Track geometry

Track geometry is three-dimensional geometry of track layouts and associated measurements used in design, construction and maintenance of railroad tracks. The subject is used in the context of standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Although, the geometry of the tracks is three-dimensional by nature, the standards are usually expressed in two separate layouts for horizontal and vertical.

Layout

Horizontal layout

Horizontal layout is the track layout on the horizontal plane. This can be thought of as the plan view which is a view of a 3-dimensional track from the position above the track. In track geometry, the horizontal layout involves the layout of three main track types: tangent track (straight line), curved track, and track transition curve (also called transition spiral or spiral) which connects between a tangent and a curved track.

In Australia, there is a special definition for a bend (or a horizontal bend) which is a connection between two tangent tracks at almost 180 degrees (with deviation not more than 1 degree 50 minutes) without an intermediate curve. There is a set of speed limits for the bends separately from normal tangent track.

Track

Track or Tracks may refer to:

Electronics and computing

Entertainment

Song

A song is a single (and often standalone) work of music intended to be sung by the human voice with distinct and fixed pitches and patterns using sound and silence and a variety of forms that often include the repetition of sections. Written words created specifically for music or for which music is specifically created, are called lyrics. If a pre-existing poem is set to composed music in classical music it is an art song. Songs that are sung on repeated pitches without distinct contours and patterns that rise and fall are called chants. Songs in a simple style that are learned informally are often referred to as folk songs. Songs that are composed for professional singers are called popular songs. These songs, which have broad appeal, are often composed by professional songwriters, composers and lyricists. Art songs are composed by trained classical composers for concert performances. Songs are performed live and recorded. Songs may also appear in plays, musical theatre, stage shows of any form, and within operas.

Trail

A trail is usually a path, track or unpaved lane or road, though the term is also applied, in North America, to routes along rivers, and sometimes to highways. In the United Kingdom and the Republic of Ireland path or footpath is the preferred term for a walking trail. Some trails are single use and can only be used for walking, cycling, horse riding, snow shoeing, cross-country skiing, etc., others, as in the case of a bridleway in the UK, are multi-use, and can be used by walkers, cyclists and equestrians.

There are also unpaved trails used by dirt bikes and other off road vehicles. In some places, like the Alps, trails are used for moving cattle and other livestock (see transhumance). In the US historically, the term was used for a route into or through wild territory used by emigrants (e.g. the Oregon Trail).

Usage

In Australia, the term track can be used interchangeably with trail, and can refer to anything from a dirt road to an unpaved pedestrian path. The term trail gained popularity during World War II, when many servicemen from the United States were stationed in Australia, which probably influenced its being adopted by elements of the Australian media at the time (see Kokoda Track).

Geometric group action

In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.

Definition

In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions:

Uniqueness

If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.

Examples

Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.

References

Geometry (disambiguation)

Geometry is a branch of mathematics dealing with spatial relationships.

Geometry or geometric may also refer to: