1.
Geography
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Geography is a field of science devoted to the study of the lands, the features, the inhabitants, and the phenomena of Earth. The first person to use the word γεωγραφία was Eratosthenes, Geography is an all-encompassing discipline that seeks an understanding of the Earth and its human and natural complexities—not merely where objects are, but how they have changed and come to be. It is often defined in terms of the two branches of geography and physical geography. Geography has been called the world discipline and the bridge between the human and the physical sciences, Geography is a systematic study of the Earth and its features. Traditionally, geography has been associated with cartography and place names, although many geographers are trained in toponymy and cartology, this is not their main preoccupation. Geographers study the space and the temporal database distribution of phenomena, processes, because space and place affect a variety of topics, such as economics, health, climate, plants and animals, geography is highly interdisciplinary. The interdisciplinary nature of the approach depends on an attentiveness to the relationship between physical and human phenomena and its spatial patterns. Names of places. are not geography. know by heart a whole gazetteer full of them would not, in itself and this is a description of the world—that is Geography. In a word Geography is a Science—a thing not of mere names but of argument and reason, of cause, just as all phenomena exist in time and thus have a history, they also exist in space and have a geography. Geography as a discipline can be split broadly into two main fields, human geography and physical geography. The former largely focuses on the environment and how humans create, view, manage. The latter examines the environment, and how organisms, climate, soil, water. The difference between these led to a third field, environmental geography, which combines physical and human geography. Physical geography focuses on geography as an Earth science and it aims to understand the physical problems and the issues of lithosphere, hydrosphere, atmosphere, pedosphere, and global flora and fauna patterns. Physical geography can be divided into broad categories, including, Human geography is a branch of geography that focuses on the study of patterns. It encompasses the human, political, cultural, social, and it requires an understanding of the traditional aspects of physical and human geography, as well as the ways that human societies conceptualize the environment. Integrated geography has emerged as a bridge between the human and the geography, as a result of the increasing specialisation of the two sub-fields. Examples of areas of research in the environmental geography include, emergency management, environmental management, sustainability, geomatics is concerned with the application of computers to the traditional spatial techniques used in cartography and topography
Geography
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Map of the Earth
Geography
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Biogeography
Geography
Geography
2.
North
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North is one of the four cardinal directions or compass points. It is the opposite of south and is perpendicular to east and west, North is a noun, adjective, or adverb indicating direction or geography. The word north is related to the Old High German nord, the Latin word borealis comes from the Greek boreas north wind, north, which, according to Ovid, was personified as the son of the river-god Strymon, the father of Calais and Zetes. Septentrionalis is from septentriones, the seven plow oxen, a name of Ursa Maior, the Greek ἀρκτικός is named for the same constellation, and is the source of the English word Arctic. For example, in Lezgian, kefer can mean both disbelief and north, since to the north of the Muslim Lezgian homeland there are areas formerly inhabited by non-Muslim Caucasian, in many languages of Mesoamerica, north also means up. The direction north is associated with colder climates because most of the worlds land at high latitudes is located in the Northern Hemisphere. By convention, the top side of a map is often north, to go north using a compass for navigation, set a bearing or azimuth of 0° or 360°. North is specifically the direction that, in Western culture, is treated as the fundamental direction, on any rotating non-astronomical object, north denotes the side appearing to rotate counter-clockwise when viewed from afar along the axis of rotation. Magnetic north is of interest because it is the direction indicated as north on a properly functioning magnetic compass, the difference between it and true north is called the magnetic declination. But simple generalizations on the subject should be treated as unsound, maps intended for usage in orienteering by compass will clearly indicate the local declination for easy correction to true north. Maps may also indicate grid north, which is a term referring to the direction northwards along the grid lines of a map projection. The visible rotation of the sky around the visible celestial pole provides a vivid metaphor of that direction corresponding to up. Thus the choice of the north as corresponding to up in the hemisphere, or of south in that role in the southern, is, prior to worldwide communication, anything. On the contrary, it is of interest that Chinese and Islamic culture even considered south as the top end for maps. Up is a metaphor for north, the notion that north should always be up and east at the right was established by the Greek astronomer Ptolemy. While the choice of north over south as prime direction reflects quite arbitrary historical factors and their folk definitions are, respectively, where the sun rises and where it sets. The true folk-astronomical definitions of east and west are the directions, an angle from the prime direction. Being the default direction on the compass, north is referred to frequently in Western popular culture, some examples include, The phrase north of X is often used by Americans to mean more than X or greater than X, i. e
North
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A 16-point compass rose with north highlighted and at top.
3.
Geoid
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The geoid is the shape that the surface of the oceans would take under the influence of Earths gravity and rotation alone, in the absence of other influences such as winds and tides. This surface is extended through the continents, all points on a geoid surface have the same gravity potential energy. The geoid can be defined at any value of gravitational potential such as within the earths crust or far out in space and it does not correspond to the actual surface of Earths crust, but to a surface which can only be known through extensive gravitational measurements and calculations. It is often described as the true figure of the Earth. The surface of the geoid is higher than the reference ellipsoid wherever there is a gravity anomaly. The geoid surface is irregular, unlike the ellipsoid which is a mathematical idealized representation of the physical Earth. Although the physical Earth has excursions of +8,848 m and −429 m, If the ocean surface were isopycnic and undisturbed by tides, currents, or weather, it would closely approximate the geoid. The permanent deviation between the geoid and mean sea level is called ocean surface topography, If the continental land masses were criss-crossed by a series of tunnels or canals, the sea level in these canals would also very nearly coincide with the geoid. This means that when traveling by ship, one does not notice the undulations of the geoid, the vertical is always perpendicular to the geoid. Likewise, spirit levels will always be parallel to the geoid, a long voyage, indicate height variations, even though the ship will always be at sea level. This is because GPS satellites, orbiting about the center of gravity of the Earth, to obtain ones geoidal height, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tidal measurement station, as in land surveying. Modern GPS receivers have a grid implemented inside where they obtain the height over the World Geodetic System ellipsoid from the current position. Then they are able to correct the height above WGS ellipsoid to the height above WGS84 geoid, in that case when the height is not zero on a ship it is due to various other factors such as ocean tides, atmospheric pressure and local sea surface topography. The gravitational field of the earth is neither perfect n If that perfect sphere were then covered in water, instead, the water level would be higher or lower depending on the particular strength of gravity in that location. Spherical harmonics are used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96, the geoid is a particular equipotential surface, and is somewhat involved to compute. The gradient of this also provides a model of the gravitational acceleration
Geoid
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Three-dimensional visualization of geoid undulations, using units of gravity.
Geoid
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Geodesy
4.
Altitude
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Altitude or height is defined based on the context in which it is used. As a general definition, altitude is a measurement, usually in the vertical or up direction. 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 direction are commonly referred to as depth. In aviation, the altitude can have several meanings, and is always qualified by explicitly adding a modifier. Parties exchanging altitude information must be clear which definition is being used, aviation altitude is measured using either mean sea level or local ground level as the reference datum. When flying at a level, the altimeter is always set to standard pressure. On the flight deck, the instrument for measuring altitude is the pressure altimeter. There are several types of altitude, Indicated altitude is the reading on the altimeter when it is set to the local barometric pressure at mean sea level. In UK aviation radiotelephony usage, the distance of a level, a point or an object considered as a point, measured from mean sea level. Absolute altitude is the height of the aircraft above the terrain over which it is flying and it can be measured using a radar altimeter. Also referred to as radar height or feet/metres above ground level, true altitude is the actual elevation above mean sea level. It is indicated altitude corrected for temperature and pressure. Height is the elevation above a reference point, commonly the terrain elevation. Pressure altitude is used to indicate flight level which is the standard for reporting in the U. S. in Class A airspace. Pressure altitude and indicated altitude are the same when the setting is 29.92 Hg or 1013.25 millibars. Density altitude is the altitude corrected for non-ISA International Standard Atmosphere atmospheric conditions, aircraft performance depends on density altitude, which is affected by barometric pressure, humidity and temperature. On a very hot day, density altitude at an airport may be so high as to preclude takeoff and these types of altitude can be explained more simply as various ways of measuring the altitude, Indicated altitude – the altitude shown on the altimeter
Altitude
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Vertical distance comparison
5.
Degree (angle)
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A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
Degree (angle)
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One degree (shown in red) and eighty nine (shown in blue)
6.
Arcminute
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A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
Arcminute
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Comparison of angular diameter of the Sun, Moon, planets and the International Space Station. To get a true representation of the sizes, view the image at a distance of 103 times the width of the "Moon: max." circle. For example, if this circle is 10 cm wide on your monitor, view it from 10.3 m away.
7.
