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Radius
In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin
Latin
radius, meaning ray but also the spoke of a chariot wheel.[1] The plural of radius can be either radii (from the Latin
Latin
plural) or the conventional English plural radiuses.[2] The typical abbreviation and mathematical variable name for radius is r. By extension, the diameter d is defined as twice the radius:[3] d ≐ 2 r ⇒ r = d 2 . displaystyle ddoteq 2rquad Rightarrow quad r= frac d 2 . If an object does not have a center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere
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Two-dimensional Space
Two-dimensional space
Two-dimensional space
or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). In Mathematics, it is commonly represented by the symbol ℝ2. For a generalization of the concept, see dimension. Two-dimensional space
Two-dimensional space
can be seen as a projection of the physical universe onto a plane
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Cartesian Coordinate System
A Cartesian coordinate system
Cartesian coordinate system
is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0)
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International Standard Serial Number
An International Standard Serial Number
International Standard Serial Number
(ISSN) is an eight-digit serial number used to uniquely identify a serial publication, such as a magazine.[1] The ISSN is especially helpful in distinguishing between serials with the same title. ISSN are used in ordering, cataloging, interlibrary loans, and other practices in connection with serial literature.[2] The ISSN system was first drafted as an International Organization for Standardization (ISO) international standard in 1971 and published as ISO 3297 in 1975.[3] ISO subcommittee TC 46/SC 9 is responsible for maintaining the standard. When a serial with the same content is published in more than one media type, a different ISSN is assigned to each media type. For example, many serials are published both in print and electronic media
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Geometry
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
Geometry
arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes
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Dimension
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.[1][2] 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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Coordinate System
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.[1][2] The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring
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Point (mathematics)
In modern mathematics, a point refers usually to an element of some set called a space. More specifically, in Euclidean geometry, a point is a primitive notion upon which the geometry is built, meaning that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy. In particular, the geometric points do not have any length, area, volume or any other dimensional attribute
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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
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Distance
Distance
Distance
is a numerical measurement of how far apart objects are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). In most cases, "distance from A to B" is interchangeable with "distance from B to A". In mathematics, a distance function or metric is a generalization of the concept of physical distance
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Ray (geometry)
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth. Lines are an idealization of such objects. Until the 17th century, lines were defined in this manner: "The [straight or curved] line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which […] will leave from its imaginary moving some vestige in length, exempt of any width
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Law Of Sines
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of a triangle (any shape) to the sines of its angles. According to the law, a sin ⁡ A = b sin ⁡ B = c sin ⁡ C = d , displaystyle frac a sin A ,=, frac b sin B ,=, frac c sin C ,=,d, where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right), while d is the diameter of the triangle's circumcircle
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Azimuth
An azimuth (/ˈæzɪməθ/ ( listen)) (from the pl. form of the Arabic noun "السَّمْت" as-samt, meaning "the direction") is an angular measurement in a spherical coordinate system. The vector from an observer (origin) to a point of interest is projected perpendicularly onto a reference plane; the angle between the projected vector and a reference vector on the reference plane is called the azimuth. An example of azimuth is the angular direction of a star in the sky. The star is the point of interest, the reference plane is the local horizontal area (e.g. a circular area 5 km in radius around an observer at sea level), and the reference vector points north. The azimuth is the angle between the north vector and the star's vector on the horizontal plane.[1] Azimuth
Azimuth
is usually measured in degrees (°)
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Cylindrical Coordinate System
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point. The origin of the system is the point where all three coordinates can be given as zero
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Spherical Coordinate System
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the radius or radial coordinate. The polar angle may be called colatitude, zenith angle, normal angle, or inclination angle. The use of symbols and the order of the coordinates differs between sources
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Filling Radius
In Riemannian geometry, the filling radius of a Riemannian manifold X is a metric invariant of X. It was originally introduced in 1983 by Mikhail Gromov, who used it to prove his systolic inequality for essential manifolds, vastly generalizing Loewner's torus inequality and Pu's inequality
Pu's inequality
for the real projective plane, and creating systolic geometry in its modern form. The filling radius of a simple loop C in the plane is defined as the largest radius, R > 0, of a circle that fits inside C: F i l l R a d ( C ⊂ R 2 ) = R . displaystyle mathrm FillRad (Csubset mathbb R ^ 2 )=R
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