Geographic coordinate system

A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers or letters, or symbols. The coordinates are often chosen such that one of the numbers represents vertical position, and two or three of the numbers represent 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.

History

The invention of a geographic coordinate system is generally credited to Eratosthenes of Cyrene, who composed his now-lost Geography at the Library of Alexandria in the 3rd century BC. A century later, Hipparchus of Nicaea improved upon his system by determining latitude from stellar measurements rather than solar altitude and determining longitude by using simultaneous timing of lunar eclipses, rather than dead reckoning. In the 1st or 2nd century, Marinus of Tyre compiled an extensive gazetteer and mathematically-plotted world map, using coordinates measured east from a Prime Meridian at the Fortunate Isles of western Africa and measured north or south of the island of Rhodes off Asia Minor. Ptolemy credited him with the full adoption of longitude and latitude, rather than measuring latitude in terms of the length of the midsummer day. Ptolemy's 2nd-century Geography used the same Prime Meridian but measured latitude from the equator instead. After their work was translated into Arabic in the 9th century, Al-Khwārizmī's Book of the Description of the Earth corrected Marinus and Ptolemy's errors regarding the length of the Mediterranean Sea, causing medieval Arabic cartography to use a Prime Meridian around 10° east of Ptolemy's line. Mathematical cartography resumed in Europe following Maximus Planudes's recovery of Ptolemy's text a little before 1300; the text was translated into Latin at Florence by Jacobus Angelus around 1407.

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.

Common coordinate systems

Number line

The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line. In this system, an arbitrary point O (the origin) is chosen on a given line. The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point.

Prime meridian

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, into two hemispheres. If one uses directions of East and West from a defined prime meridian, then they can be called Eastern Hemisphere and Western Hemisphere.

A prime meridian is ultimately arbitrary, unlike an equator, which is determined by the axis of rotation—and various conventions have been used or advocated in different regions and throughout history.

History

The notion of longitude was developed by the Greek Eratosthenes (c. 276 BC – c. 195 BC) in Alexandria and Hipparchus (c. 190 BC – c. 120 BC) in Rhodes and applied to a large number of cities by the geographer Strabo (64/63 BC – c. 24 AD). But it was Ptolemy (c. AD 90 – c. AD 168) who first used a consistent meridian for a world map in his Geographia.