Geodesy
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Geodesists also study geodynamical phenomena such as crustal motion, tides, and polar motion. For this they design global and national networks, using space and terrestrial techniques while relying on datums. Geodesy — from the Ancient Greek word γεωδαισία geodaisia — is primarily concerned with positioning within the temporally varying gravity field, such geodetic operations are also applied to other astronomical bodies in the solar system. It is also the science of measuring and understanding the earths geometric shape, orientation in space and this applies to the solid surface, the liquid surface and the Earths atmosphere. For this reason, the study of the Earths gravity field is called physical geodesy by some, the geoid is essentially the figure of the Earth abstracted from its topographical features. It is an idealized surface of sea water, the mean sea level surface in the absence of currents, air pressure variations etc. The geoid, unlike the ellipsoid, is irregular and too complicated to serve as the computational surface on which to solve geometrical problems like point positioning. The geometrical separation between the geoid and the ellipsoid is called the geoidal undulation. It varies globally between ±110 m, when referred to the GRS80 ellipsoid, a reference ellipsoid, customarily chosen to be the same size as the geoid, is described by its semi-major axis a and flattening f. The quantity f = a − b/a, where b is the axis, is a purely geometrical one. The mechanical ellipticity of the Earth can be determined to high precision by observation of satellite orbit perturbations and its relationship with the geometrical flattening is indirect. The relationship depends on the density distribution, or, in simplest terms. The 1980 Geodetic Reference System posited a 6,378,137 m semi-major axis and this system was adopted at the XVII General Assembly of the International Union of Geodesy and Geophysics. It is essentially the basis for geodetic positioning by the Global Positioning System and is also in widespread use outside the geodetic community. The locations of points in space are most conveniently described by three cartesian or rectangular coordinates, X, Y and Z. Since the advent of satellite positioning, such systems are typically geocentric. The X-axis lies within the Greenwich observatorys meridian plane, the coordinate transformation between these two systems is described to good approximation by sidereal time, which takes into account variations in the Earths axial rotation. A more accurate description also takes polar motion into account, a closely monitored by geodesists
Geodesy
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An old geodetic pillar (1855) at Ostend, Belgium
Geodesy
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Geodesy
Geodesy
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A Munich archive with lithography plates of maps of Bavaria
Geodesy
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Geodetic Control Mark (example of a deep benchmark)
8.
Prime Meridian
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A prime meridian is a meridian in a geographical coordinate system at which longitude is defined to be 0°. Together, a meridian and its antimeridian form a great circle. This great circle divides the sphere, e. g. the Earth, if one uses directions of East and West from a defined prime meridian, then they can be called Eastern Hemisphere and Western Hemisphere. The most widely used modern meridian is the IERS Reference Meridian and it is derived but deviates slightly from the Greenwich Meridian, which was selected as an international standard in 1884. The notion of longitude was developed by the Greek Eratosthenes in Alexandria, and Hipparchus in Rhodes, but it was Ptolemy who first used a consistent meridian for a world map in his Geographia. The main point is to be comfortably west of the tip of Africa as negative numbers were not yet in use. His prime meridian corresponds to 18°40 west of Winchester today, at that time the chief method of determining longitude was by using the reported times of lunar eclipses in different countries. Ptolemys Geographia was first printed with maps at Bologna in 1477, but there was still a hope that a natural basis for a prime meridian existed. The Tordesillas line was settled at 370 leagues west of Cape Verde. This is shown in Diogo Ribeiros 1529 map, in 1541, Mercator produced his famous 41 cm terrestrial globe and drew his prime meridian precisely through Fuertaventura in the Canaries. His later maps used the Azores, following the magnetic hypothesis, but by the time that Ortelius produced the first modern atlas in 1570, other islands such as Cape Verde were coming into use. In his atlas longitudes were counted from 0° to 360°, not 180°W to 180°E as is usual today and this practice was followed by navigators well into the 18th century. In 1634, Cardinal Richelieu used the westernmost island of the Canaries, Ferro, 19°55 west of Paris, the geographer Delisle decided to round this off to 20°, so that it simply became the meridian of Paris disguised. In the early 18th century the battle was on to improve the determination of longitude at sea, between 1765 and 1811, Nevil Maskelyne published 49 issues of the Nautical Almanac based on the meridian of the Royal Observatory, Greenwich. Maskelynes tables not only made the lunar method practicable, they made the Greenwich meridian the universal reference point. In 1884, at the International Meridian Conference in Washington, D. C.22 countries voted to adopt the Greenwich meridian as the meridian of the world. The French argued for a line, mentioning the Azores and the Bering Strait. In October 1884 the Greenwich Meridian was selected by delegates to the International Meridian Conference held in Washington, united States to be the common zero of longitude and standard of time reckoning throughout the world
Prime Meridian
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Gerardus Mercator in his Atlas Cosmographicae (1595) uses a prime meridian somewhere close to 25°W, passing just to the west of Santa Maria Island in the Atlantic. His 180th meridian runs along the Strait of Anián (Bering Strait)
Prime Meridian
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Ptolemy's 1st projection, redrawn under Maximus Planudes around 1300, using a prime meridian west of Africa
Prime Meridian
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Diogo Ribeiro's map of 1529, now in the Vatican library
9.
North Pole
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The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is defined as the point in the Northern Hemisphere where the Earths axis of rotation meets its surface. The North Pole is the northernmost point on the Earth, lying diametrically opposite the South Pole and it defines geodetic latitude 90° North, as well as the direction of true north. At the North Pole all directions point south, all lines of longitude converge there, along tight latitude circles, counterclockwise is east and clockwise is west. The North Pole is at the center of the Northern Hemisphere, while the South Pole lies on a continental land mass, the North Pole is located in the middle of the Arctic Ocean amid waters that are almost permanently covered with constantly shifting sea ice. This makes it impractical to construct a permanent station at the North Pole, however, the Soviet Union, and later Russia, constructed a number of manned drifting stations on a generally annual basis since 1937, some of which have passed over or very close to the Pole. Since 2002, the Russians have also established a base, Barneo. This operates for a few weeks during early spring, studies in the 2000s predicted that the North Pole may become seasonally ice-free because of Arctic ice shrinkage, with timescales varying from 2016 to the late 21st century or later. The sea depth at the North Pole has been measured at 4,261 m by the Russian Mir submersible in 2007 and at 4,087 m by USS Nautilus in 1958. The nearest land is said to be Kaffeklubben Island, off the northern coast of Greenland about 700 km away. The nearest permanently inhabited place is Alert in the Qikiqtaaluk Region, Nunavut, Canada, around the beginning of the 20th century astronomers noticed a small apparent variation of latitude, as determined for a fixed point on Earth from the observation of stars. Part of this variation could be attributed to a wandering of the Pole across the Earths surface, the wandering has several periodic components and an irregular component. The component with a period of about 435 days is identified with the eight-month wandering predicted by Euler and is now called the Chandler wobble after its discoverer and it is desirable to tie the system of Earth coordinates to fixed landforms. Of course, given plate tectonics and isostasy, there is no system in all geographic features are fixed. Yet the International Earth Rotation and Reference Systems Service and the International Astronomical Union have defined a framework called the International Terrestrial Reference System. As early as the 16th century, many eminent people correctly believed that the North Pole was in a sea and it was therefore hoped that passage could be found through ice floes at favorable times of the year. Several expeditions set out to find the way, generally with whaling ships, one of the earliest expeditions to set out with the explicit intention of reaching the North Pole was that of British naval officer William Edward Parry, who in 1827 reached latitude 82°45′ North. In 1871 the Polaris expedition, a US attempt on the Pole led by Charles Francis Hall, another British Royal Navy attempt on the pole, part of the British Arctic Expedition, by Commander Albert H. Markham reached a then-record 83°2026 North in May 1876 before turning back. An 1879–1881 expedition commanded by US naval officer George W. DeLong ended tragically when their ship, over half the crew, including DeLong, were lost
North Pole
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North Pole scenery
North Pole
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An Azimuthal projection showing the Arctic Ocean and the North Pole. The map also shows the 75th parallel north and 60th parallel north.
North Pole
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Gerardus Mercator 's map of the North Pole from 1595
North Pole
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C.G. Zorgdragers map of the North Pole from 1720
10.
South Pole
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The South Pole, also known as the Geographic South Pole or Terrestrial South Pole, is one of the two points where the Earths axis of rotation intersects its surface. It is the southernmost point on the surface of the Earth, situated on the continent of Antarctica, it is the site of the United States Amundsen–Scott South Pole Station, which was established in 1956 and has been permanently staffed since that year. The Geographic South Pole should not be confused with the South Magnetic Pole, the South Pole is at the center of the Southern Hemisphere. For most purposes, the Geographic South Pole is defined as the point of the two points where the Earths axis of rotation intersects its surface. However, the Earths axis of rotation is actually subject to very small wobbles, the geographic coordinates of the South Pole are usually given simply as 90°S, since its longitude is geometrically undefined and irrelevant. When a longitude is desired, it may be given as 0°, at the South Pole, all directions face north. For this reason, directions at the Pole are given relative to grid north, along tight latitude circles, clockwise is east, and counterclockwise is west, opposite to the North Pole. The Geographic South Pole is located on the continent of Antarctica. It sits atop a featureless, barren, windswept and icy plateau at an altitude of 2,835 metres above sea level, and is located about 1,300 km from the nearest open sea at Bay of Whales. The ice is estimated to be about 2,700 metres thick at the Pole, the polar ice sheet is moving at a rate of roughly 10 metres per year in a direction between 37° and 40° west of grid north, down towards the Weddell Sea. Therefore, the position of the station and other artificial features relative to the geographic pole gradually shift over time. The Geographic South Pole is marked by a stake in the ice alongside a small sign, these are repositioned each year in a ceremony on New Years Day to compensate for the movement of the ice. The sign records the respective dates that Roald Amundsen and Robert F. Scott reached the Pole, followed by a quotation from each man. A new marker stake is designed and fabricated each year by staff at the site, the Ceremonial South Pole is an area set aside for photo opportunities at the South Pole Station. It is located around 180 metres from the Geographic South Pole, Amundsens Tent, The tent was erected by the Norwegian expedition led by Roald Amundsen on its arrival on 14 December 1911. It is currently buried beneath the snow and ice in the vicinity of the Pole and it has been designated a Historic Site or Monument, following a proposal by Norway to the Antarctic Treaty Consultative Meeting. In 1820, several expeditions claimed to have been the first to have sighted Antarctica, with the very first being the Russian expedition led by Faddey Bellingshausen and Mikhail Lazarev. The first landing was probably just over a year later when American Captain John Davis, the basic geography of the Antarctic coastline was not understood until the mid-to-late 19th century
South Pole
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The Geographic South Pole. (The flag used on the flagpole is interchangeable.)
