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Geographic Coordinate System
A GEOGRAPHIC COORDINATE SYSTEM is a coordinate system used in geography that enables every location on Earth to be specified by a set of numbers, letters or symbols. The coordinates are often chosen such that one of the numbers represents a vertical position , and two or three of the numbers represent a horizontal position . A common choice of coordinates is latitude , longitude and elevation . To specify a location on a two-dimensional map requires a map projection
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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 a point or other geometric element on a manifold such as Euclidean space . 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 . The use of a coordinate system allows problems in geometry to be translated into problems about numbers and _vice versa_; this is the basis of analytic geometry
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Geography
GEOGRAPHY (from Greek γεωγραφία, _geographia_, literally "earth description" ) is a field of science devoted to the study of the lands, the features, the inhabitants, and the phenomena of Earth
Earth
. The first person to use the word "γεωγραφία" was Eratosthenes (276–194 BC). Geography
Geography
is an all-encompassing discipline that seeks an understanding of the Earth
Earth
and its human and natural complexities—not merely where objects are, but how they have changed and come to be. Geography
Geography
is often defined in terms of the two branches of human geography and physical geography . Human geography deals with the study of people and their communities, cultures, economies and interactions with the environment by studying their relations with and across space and place
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Altitude
ALTITUDE or HEIGHT (sometimes known as DEPTH) is defined based on the context in which it is used (aviation, geometry, geographical survey, sport, and many more). As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context. Although the term altitude is commonly used to mean the height above sea level of a location, in geography the term elevation is often preferred for this usage. Vertical distance measurements in the "down" direction are commonly referred to as depth
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N-vector
The N-VECTOR representation is a three-parameter non-singular representation well-suited for replacing latitude and longitude as horizontal position representation in mathematical calculations and computer algorithms. Geometrically, the n-vector for a given position on an ellipsoid is the outward-pointing unit vector that is normal in that position to the ellipsoid. For representing horizontal positions on Earth, the ellipsoid is a reference ellipsoid and the vector is decomposed in an Earth-centered Earth-fixed coordinate system . It behaves smoothly at all Earth positions, and it holds the mathematical one-to-one property. More in general, the concept can be applied to representing positions on the boundary of a strictly convex bounded subset of k-dimensional Euclidean space
Euclidean space
, provided that that boundary is a differentiable manifold . In this general case, the n-vector consists of k parameters
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Horizontal Position Representation
A POSITION REPRESENTATION is the parameters used to express a position relative to a reference. Representing position in three dimensions is often done by a Euclidean vector
Euclidean vector
. However, when representing position relative to the Earth
Earth
it is often more convenient to represent vertical position as altitude or depth, and to use some other parameters to represent HORIZONTAL POSITION. There are also several applications where only the horizontal position is of interest, this might e.g. be the case for ships and ground vehicles/cars. There are several options for horizontal position representations, each with different properties which makes them appropriate for different applications. Latitude
Latitude
/longitude and UTM are common horizontal position representations
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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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Longitude
LONGITUDE (/ˈlɒndʒᵻtjuːd/ or /ˈlɒndʒᵻtuːd/ , Australian and British also /ˈlɒŋɡᵻtjuːd/ ), 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
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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Elevation
The ELEVATION of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid , a mathematical model of the Earth\'s sea level as an equipotential gravitational surface (see Geodetic system, vertical datum ). Elevation, or GEOMETRIC HEIGHT, is mainly used when referring to points on the Earth's surface, while altitude or geopotential height is used for points above the surface, such as an aircraft in flight or a spacecraft in orbit, and depth is used for points below the surface. Elevation
Elevation
is not to be confused with the distance from the center of the Earth; due to equatorial bulge , the summits of Mt. Everest and Chimborazo have, respectively, the largest elevation and the largest geocentric distance
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Map Projection
