Encyclopedia > Parallel

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Parallel has two important meanings:

  • A line of latitude, so called because latitude lines appear superficially to be parallel, whereas longitude lines do not. (in fact, the converse is true: latitude lines are concentric circles, not lines, and longitude lines are great circles, that is straight lines in the local non-Euclidean geometry.
  • A property of straight lines, described below:

Parallel (in Geometry)

Parallel is a term in geometry and in everyday life which refers two a property in Euclidean space of two or more lines or planes, or a combination of these.

When lines or planes are parallel, then every point on one is located exactly the same minimum distance from the other line or plane. Another way of defining it is that any two parallel lines or planes, if extended to infinity in both directions, will never intersect. This second definition carries the condition that the extension must occur only in one additional dimension: In other words, lines must be located in the same plane and planes must be located in the same three-dimensional space. A combination of a line and a plane may be located in the same three-dimensional space. A third definition is if two lines are both intersected by a third line in the same plane, and the angles of intersection are equal, then the two lines are parallel.

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