South Pole
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1. South Geographic Pole 2. South Magnetic Pole (2007) 3. South Geomagnetic Pole (2005) 4. South Pole of Inaccessibility
South Pole
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The Ceremonial South Pole in 1998. (Background structures shown have since been replaced or altered.)
South Pole
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Argentine soldiers saluting the flag after erecting the pole in 1965
11.
Arctic Circle
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The Arctic Circle is the most northerly of the abstract five major circles of latitude as shown on maps of the Earth. The region north of this circle is known as the Arctic, the position of the Arctic Circle is not fixed, as of 7 April 2017, it runs 66°33′46. 6″ north of the Equator. Its latitude depends on the Earths axial tilt, which fluctuates within a margin of 2° over a 40, 000-year period, consequently, the Arctic Circle is currently drifting northwards at a speed of about 15 m per year. The word arctic comes from the Greek word ἀρκτικός and that from the word ἄρκτος, directly on the Arctic Circle these events occur, in principle, exactly once per year, at the June and December solstices, respectively. That is true at sea level, those limits increase with elevation above sea level, tens of thousands of years ago, waves of people migrated from eastern Siberia across the Bering Strait into North America to settle. Much later, in the period, there has been migration into some Arctic areas by Europeans. The largest communities north of the Arctic Circle are situated in Russia and Norway, Murmansk, Norilsk, Tromsø, rovaniemi in Finland is the largest settlement in the immediate vicinity of the Arctic Circle, lying slightly south of the line. In contrast, the largest North American community north of the Arctic Circle, of the Canadian and United States Arctic communities, Barrow, Alaska is the largest settlement with about 4,000 inhabitants. The Arctic Circle is roughly 16,000 kilometres, the area north of the Circle is about 20,000,000 km2 and covers roughly 4% of Earths surface. The Arctic Circle passes through the Arctic Ocean, the Scandinavian Peninsula, North Asia, Northern America, the land within the Arctic Circle is divided among eight countries, Norway, Sweden, Finland, Russia, the United States, Canada, Denmark, and Iceland. In the interior, summers can be warm, while winters are extremely cold
Arctic Circle
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A sign along the Dalton Highway marking the location of the Arctic Circle in Alaska.
Arctic Circle
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Map of the Arctic, with the Arctic Circle in blue and the July 10 °C mean isotherm in red
Arctic Circle
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Arctic Circle line in Rovaniemi, Finland
Arctic Circle
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Aurora Borealis above Arctic Circle sign along the Dempster Highway in Yukon, Canada
12.
Axial tilt
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In astronomy, axial tilt, also known as obliquity, is the angle between an objects rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. At an obliquity of zero, the two axes point in the direction, i. e. the rotational axis is perpendicular to the orbital plane. Over the course of an orbit, the obliquity usually does not change considerably, and this causes one pole to be directed more toward the Sun on one side of the orbit, and the other pole on the other side — the cause of the seasons on the Earth. Earths obliquity oscillates between 22.1 and 24.5 degrees on a 41, 000-year cycle, the mean obliquity is currently 23°26′13. 4″. There are two methods of specifying tilt. The IAU also uses the rule to define a positive pole for the purpose of determining orientation. Using this convention, Venus is tilted 177° and it is denoted by the Greek letter ε. Earth currently has a tilt of about 23. 4°. This value remains about the relative to a stationary orbital plane throughout the cycles of axial precession. But the ecliptic due to planetary perturbations, and the obliquity of the ecliptic is not a fixed quantity. At present, it is decreasing at a rate of about 47″ per century, Earths obliquity may have been reasonably accurately measured as early as 1100 BC in India and China. The ancient Greeks had good measurements of the obliquity since about 350 BC, about 830 AD, the Caliph Al-Mamun of Baghdad directed his astronomers to measure the obliquity, and the result was used in the Arab world for many years. It was widely believed, during the Middle Ages, that both precession and Earths obliquity oscillated around a value, with a period of 672 years. Earths axis remains tilted in the direction with reference to the background stars throughout a year. This means that one pole will be directed away from the Sun at one side of the orbit and this is the cause of Earths seasons. Summer occurs in the Northern hemisphere when the pole is directed toward the Sun. Variations in Earths axial tilt can influence the seasons and is likely a factor in climate change. The exact angular value of the obliquity is found by observation of the motions of Earth, from 1984, the Jet Propulsion Laboratorys DE series of computer-generated ephemerides took over as the fundamental ephemeris of the Astronomical Almanac
Axial tilt
Axial tilt
13.
Cross section (geometry)
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In geometry and science, a cross section is the intersection of a body in three-dimensional space with a plane, or the analog in higher-dimensional space. Cutting an object into slices creates many parallel cross sections, conic sections – circles, ellipses, parabolas, and hyperbolas – are formed by cross-sections of a cone at various different angles, as seen in the diagram at left. Any planar cross-section passing through the center of an ellipsoid forms an ellipse on its surface, a cross-section of a cylinder is a circle if the cross-section is parallel to the cylinders base, or an ellipse with non-zero eccentricity if it is neither parallel nor perpendicular to the base. If the cross-section is perpendicular to the base it consists of two line segments unless it is just tangent to the cylinder, in which case it is a single line segment. A cross section of a polyhedron is a polygon, if instead the cross section is taken for a fixed value of the density, the result is an iso-density contour. For the normal distribution, these contours are ellipses, a cross section can be used to visualize the partial derivative of a function with respect to one of its arguments, as shown at left. In economics, a function f specifies the output that can be produced by various quantities x and y of inputs, typically labor. The production function of a firm or a society can be plotted in three-dimensional space, also in economics, a cardinal or ordinal utility function u gives the degree of satisfaction of a consumer obtained by consuming quantities w and v of two goods. Cross sections are used in anatomy to illustrate the inner structure of an organ. A cross section of a trunk, as shown at left, reveals growth rings that can be used to find the age of the tree. Cavalieris principle states that solids with corresponding sections of equal areas have equal volumes. The cross-sectional area of an object when viewed from an angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has A ′ = π r 2 when viewed along its central axis, a sphere of radius r has A ′ = π r 2 when viewed from any angle. For a convex body, each ray through the object from the viewers perspective crosses just two surfaces, descriptive geometry Exploded view drawing Graphical projection Plans
Cross section (geometry)
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Pinus taeda cross section showing annual rings, Cheraw, South Carolina.
14.
Tropics
–
The tropics are a region of the Earth surrounding the equator. The tropics are also referred to as the zone and the torrid zone. The tropics include all the areas on the Earth where the Sun is at a point directly overhead at least once during the solar year. The tropics are distinguished from the climatic and biomatic regions of Earth, which are the middle latitudes. Tropical is sometimes used in a sense for a tropical climate to mean warm to hot and moist year-round. Many tropical areas have a dry and wet season, the wet season, rainy season or green season, is the time of year, ranging from one or more months, when most of the average annual rainfall in a region falls. Areas with wet seasons are disseminated across portions of the tropics and subtropics, under the Köppen climate classification, for tropical climates, a wet season month is defined as a month where average precipitation is 60 millimetres or more. Tropical rainforests technically do not have dry or wet seasons, since their rainfall is distributed through the year. When the wet season occurs during the season, or summer, precipitation falls mainly during the late afternoon. The wet season is a time when air quality improves, freshwater quality improves and vegetation grows significantly, floods cause rivers to overflow their banks, and some animals to retreat to higher ground. Soil nutrients diminish and erosion increases, the incidence of malaria increases in areas where the rainy season coincides with high temperatures. Animals have adaptation and survival strategies for the wetter regime, unfortunately, the previous dry season leads to food shortages into the wet season, as the crops have yet to mature. Regions within the tropics may well not have a tropical climate, there are alpine tundra and snow-capped peaks, including Mauna Kea, Mount Kilimanjaro, and the Andes as far south as the northernmost parts of Chile and Argentina. Under the Köppen climate classification, much of the area within the tropics is classed not as tropical but as dry including the Sahara Desert. Tropical plants and animals are those native to the tropics. Tropical ecosystems may consist of rainforests, dry forests, spiny forests, desert. There are often significant areas of biodiversity, and species present, particularly in rainforests. In biogeography, the tropics are divided into Paleotropics and Neotropics, together, they are sometimes referred to as the Pantropic
Tropics
–
Tropical sunset over the sea in Kota Kinabalu, Malaysia
Tropics
–
World map with the intertropical zone highlighted in red
Tropics
–
Coconut palms in the warm, tropical climate of Northern Brazil
Tropics
–
Tropical forest near Fonds-Saint-Denis, Martinique
15.
Zenith
–
The zenith is an imaginary point directly above a particular location, on the imaginary celestial sphere. Above means in the direction opposite to the apparent gravitational force at that location. The opposite direction, i. e. the direction in which gravity pulls, is toward the nadir, the zenith is the highest point on the celestial sphere. It was reduced to samt and miswritten as senit/cenit, as the m was misread as an ni, through the Old French cenith, zenith first appeared in the 17th century. The term zenith is sometimes used to refer to the highest point, way or level reached by a celestial body during its apparent orbit around a given point of observation. This sense of the word is used to describe the location of the Sun, but to an astronomer the sun does not have its own zenith. In a scientific context, the zenith is the direction of reference for measuring the zenith angle, in astronomy, the altitude in the horizontal coordinate system and the zenith angle are complementary angles, with the horizon perpendicular to the zenith. The astronomical meridian is also determined by the zenith, and is defined as a circle on the sphere that passes through the zenith, nadir. A zenith telescope is a type of telescope designed to point straight up at or near the zenith, the NASA Orbital Debris Observatory and the Large Zenith Telescope are both zenith telescopes since the use of liquid mirrors meant these telescopes could only point straight up. Azimuth Geodesy History of geodesy Keyhole problem Midheaven Subsolar point Vertical deflection Horizontal coordinate system Glickman, Todd S. Glossary of meteorology
Zenith
–
Shadows of trees when the sun is directly overhead (at the zenith). This happens at the solar noon if the tree's latitude equals the sun's declination at that moment.
Zenith
–
Diagram showing the relationship between the zenith, the nadir, and different types of horizon. Note that the zenith is opposite the nadir.
16.
Mercator projection
–
The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. So, for example, landmasses such as Greenland and Antarctica appear much larger than they actually are relative to land masses near the equator, Mercators 1569 edition was a large planisphere measuring 202 by 124 cm, printed in eighteen separate sheets. As in all cylindrical projections, parallels and meridians are straight, being a conformal projection, angles are preserved around all locations. At latitudes greater than 70° north or south the Mercator projection is practically unusable, a Mercator map can therefore never fully show the polar areas. All lines of constant bearing are represented by segments on a Mercator map. The name and explanations given by Mercator to his world map show that it was conceived for the use of marine navigation. The development of the Mercator projection represented a breakthrough in the nautical cartography of the 16th century. However, it was ahead of its time, since the old navigational. If these sheets were brought to the scale and assembled an approximation of the Mercator projection would be obtained. English mathematician Edward Wright, who published accurate tables for its construction, english mathematicians Thomas Harriot and Henry Bond who, independently, associated the Mercator projection with its modern logarithmic formula, later deduced by calculus. As on all map projections, shapes or sizes are distortions of the layout of the Earths surface. The Mercator projection exaggerates areas far from the equator, for example, Greenland appears larger than Africa, when in reality Africas area is 14 times greater and Greenlands is comparable to Algerias alone. Africa also appears to be roughly the size as Europe. Alaska takes as much area on the map as Brazil, when Brazils area is nearly five times that of Alaska, finland appears with a greater north-south extent than India, although Indias is greater. Antarctica appears as the biggest continent, although it is actually the fifth in area, the Mercator projection is still used commonly for navigation. On the other hand, because of land area distortions. Therefore, Mercator himself used the equal-area sinusoidal projection to show relative areas, the Mercator projection is still commonly used for areas near the equator, however, where distortion is minimal. Arno Peters stirred controversy when he proposed what is now called the Gall–Peters projection as the alternative to the Mercator
Mercator projection
–
Mercator projection of the world between 82°S and 82°N.
17.
Earth radius
–
Earth radius is the distance from the Earths center to its surface, about 6,371 km. This length is used as a unit of distance, especially in astronomy and geology. This article deals primarily with spherical and ellipsoidal models of the Earth, see Figure of the Earth for a more complete discussion of the models. The Earth is only approximately spherical, so no single value serves as its natural radius, distances from points on the surface to the center range from 6,353 km to 6,384 km. Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 km. It can also mean some kind of average of such distances, Aristotle, writing in On the Heavens around 350 BC, reports that the mathematicians guess the circumference of the Earth to be 400,000 stadia. Due to uncertainty about which stadion variant Aristotle meant, scholars have interpreted Aristotles figure to be anywhere from highly accurate to almost double the true value, the first known scientific measurement and calculation of the radius of the Earth was performed by Eratosthenes about 240 BC. Estimates of the accuracy of Eratosthenes’s measurement range from within 0. 5% to within 17%, as with Aristotles report, uncertainty in the accuracy of his measurement is due to modern uncertainty over which stadion definition he used. Earths rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere, local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of the Earths surface must be simpler than reality in order to be tractable, hence, we create models to approximate characteristics of the Earths surface, generally relying on the simplest model that suits the need. Each of the models in use involve some notion of the geometric radius. Strictly speaking, spheres are the solids to have radii. In the case of the geoid and ellipsoids, the distance from any point on the model to the specified center is called a radius of the Earth or the radius of the Earth at that point. It is also common to refer to any mean radius of a model as the radius of the earth. When considering the Earths real surface, on the hand, it is uncommon to refer to a radius. Rather, elevation above or below sea level is useful, regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km. Hence, the Earth deviates from a sphere by only a third of a percent. While specific values differ, the concepts in this article generalize to any major planet
Earth radius
–
For the historical development of the concept, see Spherical Earth.
Earth radius
–
Scale drawing of the oblateness of the 2003 IERS reference ellipsoid. The outer edge of the dark blue line is an ellipse with the same eccentricity as that of the Earth, with north at the top. For comparison, the outer edge of light blue area is a circle of diameter equal to the minor axis. The red line denotes the Karman line and the yellow area, the range of the International Space Station.
Earth radius
18.
Nautical mile
–
A nautical mile is a unit of measurement defined as exactly 1852 meters. Historically, it was defined as one minute of latitude, which is equivalent to one sixtieth of a degree of latitude. Today it is an SI derived unit, being rounded to a number of meters. The derived unit of speed is the knot, defined as one mile per hour. The geographical mile is the length of one minute of longitude along the Equator, there is no internationally agreed symbol. M is used as the abbreviation for the mile by the International Hydrographic Organization and by the International Bureau of Weights. NM is used by the International Civil Aviation Organization, nm is used by the U. S. National Oceanic and Atmospheric Administration. Nmi is used by the Institute of Electrical and Electronics Engineers, the word mile is from the Latin word for a thousand paces, mīlia. In 1617 the Dutch scientist Snell assessed the circumference of the Earth at 24,630 Roman miles, around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as the basis for a unit of measurement for distance, as one degree is 1/360 of a circle, one minute of arc is 1/21600 of a circle. These sexagesimal units originated in Babylonian astronomy, Gunter used Snells circumference to define a nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude.3 metres. Other countries measure the minute of arc at 45 degrees latitude, in 1929, the international nautical mile was defined by the First International Extraordinary Hydrographic Conference in Monaco as 1,852 meters. Imperial units and United States customary units used a definition of the nautical mile based on the Clarke Spheroid, the United States nautical mile was defined as 6,080.20 feet based in the Mendenhall Order foot of 1893. It was abandoned in favour of the nautical mile in 1954.181 meters. It was abandoned in 1970 and, legally, references to the unit are now converted to 1,853 meters. Conversion of units Orders of magnitude
Nautical mile
–
Historical definition – 1 nautical mile
19.
WGS84
–
The World Geodetic System is a standard for use in cartography, geodesy, and navigation including GPS. It comprises a standard system for the Earth, a standard spheroidal reference surface for raw altitude data. The latest revision is WGS84, established in 1984 and last revised in 2004, earlier schemes included WGS72, WGS66, and WGS60. WGS84 is the coordinate system used by the Global Positioning System. The coordinate origin of WGS84 is meant to be located at the Earths center of mass, the error is believed to be less than 2 cm. The WGS84 meridian of longitude is the IERS Reference Meridian,5.31 arc seconds or 102.5 metres east of the Greenwich meridian at the latitude of the Royal Observatory. The WGS84 datum surface is a spheroid with major radius a =6378137 m at the equator. The polar semi-minor axis b then equals a times, or 6356752.3142 m, currently, WGS84 uses the EGM96 geoid, revised in 2004. This geoid defines the sea level surface by means of a spherical harmonics series of degree 360. The deviations of the EGM96 geoid from the WGS84 reference ellipsoid range from about −105 m to about +85 m, EGM96 differs from the original WGS84 geoid, referred to as EGM84. Efforts to supplement the national surveying systems began in the 19th century with F. R. Helmerts famous book Mathematische und Physikalische Theorien der Physikalischen Geodäsie. Austria and Germany founded the Zentralbüro für die Internationale Erdmessung, a unified geodetic system for the whole world became essential in the 1950s for several reasons, International space science and the beginning of astronautics. The lack of inter-continental geodetic information, efforts of the U. S. Army, Navy and Air Force were combined leading to the DoD World Geodetic System 1960. Heritage surveying methods found elevation differences from a local horizontal determined by the level, plumb line. As a result, the elevations in the data are referenced to the geoid, the latter observational method is more suitable for global mapping. The sole contribution of data to the development of WGS60 was a value for the ellipsoid flattening which was obtained from the nodal motion of a satellite. Prior to WGS60, the U. S. Army, the Army performed an adjustment to minimize the difference between astro-geodetic and gravimetric geoids. By matching the relative astro-geodetic geoids of the selected datums with an earth-centered gravimetric geoid, since the Army and Air Force systems agreed remarkably well for the NAD, ED and TD areas, they were consolidated and became WGS60
WGS84
–
Handheld GPS receiver indicating the Greenwich meridian is 0.089 arcminutes (or 5.34 arcseconds) west to the WGS84 datum
WGS84
–
Geodesy
20.
Datum (geodesy)
–
A geodetic datum or geodetic system is a coordinate system, and a set of reference points, used to locate places on the Earth. An approximate definition of sea level is the datum WGS84, other datums are defined for other areas or at other times, ED50 was defined in 1950 over Europe and differs from WGS84 by a few hundred meters depending on where in Europe you look. Mars has no oceans and so no sea level, but at least two martian datums have been used to locate places there. Datums are used in geodesy, navigation, and surveying by cartographers, each starts with an ellipsoid, and then defines latitude, longitude and altitude coordinates. One or more locations on the Earths surface are chosen as anchor base-points, the difference in co-ordinates between datums is commonly referred to as datum shift. The datum shift between two particular datums can vary from one place to another within one country or region, the North Pole, South Pole and Equator will be in different positions on different datums, so True North will be slightly different. Different datums use different interpolations for the shape and size of the Earth. Because the Earth is an ellipsoid, localised datums can give a more accurate representation of the area of coverage than WGS84. OSGB36, for example, is an approximation to the geoid covering the British Isles than the global WGS84 ellipsoid. However, as the benefits of a global system outweigh the greater accuracy, horizontal datums are used for describing a point on the Earths surface, in latitude and longitude or another coordinate system. Vertical datums measure elevations or depths, in surveying and geodesy, a datum is a reference system or an approximation of the Earths surface against which positional measurements are made for computing locations. Horizontal datums are used for describing a point on the Earths surface, vertical datums are used to measure elevations or underwater depths. The horizontal datum is the used to measure positions on the Earth. A specific point on the Earth can have different coordinates. There are hundreds of local horizontal datums around the world, usually referenced to some convenient local reference point, contemporary datums, based on increasingly accurate measurements of the shape of the Earth, are intended to cover larger areas. The WGS84 datum, which is almost identical to the NAD83 datum used in North America, a vertical datum is used as a reference point for elevations of surfaces and features on the Earth including terrain, bathymetry, water levels, and man-made structures. Vertical datums are either, tidal, based on sea levels, gravimetric, based on a geoid, or geodetic, for the purpose of measuring the height of objects on land, the usual datum used is mean sea level. This is a datum which is described as the arithmetic mean of the hourly water elevation taken over a specific 19 years cycle
Datum (geodesy)
–
City of Chicago Datum Benchmark
Datum (geodesy)
–
Geodesy
21.
Ellipse
–
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a type of an ellipse having both focal points at the same location. The shape of an ellipse is represented by its eccentricity, which for an ellipse can be any number from 0 to arbitrarily close to, ellipses are the closed type of conic section, a plane curve resulting from the intersection of a cone by a plane. Ellipses have many similarities with the two forms of conic sections, parabolas and hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder and this ratio is called the eccentricity of the ellipse. Ellipses are common in physics, astronomy and engineering, for example, the orbit of each planet in our solar system is approximately an ellipse with the barycenter of the planet–Sun pair at one of the focal points. The same is true for moons orbiting planets and all other systems having two astronomical bodies, the shapes of planets and stars are often well described by ellipsoids. It is also the simplest Lissajous figure formed when the horizontal and vertical motions are sinusoids with the same frequency, a similar effect leads to elliptical polarization of light in optics. The name, ἔλλειψις, was given by Apollonius of Perga in his Conics, in order to omit the special case of a line segment, one presumes 2 a > | F1 F2 |, E =. The midpoint C of the segment joining the foci is called the center of the ellipse. The line through the foci is called the major axis and it contains the vertices V1, V2, which have distance a to the center. The distance c of the foci to the center is called the distance or linear eccentricity. The quotient c a is the eccentricity e, the case F1 = F2 yields a circle and is included. C2 is called the circle of the ellipse. This property should not be confused with the definition of an ellipse with help of a directrix below, for an arbitrary point the distance to the focus is 2 + y 2 and to the second focus 2 + y 2. Hence the point is on the ellipse if the condition is fulfilled 2 + y 2 +2 + y 2 =2 a. The shape parameters a, b are called the major axis. The points V3 =, V4 = are the co-vertices and it follows from the equation that the ellipse is symmetric with respect to both of the coordinate axes and hence symmetric with respect to the origin
Ellipse
–
Drawing an ellipse with two pins, a loop, and a pen
Ellipse
–
An ellipse obtained as the intersection of a cone with an inclined plane.
22.
Flattening
–
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution respectively. Other terms used are ellipticity, or oblateness, the usual notation for flattening is f and its definition in terms of the semi-axes of the resulting ellipse or ellipsoid is f l a t t e n i n g = f = a − b a. The compression factor is b/a in each case, for the ellipse, this factor is also the aspect ratio of the ellipse. There are two variants of flattening and when it is necessary to avoid confusion the above flattening is called the first flattening. The following definitions may be found in texts and online web texts In the following. All flattenings are zero for a circle, the flattenings are related to other parameters of the ellipse. For example, b = a = a, e 2 =2 f − f 2 =4 n 2, other values in the Solar System are Jupiter, f=1/16, Saturn, f= 1/10, the Moon f= 1/900. The flattening of the Sun is about 9×10−6, in 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid of revolution. The amount of flattening depends on the density and the balance of gravitational force, astronomy Earth ellipsoid Earths rotation Eccentricity Equatorial bulge Gravitational field Gravity formula Ovality Planetology Sphericity Roundness
Flattening
–
A circle of radius a compressed to an ellipse.
23.
National Geospatial-Intelligence Agency
–
NGA was known as the National Imagery and Mapping Agency until 2003. NGA headquarters is located at Fort Belvoir in Springfield, Virginia, the NGA campus, at 2.3 million square feet, is the third-largest government building in the Washington metropolitan area after The Pentagon and the Ronald Reagan Building. U. S. mapping and charting efforts remained relatively unchanged until World War I, using stereo viewers, photo-interpreters reviewed thousands of images. Many of these were of the target at different angles and times, giving rise to what became modern imagery analysis. The Engineer Reproduction Plant was the Army Corps of Engineerss first attempt to centralize mapping production, printing and it was located on the grounds of the Army War College in Washington, D. C. Previously, topographic mapping had largely been a function of individual field engineer units using field surveying techniques or copying existing or captured products, in addition, ERP assumed the supervision and maintenance of the War Department Map Collection, effective April 1,1939. With the advent of the Second World War aviation, field surveys began giving way to photogrammetry, photo interpretation, during wartime, it became increasingly possible to compile maps with minimal field work. Out of this emerged AMS, which absorbed the existing ERP in May 1942 and it was located at the Dalecarlia Site on MacArthur Blvd. just outside Washington, D. C. in Montgomery County, Maryland, and adjacent to the Dalecarlia Reservoir. AMS was designated as an Engineer field activity, effective July 1,1942, by General Order 22, OCE, the Army Map Service also combined many of the Armys remaining geographic intelligence organizations and the Engineer Technical Intelligence Division. The agencys credit union, Constellation Federal Credit Union, was chartered during the Army Map Service era and it has continued to serve all successive legacy agencies employees and their families. After the war, as capacity and range improved, the need for charts grew. The Army Air Corps established its map unit, which was renamed ACP in 1943 and was located in St. Louis, ACP was known as the U. S. Air Force Aeronautical Chart and Information Center from 1952 to 1972. A credit union was chartered for the ACP in 1948, called Aero Chart Credit Union and it was renamed Arsenal Credit Union in 1952, a nod to the St. Louis sites Civil War-era use as an arsenal. Shortly before leaving office in January 1961, President Dwight D. Eisenhower authorized the creation of the National Photographic Interpretation Center, lundahl, combining Central Intelligence Agency, Army, Navy, and Air Force assets to solve national intelligence problems. NPIC was a component of the CIAs Directorate of Science and Technology, NPIC first identified the Soviet Unions basing of missiles in Cuba in 1962. The Defense Mapping Agency was created on January 1,1972, dMAs birth certificate, DoD Directive 5105.40, resulted from a formerly classified Presidential directive, Organization and Management of the U. S. Foreign Intelligence Community, which directed the consolidation of mapping functions previously dispersed among the military services, DMA became operational on July 1,1972, pursuant to General Order 3, DMA. On Oct.1,1996, DMA was folded into the National Imagery, DMA was first headquartered at the United States Naval Observatory in Washington, D. C, then at Falls Church, Virginia
National Geospatial-Intelligence Agency
–
NGA Campus East, the headquarters of the agency, features trapezoidal windows and color-coded interior sections.
National Geospatial-Intelligence Agency
–
Seal of the U.S. National Geospatial-Intelligence Agency
National Geospatial-Intelligence Agency
–
The U.S. national security team gathered in the Situation Room to await the outcome of Operation Neptune's Spear. A document from NGA can be seen on the table, although it has been obscured.
National Geospatial-Intelligence Agency
–
New Headquarters of the National Geospatial-Intelligence Agency
24.
Authalic radius
–
Earth radius is the distance from the Earths center to its surface, about 6,371 km. This length is used as a unit of distance, especially in astronomy and geology. This article deals primarily with spherical and ellipsoidal models of the Earth, see Figure of the Earth for a more complete discussion of the models. The Earth is only approximately spherical, so no single value serves as its natural radius, distances from points on the surface to the center range from 6,353 km to 6,384 km. Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 km. It can also mean some kind of average of such distances, Aristotle, writing in On the Heavens around 350 BC, reports that the mathematicians guess the circumference of the Earth to be 400,000 stadia. Due to uncertainty about which stadion variant Aristotle meant, scholars have interpreted Aristotles figure to be anywhere from highly accurate to almost double the true value, the first known scientific measurement and calculation of the radius of the Earth was performed by Eratosthenes about 240 BC. Estimates of the accuracy of Eratosthenes’s measurement range from within 0. 5% to within 17%, as with Aristotles report, uncertainty in the accuracy of his measurement is due to modern uncertainty over which stadion definition he used. Earths rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere, local topography increases the variance, resulting in a surface of profound complexity. Our descriptions of the Earths surface must be simpler than reality in order to be tractable, hence, we create models to approximate characteristics of the Earths surface, generally relying on the simplest model that suits the need. Each of the models in use involve some notion of the geometric radius. Strictly speaking, spheres are the solids to have radii. In the case of the geoid and ellipsoids, the distance from any point on the model to the specified center is called a radius of the Earth or the radius of the Earth at that point. It is also common to refer to any mean radius of a model as the radius of the earth. When considering the Earths real surface, on the hand, it is uncommon to refer to a radius. Rather, elevation above or below sea level is useful, regardless of the model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km. Hence, the Earth deviates from a sphere by only a third of a percent. While specific values differ, the concepts in this article generalize to any major planet
Authalic radius
–
For the historical development of the concept, see Spherical Earth.
Authalic radius
–
Scale drawing of the oblateness of the 2003 IERS reference ellipsoid. The outer edge of the dark blue line is an ellipse with the same eccentricity as that of the Earth, with north at the top. For comparison, the outer edge of light blue area is a circle of diameter equal to the minor axis. The red line denotes the Karman line and the yellow area, the range of the International Space Station.
