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Dimensions
In physics and mathematics , the DIMENSION of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube , a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces. In classical mechanics , space and time are different categories and refer to absolute space and time . That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism
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Longitude
LONGITUDE (/ˈlɒndʒɪtjuːd/ or /ˈlɒndʒɪtuːd/ , Australian and British also /ˈlɒŋɡɪtjuːd/ ), is a geographic coordinate that specifies the east -west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians (lines running from the North Pole
North Pole
to the South Pole ) connect points with the same longitude. By convention, one of these, the Prime Meridian
Prime Meridian
, which passes through the Royal Observatory, Greenwich , England, was allocated the position of zero degrees longitude. The longitude of other places is measured as the angle east or west from the Prime Meridian, ranging from 0° at the Prime Meridian
Prime Meridian
to +180° eastward and −180° westward
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Size
SIZE is the magnitude or dimensions of a thing, or how big something is. Size
Size
can be measured as length , width , height , diameter , perimeter , area , volume , or mass . Play media This animation gives a sense of the awe-inspiring scale of some of the known objects in our universe. In mathematical terms, "size is a concept abstracted from the process of measuring by comparing a longer to a shorter". Size
Size
is determined by the process of comparing or measuring objects, which results in the determination of the magnitude of a quantity, such as length or mass, relative to a unit of measurement. Such a magnitude is usually expressed as a numerical value of units on a previously established spatial scale , such as meters or inches . The sizes with which humans tend to be most familiar are body dimensions (measures of anthropometry ), which include measures such as human height , and human body weight
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Classical Mechanics
In physics , CLASSICAL MECHANICS is one of two major sub-fields of mechanics . The other sub-field is quantum mechanics . Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces . The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science , engineering and technology . It is also known as NEWTONIAN MECHANICS, though textbook authors often consider Newtonian mechanics, along with Lagrangian mechanics and Hamiltonian mechanics , as the three main formalisms of classical mechanics. Classical mechanics
Classical mechanics
describes the motion of macroscopic objects, from projectiles to parts of machinery , and astronomical objects , such as spacecraft , planets , stars and galaxies
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Latitude
In geography , LATITUDE is a geographic coordinate that specifies the north –south position of a point on the Earth's surface. Latitude
Latitude
is an angle (defined below) which ranges from 0° at the Equator
Equator
to 90° ( North
North
or South) at the poles. Lines of constant latitude, or parallels, run east–west as circles parallel to the equator. Latitude
Latitude
is used together with longitude to specify the precise location of features on the surface of the Earth. Without qualification the term latitude should be taken to be the geodetic latitude as defined in the following sections. Also defined are six auxiliary latitudes which are used in special applications
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Sphere
A SPHERE (from Greek σφαῖρα — sphaira, "globe, ball" ) is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball , (viz., analogous to a circular object in two dimensions). Like a circle , which geometrically is an object in two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of the ball
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Surface (topology)
In topology and differential geometry , a SURFACE is a two-dimensional manifold , and, as such, may be an "abstract surface" not embedded in any Euclidean space. For example, the Klein bottle
Klein bottle
is a surface, which cannot be represented in the three-dimensional Euclidean space
Euclidean space
without introducing self-intersections (it cannot be embedded in the three dimensional Euclidean space)
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Plane (mathematics)
In mathematics , a PLANE is a flat, two-dimensional surface that extends infinitely far. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space . Planes can arise as subspaces of some higher-dimensional space, as with a room's walls extended infinitely far, or they may enjoy an independent existence in their own right, as in the setting of Euclidean geometry
Euclidean geometry
. When working exclusively in two-dimensional Euclidean space
Euclidean space
, the definite article is used, so, the plane refers to the whole space. Many fundamental tasks in mathematics, geometry , trigonometry , graph theory , and graphing are performed in a two-dimensional space, or, in other words, in the plane
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Cylinder (geometry)
In its simplest form, a CYLINDER (from Greek κύλινδρος – kulindros, "roller, tumbler" ) is the surface formed by the points at a fixed distance from a given straight line called the AXIS of the cylinder. It is one of the most basic curvilinear geometric shapes. CONTENTS* 1 Common use * 1.1 Volume * 1.2 Surface area * 1.3 Cylindric sections * 2 Other types of cylinders * 2.1 Right circular hollow cylinder * 3 About an arbitrary axis * 4 Projective geometry * 5 Related polyhedra * 6 See also * 7 References * 8 External links COMMON USECommonly the word cylinder is understood to refer to a finite section of a RIGHT CIRCULAR CYLINDER having a finite height with circular ends perpendicular to the axis as shown in the figure. If the ends are open, it is called an open cylinder. If the ends are closed by flat surfaces it is called a solid cylinder