A MAP PROJECTION is a systematic transformation of the latitudes and longitudes of locations from the surface of a sphere or an ellipsoid into locations on a plane . Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. There is no limit to the number of possible map projections. :1 More generally, the surfaces of planetary bodies can be mapped even if they are too irregular to be modeled well with a sphere or ellipsoid; see below . Even more generally, projections are a subject of several pure mathematical fields, including differential geometry , projective geometry , and manifolds . However, "map projection" refers specifically to a cartographic projection
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History Of Geodesy
Geodesy
Geodesy
(/dʒiːˈɒdɨsi/), also named geodetics, is the scientific discipline that deals with the measurement and representation of the Earth. The HISTORY OF GEODESY began in antiquity and blossomed during the Age of Enlightenment . Early ideas about the figure of the Earth
Earth
held the Earth
Earth
to be flat (see flat Earth
Earth
), and the heavens a physical dome spanning over it. Two early arguments for a spherical Earth
Earth
were that lunar eclipses were seen as circular shadows which could only be caused by a spherical Earth, and that Polaris
Polaris
is seen lower in the sky as one travels South
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History Of Longitude
The HISTORY OF LONGITUDE is a record of the effort, by astronomers, cartographers and navigators over several centuries, to discover a means of determining longitude . The measurement of longitude is important to both cartography and navigation , in particular to provide safe ocean navigation. Knowledge of both latitude and longitude was required. Finding an accurate and reliable method of determining longitude took centuries of study, and involved some of the greatest scientific minds in human history
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History Of Prime Meridians
A PRIME MERIDIAN is a meridian (a line of longitude ) in a geographical coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its antimeridian (the 180th meridian in a 360°-system ) form a great circle . This great circle divides the sphere, e.g., the Earth
Earth
, into two hemispheres . If one uses directions of East and West from a defined prime meridian, then they can be called Eastern Hemisphere
Eastern Hemisphere
and Western Hemisphere
Western Hemisphere
. Gerardus Mercator
Gerardus Mercator
in his Atlas Cosmographicae
Atlas Cosmographicae
(1595) uses a prime meridian somewhere close to 25°W , passing just to the west of Santa Maria Island in the Atlantic
Atlantic

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Invention
An INVENTION is a unique or novel device , method, composition or process. The invention process is a process within an overall engineering and product development process. It may be an improvement upon a machine or product or a new process for creating an object or a result. An invention that achieves a completely unique function or result may be a radical breakthrough. Such works are novel and not obvious to others skilled in the same field . An inventor may be taking a big step in success or failure. Some inventions can be patented. A patent legally protects the intellectual property rights of the inventor and legally recognizes that a claimed invention is actually an invention. The rules and requirements for patenting an invention vary from country to country and the process of obtaining a patent is often expensive. Another meaning of invention is CULTURAL INVENTION , which is an innovative set of useful social behaviours adopted by people and passed on to others
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Eratosthenes
ERATOSTHENES OF CYRENE (/ɛrəˈtɒsθəniːz/ ; Greek : Ἐρατοσθένης ὁ Κυρηναῖος, IPA: ; c. 276 BC – c. 195/194 BC ) was a Greek mathematician , geographer , poet , astronomer , and music theorist . He was a man of learning, becoming the chief librarian at the Library of Alexandria
Alexandria
. He invented the discipline of geography , including the terminology used today. He is best known for being the first person to calculate the circumference of the Earth , which he did by applying a measuring system using stadia , a standard unit of measure during that time period. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth\'s axis (again with remarkable accuracy). Additionally, he may have accurately calculated the distance from the Earth to the Sun
Sun
and invented the leap day
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Cyrene, Libya
CYRENE (/saɪˈriːniː/ ; Ancient Greek : Κυρήνη, translit. Kyrēnē) was an ancient Greek and Roman city near present-day Shahhat , Libya
Libya
. It was the oldest and most important of the five Greek cities in the region. It gave eastern Libya
Libya
the classical name Cyrenaica
Cyrenaica
that it has retained to modern times. Nearby located, the ancient Necropolis of Cyrene
Necropolis of Cyrene
. Cyrene lies in a lush valley in the Jebel Akhdar uplands. The city was named after a spring , Kyre, which the Greeks
Greeks
consecrated to Apollo
Apollo
. It was also the seat of the Cyrenaics
Cyrenaics
, a famous school of philosophy in the 4th century BC, founded by Aristippus
Aristippus
, a disciple of Socrates
Socrates
. It was then nicknamed the " Athens
Athens
of Africa"
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