Authalic radius
25.
Gudermannian function
–
The Gudermannian function, named after Christoph Gudermann, relates the circular functions and hyperbolic functions without explicitly using complex numbers. Some related formula, such as arccot , doesnt quite work as definition. Sin = tanh x, csc = coth x, cos = sech x, sec = cosh x, tan = sinh x, cot = csch x, tan = tanh . D d x gd x = sech x, d d x gd −1 x = sec x, the function was introduced by Johann Heinrich Lambert in the 1760s at the same time as the hyperbolic functions. Gudermann had published articles in Crelles Journal that were collected in Theorie der potenzial- oder cyklisch-hyperbolischen Functionen, the notation gd was introduced by Cayley where he starts by calling gd. The Gudermannian may be used in the definition of the transverse Mercator projection, the Gudermannian appears in a non-periodic solution of the inverted pendulum. The Gudermannian also appears in a moving mirror solution of the dynamical Casimir effect, hyperbolic secant distribution Mercator projection Tangent half-angle formula Tractrix Trigonometric identity
Gudermannian function
–
Graph of the Gudermannian function
26.
Fixed-point iteration
–
In numerical analysis, fixed-point iteration is a method of computing fixed points of iterated functions. If f is continuous, then one can prove that the x is a fixed point of f, i. e. f = x. More generally, the function f can be defined on any space with values in that same space. A first simple and useful example is the Babylonian method for computing the root of a>0. This is a case of Newtons method quoted below. The fixed-point iteration x n +1 = cos x n converges to the fixed point of the function f = cos x for any starting point x 0. This example does satisfy the assumptions of the Banach fixed point theorem, the Banach fixed-point theorem allows one to obtain fixed-point iterations with linear convergence. The fixed-point iteration x n +1 =2 x n will diverge unless x 0 =0 and we say that the fixed point of f =2 x is repelling. The requirement that f is continuous is important, as the example shows. The iteration x n +1 = { x n 2, x n ≠01, x n =0 converges to 0 for all values of x 0. However,0 is not a point of the function f = { x 2, x ≠01, x =0 as this function is not continuous at x =0. Newtons method for finding roots of a differentiable function f is x n +1 = x n − f f ′. If we write g = x − f f ′, we may rewrite the Newton iteration as the fixed-point iteration x n +1 = g. If this iteration converges to a point x of g, then x = g = x − f f ′. The reciprocal of anything is nonzero, therefore f =0, x is a root of f, under the assumptions of the Banach fixed point theorem, the Newton iteration, framed as the fixed point method, demonstrates linear convergence. However, a detailed analysis shows quadratic convergence, i. e. | x n − x | < C q 2 n. Halleys method is similar to Newtons method but, when it works correctly, in general, it is possible to design methods that converge with speed C q k n for any k ∈ N. As a general rule, the higher the k, the less stable it is, for these reasons, higher order methods are typically not used
Fixed-point iteration
–
The fixed-point iteration x n +1 = sin x n with initial value x 0 = 2 converges to 0. This example does not satisfy the assumptions of the Banach fixed point theorem and so its speed of convergence is very slow.
27.
Newton's method
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In numerical analysis, Newtons method, named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots of a real-valued function. If the function satisfies the assumptions made in the derivation of the formula, geometrically, is the intersection of the x-axis and the tangent of the graph of f at. The process is repeated as x n +1 = x n − f f ′ until an accurate value is reached. This algorithm is first in the class of Householders methods, succeeded by Halleys method, the method can also be extended to complex functions and to systems of equations. This x-intercept will typically be an approximation to the functions root than the original guess. Suppose f, → ℝ is a function defined on the interval with values in the real numbers ℝ. The formula for converging on the root can be easily derived, suppose we have some current approximation xn. Then we can derive the formula for an approximation, xn +1 by referring to the diagram on the right. The equation of the tangent line to the curve y = f at the point x = xn is y = f ′ + f, the x-intercept of this line is then used as the next approximation to the root, xn +1. In other words, setting y to zero and x to xn +1 gives 0 = f ′ + f, Solving for xn +1 gives x n +1 = x n − f f ′. We start the process off with some arbitrary initial value x0, the method will usually converge, provided this initial guess is close enough to the unknown zero, and that f ′ ≠0. More details can be found in the section below. The Householders methods are similar but have higher order for even faster convergence, however, his method differs substantially from the modern method given above, Newton applies the method only to polynomials. He does not compute the successive approximations xn, but computes a sequence of polynomials, finally, Newton views the method as purely algebraic and makes no mention of the connection with calculus. Newton may have derived his method from a similar but less precise method by Vieta, a special case of Newtons method for calculating square roots was known much earlier and is often called the Babylonian method. Newtons method was used by 17th-century Japanese mathematician Seki Kōwa to solve single-variable equations, Newtons method was first published in 1685 in A Treatise of Algebra both Historical and Practical by John Wallis. In 1690, Joseph Raphson published a description in Analysis aequationum universalis. Finally, in 1740, Thomas Simpson described Newtons method as a method for solving general nonlinear equations using calculus
Newton's method
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The tangent lines of x 3 - 2 x + 2 at 0 and 1 intersect the x -axis at 1 and 0 respectively, illustrating why Newton's method oscillates between these values for some starting points.
Newton's method
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The function ƒ is shown in blue and the tangent line is in red. We see that x n +1 is a better approximation than x n for the root x of the function f.
28.
Spherical polar coordinates
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It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is called the radius or radial coordinate. The polar angle may be called colatitude, zenith angle, normal angle, the use of symbols and the order of the coordinates differs between sources. In both systems ρ is often used instead of r, other conventions are also used, so great care needs to be taken to check which one is being used. A number of different spherical coordinate systems following other conventions are used outside mathematics, in a geographical coordinate system positions are measured in latitude, longitude and height or altitude. There are a number of different celestial coordinate systems based on different fundamental planes, the polar angle is often replaced by the elevation angle measured from the reference plane. Elevation angle of zero is at the horizon, the spherical coordinate system generalises the two-dimensional polar coordinate system. It can also be extended to spaces and is then referred to as a hyperspherical coordinate system. To define a coordinate system, one must choose two orthogonal directions, the zenith and the azimuth reference, and an origin point in space. These choices determine a plane that contains the origin and is perpendicular to the zenith. The spherical coordinates of a point P are then defined as follows, the inclination is the angle between the zenith direction and the line segment OP. The azimuth is the angle measured from the azimuth reference direction to the orthogonal projection of the line segment OP on the reference plane. The sign of the azimuth is determined by choosing what is a sense of turning about the zenith. This choice is arbitrary, and is part of the coordinate systems definition, the elevation angle is 90 degrees minus the inclination angle. If the inclination is zero or 180 degrees, the azimuth is arbitrary, if the radius is zero, both azimuth and inclination are arbitrary. In linear algebra, the vector from the origin O to the point P is often called the vector of P. Several different conventions exist for representing the three coordinates, and for the order in which they should be written. The use of to denote radial distance, inclination, and azimuth, respectively, is common practice in physics, and is specified by ISO standard 80000-2,2009, and earlier in ISO 31-11
Spherical polar coordinates
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Spherical coordinates (r, θ, φ) as commonly used in physics: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi). The symbol ρ (rho) is often used instead of r.
29.
Geographic coordinate conversion
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In geodesy, conversion among different geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion comprises a number of different types of conversion, format change of coordinates, conversion of coordinate systems. Geographic coordinate conversion has applications in cartography, surveying, navigation, in geodesy, geographic coordinate conversion is defined as translation among different coordinate formats or map projections all referenced to the same geodetic datum. A geographic coordinate transformation is a translation among different geodetic datums, both geographic coordinate conversion and transformation will be considered in this article. This article assumes readers are already familiar with the content in the geographic coordinate system. Informally, specifying a location usually means giving the locations latitude and longitude. A coordinate system conversion is a conversion from one system to another. Common conversion tasks include conversion between geodetic and ECEF coordinates and conversion from one type of map projection to another, the normal N is the distance from the surface to the Z-axis along the ellipsoid normal. The orthogonality of the coordinates is confirmed via differentiation, =, =, there are several methods that solve the equation, two are shown. The following Bowrings irrational geodetic-latitude equation is efficient to be solved by Newton–Raphson iteration method, κ −1 − e 2 a κ p 2 + z 2 κ2 =0, where κ = p z tan ϕ. The height is calculated as, h = e −2 p 2 + z 2 κ2, κ0 = −1, the constant κ0 is a good starter value for the iteration when h ≈0. Bowring showed that the single iteration produces a sufficiently accurate solution and he used extra trigonometric functions in his original formulation. A number of techniques and algorithms are available but the most accurate according to Zhu, is the following 15 step procedure summarised by Kaplan. If a radar is located at and an aircraft at then the vector pointing from the radar to the aircraft in the ENU frame is = Note, a prior version of this page showed use of the geocentric latitude. The geocentric latitude is not the appropriate up direction for the tangent plane. The geocentric and geodetic longitude have the same value and this is true for the Earth and other similar shaped planets because their latitude lines can be considered in much more degree perfect circles when compared to their longitude lines. Tan λ = Y r X r Note, Unambiguous determination of ϕ and λ requires knowledge of which quadrant the coordinates lie in. The formulas involved can be complex and in cases, such as in the ECEF to geodetic conversion above
Geographic coordinate conversion
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The length PQ is called Normal (). The length IQ is equal to. R =.
30.
