household rating of 10.8, being watched by 18.20 million viewers in its initial broadcast. The episode generally received positive reviews, with many critics commenting on the episode's unique directing style.

The show centers on FBI special agents Fox Mulder (David Duchovny) and Dana Scully (Gillian Anderson), who work on cases linked to the paranormal, called X-Files. Mulder is a believer in the paranormal, and the skeptical Scully has been assigned to debunk his work. However, the two have developed a close friendship. In this episode, Mulder races to a luxury passenger liner which has mysteriously appeared on the edge of the Bermuda Triangle. Once there, he realizes he has traveled back in time to September 3, 1939—the outbreak of World War II. Nazi soldiers have boarded the ship in search of "Thor's Hammer", something that could ensure victory in the coming conflict. Meanwhile, Scully, after being informed of Mulder's disappearance by The Lone Gunmen, rushes through the J. Edgar Hoover Building, looking for someone who can help find her missing partner.

Triangle (1981 TV series)

Triangle was a BBC Television soap opera in the early 1980s, set aboard a North Sea ferry which sailed from Felixstowe to Gothenburg and Gothenburg to Amsterdam. A third imaginary leg existed between Amsterdam and Felixstowe to justify the programme title, but this was not operated by the ferry company. The show ran for three series before being cancelled, but is still generally remembered as "some of the most mockable British television ever produced". The scripts involved clichéd relationships and stilted dialogue, making the show the butt of several jokes - particularly on Terry Wogan's morning Radio 2 programme - which caused some embarrassment to the BBC.

In 1992, the BBC screened TV Hell, an evening of programming devoted to the worst television had to offer, and the first episode of Triangle was broadcast as part of the line-up.

The ferry used in the first series was the Tor Line's MS Tor Scandinavia. In the second and third series this was replaced by the DFDS vessel Dana Anglia (DFDS having acquired Tor Line by this time) probably because she had a less intensive schedule and the longer time she spent in port made on-board filming easier.

The Triangle (newspaper)

The Triangle is the independent student newspaper of Drexel University in Philadelphia, Pennsylvania. Editions of the paper are printed early every Friday morning; they are distributed in buildings on Drexel's campus as well as in select locations in University City, Philadelphia.

The Triangle was first published on February 1, 1926, under the direction of students with University advisors functioning only to offer advice. Publication has been on a weekly schedule during the academic school year with bi-weekly publication during summer. The Triangle began publishing in color in the summer of 2004. During the summer of 2007 publishing switched from tabloid to broadsheet format. Sections include News, Op-ed (also called Ed-op), Arts & Entertainment, Sports, Comics, and Classified ads.

The Triangle has won several Mark of Excellence Awards which honor the best in Student Journalism from the Society of Professional Journalists. First place in Editorial Writing (2000), General Column Writing (2000), Second place in Editorial Writing (2001), and third place in Sports Column Writing (2001). In 2004 it won two National Pacemaker Awards for excellence in college newspapers.

Rack (billiards)

A rack (sometimes known as a triangle) is the name given to a frame (usually wood, plastic or metal) used to organize billiard balls at the beginning of a game. Rack may also be used as a verb to describe the act of setting billiard balls in starting position in billiards games that make use of racks (usually, but not always, using a physical rack), as well as a noun to describe the balls in that starting position.

The most common shape of a physical rack is that of a triangle, with the ball pattern of 5-4-3-2-1. Racks are sometimes called simply "triangles" (most often by amateur shooters) based on the predominance of this form. Triangular-shaped racks are used for eight-ball, straight pool, one-pocket, bank pool, snooker and many other games. Although diamond-shaped racks, with an intended pattern of 1-2-3-2-1, are made for the game of nine-ball, the triangular rack is more often employed in nine ball as well.

Racking in specific billiards games

Eight-ball

In eight-ball, fifteen object balls are used. Under the Billiard Congress of America's World Standardized Rules: 8-Ball it is prescribed that: