Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line distances along each axis from O to P:

The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces in any number of dimensions.

Definition

Three dimensions

In three dimensions, any set of three dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used.

Commonly, one uses the familiar Cartesian coordinate system, or sometimes spherical polar coordinates, or cylindrical coordinates;

where t is a parameter, owing to their rectangular or circular symmetry. These different coordinates and corresponding basis vectors represent the same position vector. More general curvilinear coordinates could be used instead, and are in contexts like continuum mechanics and general relativity (in the latter case one needs an additional time coordinate).

Position (music)

On a string instrument, position is the relative location of the hand on the instrument's neck, indicated by ordinal numbers (e.g., 3rd). Fingering, independent of position, is indicated by numbers, 1-4, and string is indicated by Roman numerals, I-IV. Different positions on the same string are reached through shifting.

With experience, string players become accustomed to the required shape and position of the left hand. Some positions are located relative to certain touch references, or landmarks on the instrument. For example, fourth position on the cello (used in the example below) has the player's thumb resting in the "saddle" of the neck root. Similarly, higher positions on the violin make use of the instrument's "shoulder" (treble-side edge of the top's upper bout) as a touch reference. Some electric string instruments, without a traditionally shaped body, still incorporate a reference feature imitating that shoulder's shape.

Trombone position

The trombone produces notes within its range by extending the main slide to different positions. In first position, the length of the bore is at its shortest; seventh position puts the slide at its furthest extension, at the edge of the inner slide's stockings. (These are sections of slightly greater diameter at the ends of the inner slide tubes.) Positions 3 and 4 may be located by referring the player's right hand to the bell of the instrument. Each player "has a different way of visualizing where the positions of the slide trombone are in relation to each other" Positions, especially in the higher register, may need to be shortened or lengthened (sharpened or flattened) to play in tune. Lower-numbered (shorter) positions are closer together than higher-numbered ones. Positions six and seven are primarily useful in the lower part of the trombone's range.

Position (obstetrics)

In obstetrics, position is the orientation of the fetus in the womb, identified by the location of the presenting part of the fetus relative to the pelvis of the mother. Conventionally, it is the position assumed by the fetus before the process of birth, as the fetus assumes various positions and postures during the course of childbirth.

Positions

Depending upon which part of the fetus is expected to be delivered first (fetal presentation), there are many possible positions:

ULTra (rapid transit)

ULTra (Urban Light Transit) is a personal rapid transit system developed by the British engineering company ULTra Global PRT (formerly Advanced Transport Systems).

The first public system opened at London's Heathrow Airport in May 2011. It consists of 21 vehicles operating on a 3.9-kilometre (2.4 mi) route connecting Terminal 5 to its business passenger car park, just north of the airport. ULTra is in contention to develop an urban system in Amritsar, India projected to carry up to 100,000 passengers per day using 200 vehicles.

To reduce fabrication costs, ULTra uses largely off-the-shelf technologies, such as rubber tyres running on an open guideway. This approach has resulted in a system that ULTra believes to be economical; the company reports that the total cost (vehicles, infrastructure and control systems) is between £3 million and £5 million per kilometre of guideway.

Inception

The system was originally designed by Martin Lowson and his design team, Lowson having put £10 million into the project. He formed Advanced Transport Systems (ATS) in Cardiff to develop the system, and their site was later the location of its test track. ULTra has twice been awarded funding from the UK National Endowment for Science, Technology and the Arts (NESTA). Much of the original research on ULTra was done by the Aerospace Engineering department at the University of Bristol during the 1990s. Recently the company renamed itself "ULTra PRT Limited" to better reflect its primary business, and moved its corporate headquarters to Bristol.

Pod (sculpture)

Pod is the name of a 2002 modern sculpture by American artist Pete Beeman, currently installed at Southwest 10th Avenue and West Burnside Street in downtown Portland, Oregon. The 30-foot sculpture, intended to represent the "infrastructure, energy, and vibrancy of Portland", is supported by its static tripod base with a 15-foot diameter. It is constructed from stainless steel, galvanized steel, bronze, titanium, lead and other materials. Pod was fabricated by Beeman and David Bermudez, and engineered by Beeman and Peterson Structural Engineers. It is considered interactive and kinetic, with a central, vertical pendulum that swings back and forth when pushed. The sculpture cost as much as $50,000 and was funded by the Portland Streetcar Project. Pod is part of the City of Portland and Multnomah County Public Art Collection courtesy of the Regional Arts & Culture Council.

Description and history

Pod was designed by native Portland resident Pete Beeman as a public art project for the Portland Streetcar. According to Beeman and the Regional Arts & Culture Council, the modern sculpture is designed to represent the "infrastructure, energy, and vibrancy of Portland". Of the work's design, Beeman said:

Pod (Afro Celt Sound System album)

Pod, released May 4, 2004 by Real World Records, is essentially a remix album by Afro Celt Sound System of their first three albums, Volume 1: Sound Magic, Volume 2: Release, and Volume 3: Further in Time, done by members of the band and new artists as well, including some songs previously unavailable. It is also accompanied by a DVD of some music videos and some clips of their live tour.

Track listing

Two pounds (British coin)

The British two pound (£2) coin is a denomination of the pound sterling. Its obverse has featured the profile of Queen Elizabeth II since the coin’s introduction. Two different portraits of the Queen have been used, with the latest design by Jody Clark being introduced in 2015. The reverse features an abstract design symbolising the history of technological achievement. A new reverse design featuring Britannia began to enter circulation during 2015.

The coin was introduced on 15 June 1998 (coins minted 1997) after a review of the United Kingdom's coinage decided that a general-circulation £2 coin was needed. The new bi-metallic design replaced a series of commemorative, uni-metallic coins which were issued between 1986 and 1996 to celebrate special occasions. Although legal tender, these coins have never been common in everyday circulation.

As of March 2014 there were an estimated 417 million £2 coins in circulation with an estimated face value of £831.756 million.