Vertical line
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The vertical bar is a computer character and glyph with various uses in mathematics, computing, and typography. It has many names, often related to particular meanings, Sheffer stroke, verti-bar, vbar, stick, broken bar, vertical line, vertical slash, bar, glidus, obelisk, or pipe. The vertical bar is used as a symbol in absolute value, | x |, read the absolute value of x. set-builder notation. Often a colon, is used instead of a vertical bar, sometimes a vertical bar following a function, with sub- and super-script limits a and b is used when evaluating definite integrals to mean f from a to b, or f-f. A vertical bar can be used to separate variables from fixed parameters in a function, examples, | ψ ⟩, The quantum physical state ψ. ⟨ ψ |, The dual state corresponding to the state above, ⟨ ψ | ρ ⟩, The inner product of states ψ and ρ. A pipe is a communication mechanism originating in Unix, which allows the output of one process to be used as input to another. In this way, a series of commands can be piped together, in most Unix shells, this is represented by the vertical bar character. For example, grep -i blair filename. log | more where the output from the process is piped to the more process. The same pipe feature is found in later versions of DOS. This usage has led to the character itself being called pipe, in many programming languages, the vertical bar is used to designate the logic operation or, either bitwise or or logical or. Specifically, in C and other languages following C syntax conventions, such as C++, Perl, Java and C#, since the character was originally not available in all code pages and keyboard layouts, ANSI C can transcribe it in form of the trigraph. Which, outside string literals, is equivalent to the | character, in regular expression syntax, the vertical bar again indicates logical or. For example, the Unix command grep -E fu|bar matches lines containing fu or bar, the double vertical bar operator || denotes string concatenation in PL/I, standard ANSI SQL, and theoretical computer science. Although not as common as commas or tabs, the bar can be used as a delimiter in a flat file. Examples of a standard data format are LEDES 1998B and HL7. It is frequently used because vertical bars are typically uncommon in the data itself, similarly, the vertical bar may see use as a delimiter for regular expression operations. This is useful when the expression contains instances of the more common forward slash delimiter
Vertical line
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The code point 124 (7C hexadecimal) is occupied by a broken bar in a dot matrix printer of the late 1980s, which apparently lacks a solid vertical bar. Due to this, broken bar is also used for vertical line approximation. See the full picture (3,000 × 2,500 pixels).
31.
Plumb line
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A plumb bob, or plummet, is a weight, usually with a pointed tip on the bottom, suspended from a string and used as a vertical reference line, or plumb-line. It is essentially the equivalent of a water level. The instrument has been used since at least the time of ancient Egypt to ensure that constructions are plumb and it is also used in surveying, to establish the nadir with respect to gravity of a point in space. It is used with a variety of instruments to set the instrument exactly over a survey marker or to transcribe positions onto the ground for placing a marker. The plumb in plumb-bob comes from the fact that tools were originally made of lead. The adjective plumb developed by extension, as did the noun aplomb, until the modern age, plumb-bobs were used on most tall structures to provide vertical datum lines for the building measurements. A section of the scaffolding would hold a line, which was centered over a datum mark on the floor. As the building proceeded upward, the line would also be taken higher. Many cathedral spires, domes and towers still have brass datum marks inlaid into their floors, which signify the center of the structure above. Although a plumb-bob and line alone can determine only a vertical if they are mounted on a suitable scale, the early skyscrapers used heavy plumb-bobs, hung on wire in their elevator shafts. A plumb bob may be in a container of water, molasses, very viscous oils or other liquids to dampen any swinging movement, functioning as a shock absorber. Students of figure drawing will also use of a plumb line to find the vertical axis through the center of gravity of their subject. The device used may be purpose-made plumb lines, or simply makeshift devices made from a piece of string and this plumb line is important for lining up anatomical geometries and visualizing the subjects center of balance. Bob Centre of mass – used to find the centre of mass on a 2D shape which has uniform density Chalk line Vertical direction 60 oz. Plumb Bob
Plumb line
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A plumb-bob
Plumb line
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Plumb-bob with scale as an inclinometer
32.
Declination
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In astronomy, declination is one of the two angles that locate a point on the celestial sphere in the equatorial coordinate system, the other being hour angle. Declinations angle is measured north or south of the celestial equator, the root of the word declination means a bending away or a bending down. It comes from the root as the words incline and recline. Declination in astronomy is comparable to geographic latitude, projected onto the celestial sphere, points north of the celestial equator have positive declinations, while those south have negative declinations. Any units of measure can be used for declination, but it is customarily measured in the degrees, minutes. Declinations with magnitudes greater than 90° do not occur, because the poles are the northernmost and southernmost points of the celestial sphere, the Earths axis rotates slowly westward about the poles of the ecliptic, completing one circuit in about 26,000 years. This effect, known as precession, causes the coordinates of stationary celestial objects to change continuously, therefore, equatorial coordinates are inherently relative to the year of their observation, and astronomers specify them with reference to a particular year, known as an epoch. Coordinates from different epochs must be rotated to match each other. The currently used standard epoch is J2000.0, which is January 1,2000 at 12,00 TT, the prefix J indicates that it is a Julian epoch. Prior to J2000.0, astronomers used the successive Besselian Epochs B1875.0, B1900.0, the declinations of Solar System objects change very rapidly compared to those of stars, due to orbital motion and close proximity. This similarly occurs in the Southern Hemisphere for objects with less than −90° − φ. An extreme example is the star which has a declination near to +90°. Circumpolar stars never dip below the horizon, conversely, there are other stars that never rise above the horizon, as seen from any given point on the Earths surface. Generally, if a star whose declination is δ is circumpolar for some observer, then a star whose declination is −δ never rises above the horizon, as seen by the same observer. Likewise, if a star is circumpolar for an observer at latitude φ, neglecting atmospheric refraction, declination is always 0° at east and west points of the horizon. At the north point, it is 90° − |φ|, and at the south point, from the poles, declination is uniform around the entire horizon, approximately 0°. Non-circumpolar stars are visible only during certain days or seasons of the year, the Suns declination varies with the seasons. As seen from arctic or antarctic latitudes, the Sun is circumpolar near the summer solstice, leading to the phenomenon of it being above the horizon at midnight
Declination
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Right ascension (blue) and declination (green) as seen from outside the celestial sphere.
33.
Celestial equator
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The celestial equator is a great circle on the imaginary celestial sphere, in the same plane as the Earths equator. In other words, it is a projection of the terrestrial equator out into space, as a result of the Earths axial tilt, the celestial equator is inclined by 23. 4° with respect to the ecliptic plane. An observer standing on the Earths equator visualizes the celestial equator as a semicircle passing directly overhead through the zenith, as the observer moves north, the celestial equator tilts towards the opposite horizon. Celestial objects near the equator are visible worldwide, but they culminate the highest in the sky in the tropics. The celestial equator currently passes through these constellations, Celestial bodies other than Earth also have similarly defined celestial equators, Celestial pole Celestial sphere Declination Equatorial coordinate system
Celestial equator
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The celestial equator is inclined by 23.4° to the ecliptic plane. The image shows the relations between Earth's axial tilt (or obliquity), rotation axis and plane of orbit.
34.
Ecliptic coordinates
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The ecliptic coordinate system is a celestial coordinate system commonly used for representing the positions and orbits of Solar System objects. Because most planets, and many small Solar System bodies have orbits with small inclinations to the ecliptic, using it as the fundamental plane is convenient. The systems origin can be either the center of the Sun or the center of the Earth, its direction is towards the vernal equinox. It may be implemented in spherical coordinates or rectangular coordinates, a slow motion of Earths axis, precession, causes a slow, continuous turning of the coordinate system westward about the poles of the ecliptic, completing one circuit in about 26,000 years. Superimposed on this is a motion of the ecliptic. The three most commonly used are, Mean equinox of an epoch is a fixed standard direction. Mean equinox of date is the intersection of the ecliptic of date with the mean equator, commonly used in planetary orbit calculation. True equinox of date is the intersection of the ecliptic of date with the true equator and this is the actual intersection of the two planes at any particular moment, with all motions accounted for. A position in the coordinate system is thus typically specified true equinox and ecliptic of date, mean equinox and ecliptic of J2000.0. Note that there is no mean ecliptic, as the ecliptic is not subject to small periodic oscillations, ecliptic longitude or celestial longitude measures the angular distance of an object along the ecliptic from the primary direction. Like right ascension in the coordinate system, the primary direction points from the Earth towards the Sun at the vernal equinox of the Northern Hemisphere. Because it is a system, ecliptic longitude is measured positive eastwards in the fundamental plane from 0° to 360°. Because of axial precession, the longitude of most fixed stars increases by about 50.3 arcseconds per year, or 83.8 arcminutes per century. Ecliptic latitude or celestial latitude, measures the distance of an object from the ecliptic towards the north or south ecliptic pole. For example, the ecliptic pole has a celestial latitude of +90°. Ecliptic latitude for fixed stars is not affected by precession, distance is also necessary for a complete spherical position. Different distance units are used for different objects, within the Solar System, astronomical units are used, and for objects near the Earth, Earth radii or kilometers are used. From antiquity through the 18th century, ecliptic longitude was measured using twelve zodiacal signs, each of 30° longitude
Ecliptic coordinates
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Earth-centered ecliptic coordinates as seen from outside the celestial sphere. Ecliptic longitude (red) is measured along the ecliptic from the vernal equinox. Ecliptic latitude (yellow) is measured perpendicular to the ecliptic. A full globe is shown here, although high-latitude coordinates are seldom seen except for certain comets and asteroids.
35.