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Space
SPACE is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three linear dimensions , although modern physicists usually consider it, with time , to be part of a boundless four-dimensional continuum known as spacetime . The concept of space is considered to be of fundamental importance to an understanding of the physical universe . However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework . Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato
Plato
, or Socrates
Socrates
in his reflections on what the Greeks called khôra (i.e
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Time
TIME (styled TIME) is an American weekly news magazine published in New York City
New York City
. It was founded in 1923 and originally run by Henry Luce . A European edition ( Time
Time
Europe, formerly known as Time
Time
Atlantic) is published in London and also covers the Middle East, Africa and, since 2003, Latin America. An Asian edition ( Time
Time
Asia) is based in Hong Kong . The South Pacific edition, which covers Australia, New Zealand and the Pacific Islands , is based in Sydney
Sydney
. In December 2008, Time discontinued publishing a Canadian advertiser edition. Time
Time
has the world's largest circulation for a weekly news magazine, and has a readership of 26 million, 20 million of which are based in the United States. In mid-2016, its circulation was 3,032,581, having fallen from 3.3 million in 2012
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Observer (special Relativity)
In special relativity , an OBSERVER is a frame of reference from which a set of objects or events are being measured. Usually this is an inertial reference frame or "inertial observer". Less often an observer may be an arbitrary non-inertial reference frame such as a Rindler frame which may be called an "accelerating observer". The special relativity usage differs significantly from the ordinary English meaning of "observer". Reference frames are inherently nonlocal constructs, covering all of space and time or a nontrivial part of it; thus it does not make sense to speak of an observer (in the special relativistic sense) having a location. Also, an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating. Physicists use the term "observer" as shorthand for a specific reference frame from which a set of objects or events is being measured
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Minkowski Space
In mathematical physics , MINKOWSKI SPACE or MINKOWSKI SPACETIME is a combination of 3-dimensional Euclidean space
Euclidean space
and time into a 4-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell\'s equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity . Minkowski space
Minkowski space
is closely associated with Einstein\'s theory of special relativity , and is the most common mathematical structure on which special relativity is formulated
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Quantum Mechanics
QUANTUM MECHANICS (QM; also known as QUANTUM PHYSICS or QUANTUM THEORY), including quantum field theory , is a branch of physics which is the fundamental theory of nature at the small scales and energy levels of atoms and subatomic particles . Classical physics
Classical physics
(the physics existing before quantum mechanics) derives from quantum mechanics as an approximation valid only at large (macroscopic ) scales. Quantum mechanics
Quantum mechanics
differs from classical physics in that: energy , momentum and other quantities are often restricted to discrete values (quantization ), objects have characteristics of both particles and waves (i.e. wave-particle duality ), and there are limits to the precision with which quantities can be known (uncertainty principle )
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Event (relativity)
In physics , and in particular relativity , an EVENT is a point in spacetime (that is, a specific place and time) and the physical situation or occurrence associated with it. For example, a glass breaking on the floor is an event; it occurs at a unique place and a unique time. Strictly speaking, the notion of an event is an idealization, in the sense that it specifies a definite time and place, whereas any actual event is bound to have a finite extent, both in time and in space. Upon choosing a frame of reference, one can assign coordinates to the event: three spatial coordinates x = ( x , y , z ) {displaystyle {vec {x}}=(x,y,z)} to describe the location and one time coordinate t {displaystyle t} to specify the moment at which the event occurs. These four coordinates ( x , t ) {displaystyle ({vec {x}},t)} together form a four-vector associated to the event
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Function Space
In mathematics , a FUNCTION SPACE is a set of functions of a given kind from a set X to a set Y. It is called a space because in many applications it is a topological space (including metric spaces ), a vector space , or both. Namely, if Y is a field , functions have inherent vector structure with two operations of pointwise addition and multiplication to a scalar . Topological and metrical structures of function spaces are more diverse. CONTENTS * 1 Examples * 2 Functional analysis
Functional analysis
* 3 Norm * 4 Bibliography * 5 See also * 6 Footnotes EXAMPLESFunction spaces appear in various areas of mathematics: * In set theory , the set of functions from X to Y may be denoted X → Y or YX. * As a special case, the power set of a set X may be identified with the set of all functions from X to {0, 1}, denoted 2X. * The set of bijections from X to Y is denoted X ↔ Y
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