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In geometry the **orientation**, **angular position**, or **attitude** of an object such as a line, plane or rigid body is part of the description of how it is placed in the space it is in.
Namely, it is the imaginary rotation that is needed to move the object from a reference placement to its current placement. A rotation may not be enough to reach the current placement. It may be necessary to add an imaginary translation, called the object's location (or position, or linear position). The location and orientation together fully describe how the object is placed in space. The above mentioned imaginary rotation and translation may be thought to occur in any order, as the orientation of an object does not change when it translates, and its location does not change when it rotates.

Euler's rotation theorem shows that in three dimensions any orientation can be reached with a single rotation around a fixed axis. This gives one common way of representing the orientation using an axis–angle representation. Other widely used methods include rotation quaternions, Euler angles, or rotation matrices. More specialist uses include Miller indices in crystallography, strike and dip in geology and grade on maps and signs.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Orientation_(geometry)

**Geometry** (from the Ancient Greek: γεωμετρία; *geo-* "earth", *-metron* "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of formal mathematical science emerging in the West as early as Thales (6th century BC). By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow.Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially as it relates to mapping the positions of stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. In the classical world, both geometry and astronomy were considered to be part of the Quadrivium, a subset of the seven liberal arts considered essential for a free citizen to master.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Geometry

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

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:

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*.

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

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Geometric_group_action

* Geometry* is the second album by electronic musician Jega, released in 2000 on the Planet Mu label.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Geometry_(Jega_album)

In mathematics, **orientation** is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed. In linear algebra, the notion of orientation makes sense in arbitrary finite dimension. In this setting, the orientation of an ordered basis is a kind of asymmetry that makes a reflection impossible to replicate by means of a simple rotation. Thus, in three dimensions, it is impossible to make the left hand of a human figure into the right hand of the figure by applying a rotation alone, but it is possible to do so by reflecting the figure in a mirror. As a result, in the three-dimensional Euclidean space, the two possible basis orientations are called right-handed and left-handed (or right-chiral and left-chiral).

The orientation on a real vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space, right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an **oriented** vector space, while one not having an orientation selected, is called **unoriented**.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Orientation_(vector_space)

* Orientation* is Sonata Arctica's second EP released on August 22, 2001 through the label Spinefarm Records.

All songs written and composed by Tony Kakko.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Orientation_(EP)

In **passive solar building design**, windows, walls, and floors are made to collect, store, and distribute solar energy in the form of heat in the winter and reject solar heat in the summer. This is called passive solar design because, unlike active solar heating systems, it does not involve the use of mechanical and electrical devices.

The key to design a passive solar building is to best take advantage of the local climate performing an accurate site analysis. Elements to be considered include window placement and size, and glazing type, thermal insulation, thermal mass, and shading. Passive solar design techniques can be applied most easily to new buildings, but existing buildings can be adapted or "retrofitted".

*Passive solar* technologies use sunlight without active mechanical systems (as contrasted to active solar). Such technologies convert sunlight into usable heat (in water, air, and thermal mass), cause air-movement for ventilating, or future use, with little use of other energy sources. A common example is a solarium on the equator-side of a building. Passive cooling is the use of the same design principles to reduce summer cooling requirements.

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Passive_solar_building_design

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