What is "parabola"

Parabola \Pa*rab"o*la\, n.; pl. Parabolas. [NL., fr. Gr. ?; -- so called because its axis is parallel to the side of the cone. See Parable, and cf. Parabole.] (Geom.)

1. A kind of curve; one of the conic sections formed by the intersection of the surface of a cone with a plane parallel to one of its sides. It is a curve, any point of which is equally distant from a fixed point, called the focus, and a fixed straight line, called the directrix. See Focus.

2. One of a group of curves defined by the equation y = ax^ n where n is a positive whole number or a positive fraction. For the cubical parabola n = 3; for the semicubical parabola n = 3/2. See under Cubical, and Semicubical. The parabolas have infinite branches, but no rectilineal asymptotes.

1570s, from Modern Latin parabola, from Greek parabole "parabola, comparison, analogy; application" (see parable), so called by Apollonius of Perga c.210 B.C.E. because it is produced by "application" of a given area to a given straight line. It had a different sense in Pythagorean geometry. Related: Parabolic.

n. 1 (context geometry English) The conic section formed by the intersection of a cone with a plane parallel to a tangent plane to the cone; the locus of points equidistant from a fixed point (the focus) and line (the directrix). 2 (context rhetoric English) The explicit drawing of a parallel between two essentially dissimilar things, especially with a moral or didactic purpose. A parable.

n. a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve

A parabola is a mathematical curve.

Parabola may also refer to:

Parabola is a genus of moth in the family Gelechiidae. It contains the species Parabola butyraula, which is found in South Africa ( Mpumalanga).

The wingspan is about 15 mm. The forewings are fuscous with a broad light ochreous-yellow streak along the dorsum throughout, from beyond the middle dilated so as to reach half across the wing. There is a fine strongly-curved violet-whitish line from three-fourths of the costa to the tornus, finely edged with dark fuscous posteriorly, margined anteriorly by an ochreous-yellow line edged with a few fuscous scales, and posteriorly on the upper half by a similar line terminated beneath by a blackish dot. The apical prominence is silvery-whitish. The hindwings are pale greyish, on the tornus tinged with whitish-ochreous.

"Parabola" is a song by the American rock band Tool, the song was released as the second single from their third studio album Lateralus. It was released in 2002 as a promo only, however, on December 20, 2005, the single was re-released, which includes the song and a DVD containing the music video and an optional "dual" audio commentary on the video by Jello Biafra of Dead Kennedys fame. The dual commentary consists of two separate recordings of Biafra's voice, one playing in each stereo channel. The DVD was released alongside a DVD single for " Schism" as well.

The song is featured on the video game Guitar Hero World Tour. The song was played onboard Space Shuttle mission STS-130, as a wake-up call for astronaut Robert Behnken.

Parabola is a double album by jazz composer, arranger, conductor and pianist Gil Evans recorded in Italy in 1978 by Evans with an orchestra featuring Arthur Blythe, Steve Lacy, and Lew Soloff and released on the Italian Horo label.

A parabola (; plural parabolas or parabolae, adjective parabolic, from ) is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several superficially different mathematical descriptions which can all be proved to define curves of exactly the same shape.

One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane which is parallel to another plane which is tangential to the conical surface. A third description is algebraic. A parabola is a graph of a quadratic function, y = x, for example.

The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the " axis of symmetry". The point on the parabola that intersects the axis of symmetry is called the " vertex", and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola which is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are geometrically similar.

Parabolas have the property that, if they are made of material that reflects light, then light which travels parallel to the axis of symmetry of a parabola and strikes its concave side is reflected to its focus, regardless of where on the parabola the reflection occurs. Conversely, light that originates from a point source at the focus is reflected into a parallel (" collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other forms of energy. This reflective property is the basis of many practical uses of parabolas.

The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas.

Strictly, the adjective parabolic should be applied only to things that are shaped as a parabola, which is a two-dimensional shape. However, as shown in the last paragraph, the same adjective is commonly used for three-dimensional objects, such as parabolic reflectors, which are really paraboloids. Sometimes, the noun parabola is also used to refer to these objects. Though not perfectly correct, this usage is generally understood.

Parabola: Where Spiritual Traditions Meet, whose founder and editor was D.M. Dooling, began publishing in 1976 as a quarterly magazine on the subjects of mythology and the world's religious and cultural traditions. It is published by The Society for the Study of Myth and Tradition, a not-for-profit organization. The name of the magazine is explained by the editors as follows:

The parabola represents the epitome of a quest. It is the metaphorical journey to a particular point, and then back home, along a similar path perhaps, but in a different direction, after which the traveler is essentially, irrevocably changed.

The magazine's subtitle has changed over the years. In its first years, it was Parabola: Myth and the Quest for Meaning, then Parabola: The Magazine of Myth and Tradition, later Parabola: Myth, Tradition, and the Search for Meaning, and now its current form.