Projective range

In mathematics, a projective range is a set of points in projective geometry considered in a unified fashion. A projective range may be a projective line or a conic. A projective range is the dual of a pencil of lines on a given point. For instance, a correlation interchanges the points of a projective range with the lines of a pencil. A projectivity is said to act from one range to another, though the two ranges may coincide as sets.

A projective range expresses projective invariance of the relation of projective harmonic conjugates. Indeed, three points on a projective line determine a fourth by this relation. Application of a projectivity to this quadruple results in four points likewise in the harmonic relation. Such a quadruple of points is termed a harmonic range. In 1940 Julian Coolidge described this structure and identified its originator:

Conic ranges

When a conic is chosen for a projective range, and a particular point E is selected as origin on the conic, then addition of points may be defined as follows:

Range

Range may refer to:

Mathematics, science, technology, and music

In mathematics

In science

In technology

Orange Range

Orange Range (オレンジレンジ, Orenji Renji) is a 5-member Japanese rock band, based in Okinawa, Japan. Formed in 2001, the band began with Spice Music and later signed with Sony Music Japan's gr8! records division in 2003. The group left gr8! records in 2010 to start their own label, Super Echo.

History

2002

The band has roots in Okinawa, an area famous for being the home of many well-known acts. Before they were signed by a major label, Orange Range played mostly in small art houses and clubs until they were found by a record agent. The band is mix of pop- and rock-style music as can be heard by the vocals and the instrumentals. Their style is also made up of many different cultures and musical styles from around the world. This is attributed to their hometown being Okinawa, a well-known station for American military bases and, thus, cultures and different styles often blend. Due to high sales of their works, Orange Range's singles are often attached to various movies, shows or Japanese products. This is usually seen as a sign of a band or singer having hit "the big time" in the Japanese media.

Range (computer programming)

In computer science, the term range may refer to one of three things:

Range of a variable

The range of a variable is given as the set of possible values that that variable can hold. In the case of an integer, the variable definition is restricted to whole numbers only, and the range will cover every number within its range (including the maximum and minimum). For example, the range of a signed 16-bit integer variable is all the integers from −32,768 to +32,767.

Range of an array

When an array is numerically indexed, its range is the upper and lower bound of the array. Depending on the environment, a warning, a fatal error, or unpredictable behavior will occur if the program attempts to access an array element that is outside the range. In some programming languages, such as C, arrays have a fixed lower bound (zero) and will contain data at each position up to the upper bound (so an array with 5 elements will have a range of 0 to 4). In others, such as PHP, an array may have holes where no element is defined, and therefore an array with a range of 0 to 4 will have up to 5 elements (and a minimum of 2).