Cardinal direction
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The four cardinal directions or cardinal points are the directions of north, east, south, and west, commonly denoted by their initials, N, E, S, W. East and west are at angles to north and south, with east being in the clockwise direction of rotation from north. Intermediate points between the four cardinal directions form the points of the compass, the intermediate directions are northeast, southeast, southwest, and northwest. To keep to a bearing is not, in general, the same as going in a straight direction along a great circle, conversely, one can keep to a great circle and the bearing may change. Thus the bearing of a path crossing the North Pole changes abruptly at the Pole from North to South. When traveling East or West, it is only on the Equator that one can keep East or West, anywhere else, maintaining latitude requires a change in direction, requires steering. However, this change in direction becomes increasingly negligible as one moves to lower latitudes, the Earth has a magnetic field which is approximately aligned with its axis of rotation. A magnetic compass is a device uses this field to determine the cardinal directions. Magnetic compasses are used, but only moderately accurate. The position of the Sun in the sky can be used for orientation if the time of day is known. In the morning the Sun rises roughly in the east and tracks upwards, in the evening it sets in the west, again roughly and only due west exactly on the equinoxes. This method does not work well when closer to the equator since, in the northern hemisphere. Conversely, at low latitudes in the hemisphere the sun may be to the south of the observer in summer. If they move clockwise, the sun will be in the south at midday, because of the Earths axial tilt, no matter what the location of the viewer, there are only two days each year when the sun rises precisely due east. On all other days, depending on the time of year, for all locations the sun is seen to rise north of east from the Northward equinox to the Southward equinox, and rise south of east from the Southward equinox to the Northward equinox. There is a method by which an analog watch can be used to locate north and south. The Sun appears to move in the sky over a 24-hour period while the hand of a 12-hour clock face takes twelve hours to complete one rotation. In the northern hemisphere, if the watch is rotated so that the hand points toward the Sun
Cardinal direction
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Specialized 24-hour watch with compass card dial
Cardinal direction
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A compass rose showing the four cardinal directions, the four intercardinal directions, plus eight further divisions.
36.
ArXiv
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In many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 14,1991, arXiv. org passed the half-million article milestone on October 3,2008, by 2014 the submission rate had grown to more than 8,000 per month. The arXiv was made possible by the low-bandwidth TeX file format, around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Additional modes of access were added, FTP in 1991, Gopher in 1992. The term e-print was quickly adopted to describe the articles and its original domain name was xxx. lanl. gov. Due to LANLs lack of interest in the rapidly expanding technology, in 1999 Ginsparg changed institutions to Cornell University and it is now hosted principally by Cornell, with 8 mirrors around the world. Its existence was one of the factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists regularly upload their papers to arXiv. org for worldwide access, Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv. The annual budget for arXiv is approximately $826,000 for 2013 to 2017, funded jointly by Cornell University Library, annual donations were envisaged to vary in size between $2,300 to $4,000, based on each institution’s usage. As of 14 January 2014,174 institutions have pledged support for the period 2013–2017 on this basis, in September 2011, Cornell University Library took overall administrative and financial responsibility for arXivs operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it was supposed to be a three-hour tour, however, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. The lists of moderators for many sections of the arXiv are publicly available, additionally, an endorsement system was introduced in 2004 as part of an effort to ensure content that is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, new authors from recognized academic institutions generally receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for allegedly restricting scientific inquiry, perelman appears content to forgo the traditional peer-reviewed journal process, stating, If anybody is interested in my way of solving the problem, its all there – let them go and read about it. The arXiv generally re-classifies these works, e. g. in General mathematics, papers can be submitted in any of several formats, including LaTeX, and PDF printed from a word processor other than TeX or LaTeX. The submission is rejected by the software if generating the final PDF file fails, if any image file is too large. ArXiv now allows one to store and modify an incomplete submission, the time stamp on the article is set when the submission is finalized
ArXiv
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arXiv
ArXiv
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A screenshot of the arXiv taken in 1994, using the browser NCSA Mosaic. At the time, HTML forms were a new technology.
37.
Sourceforge
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SourceForge is a Web-based service that offers software developers a centralized online location to control and manage free and open-source software projects. SourceForge was one of the first to offer this service free of charge to open source projects, since 2012 the website runs on Apache Allura software. As of March 2014, the SourceForge repository claimed to host more than 430,000 projects and had more than 3.7 million registered users, the domain sourceforge. net attracted at least 33 million visitors by August 2009 according to a Compete. com survey. Negative community reactions to the program led to review of the program, nonetheless. The program was cancelled by new owners BizX on February 9,2016, on May 17,2016 they announced that it would scan all projects for malware, SourceForge is a web-based source code repository. It acts as a location for free and open-source software projects. It was the first to offer service for free to open-source projects. Project developers have access to centralized storage and tools for managing projects, though it is best known for providing revision control systems such as CVS, SVN, Bazaar, Git and Mercurial. Major features include project wikis, metrics and analysis, access to a MySQL database, the vast number of users at SourceForge. net exposes prominent projects to a variety of developers and can create a positive feedback loop. As a projects activity rises, SourceForge. nets internal ranking system makes it visible to other developers through SourceForge directory. Given that many projects fail due to lack of developer support. SourceForges traditional revenue model is through advertising sales on their site. In 2006 SourceForge Inc. reported quarterly takings of US$6.5 million, in 2009 SourceForge reported a gross quarterly income of US$23 million through media and e-commerce streams. In 2011 a revenue of 20 million USD was reported for the value of the SourceForge, slashdot and freecode holdings. Since 2013 additional revenue generation schemes, such as models, were trialled. The result has in some cases been the appearance of malware bundled with SourceForge downloads, on February 9,2016, SourceForge announced they had eliminated their DevShare program practice of bundling installers with project downloads. The software running the SourceForge site was released as software in January 2000 and was later named SourceForge Alexandria. In September 2002 SourceForge was temporarily banned in China, the site was banned again in China, for about a month, in July 2008
Sourceforge
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Screenshot of SourceForge main page in 2014
38.
Eastern Hemisphere
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The Eastern Hemisphere is a geographical term for the half of the earth that is east of the prime meridian and west of the antimeridian. It is also used to refer to Europe, Asia, Africa, and Australia, in contrast with the Western Hemisphere and this hemisphere may also be called the Oriental Hemisphere. In addition, it may be used in a cultural or geopolitical sense as a synonym for the Old World, the line demarcating the Eastern and Western Hemispheres is an arbitrary convention, unlike the Equator which divides the Northern and Southern Hemispheres. The prime meridian at 0° longitude and the antimeridian, at 180° longitude are the accepted boundaries. Prior to the adoption of standard time, numerous prime meridians were decreed by various countries where time was defined by local noon. The center of the Eastern Hemisphere is located in the Indian Ocean at the intersection of the equator, the land mass of the Eastern Hemisphere is larger than that of the Western Hemisphere and has a wide variety of habitats. 82% of humans live in the Eastern Hemisphere, compared to 18% in Western Hemisphere, media related to Eastern Hemisphere at Wikimedia Commons
Eastern Hemisphere
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Eastern Hemisphere
39.
180th meridian
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The 180th meridian or antimeridian is the meridian 180° east or west of the Prime Meridian, with which it forms a great circle dividing the earth into the Western and Eastern Hemispheres. It is common to both east longitude and west longitude and it is used as the basis for the International Date Line because it for the most part passes through the open waters of the Pacific Ocean. However, the passes through Russia and Fiji as well as Antarctica. The only place where roads cross this meridian, and where there are very close to it, is in Fiji. Many geographic software libraries or data formats project the world to a rectangle and this often makes it non-trivial to do simple tasks over the 180th meridian. Some examples, The GeoJSON specification strongly suggests splitting geometries so that neither of their parts cross the antimeridian, in OpenStreetMap, areas are split at the 180th meridian. 179th meridian east 179th meridian west Prime meridian
180th meridian
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180th meridian
180th meridian
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180° Meridian, Taveuni, Fiji
40.
100th meridian west
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The 100th meridian west forms a great circle with the 80th meridian east. Dodge City, Kansas lies exactly at the intersection of the Arkansas River, the type of agriculture west of the meridian typically relies heavily on irrigation. Historically the meridian has often taken as a rough boundary between the eastern and western United States. White settlement, spreading westward after the American Civil War, settled the area around this meridian during the 1870s, wallace Stegners Beyond the Hundredth Meridian, is a biography of John Wesley Powell, an explorer of the American West. The song At the Hundredth Meridian by The Tragically Hip is about the 100th meridian west, specifically in Canada, 99th meridian west 101st meridian west Rain follows the plow
100th meridian west
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Sign marking the 100th meridian in Cozad, Nebraska
41.
40th parallel north
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The 40th parallel north is a circle of latitude that is 40 degrees north of the Earths equatorial plane. It crosses Europe, the Mediterranean Sea, Asia, the Pacific Ocean, North America, at this latitude the sun is visible for 15 hours,1 minute during the summer solstice and 9 hours,20 minutes during the winter solstice. On 21 June, the altitude of the sun is 73.83 degrees and 26.17 degrees on 21 December. Starting in Spain at the Prime Meridian and heading eastwards, the parallel 40° north passes through, on 30 May 1854, the Kansas–Nebraska Act created the Territory of Kansas and the Territory of Nebraska divided by the parallel 40° north. Both territories were required to determine for themselves whether to permit slavery, open conflict between free-state and pro-slavery forces in the Kansas Territory was one of the root causes of the American Civil War. The parallel 40° north formed the northern boundary of the British Colony of Maryland. A subsequent royal grant gave the Colony of Pennsylvania land north of the 40th parallel but mistakenly assumed it would intersect the Twelve Mile Circle, pennsylvanias border was thus unclear and the colony pushed for a border far south of the 40th parallel. The Mason–Dixon Line was drawn between 1763 and 1767 as the boundary between the overlapping claims of these two colonies. The parallel 40° north passes through the cities of Philadelphia, Pennsylvania and Columbus, Ohio, as well as suburbs of Indianapolis, Indiana and Denver. Baseline Road in Boulder, Colorado, traces the parallel 40° north, thistle, Utah, a ghost town since 1983, is slightly below 40° north. 39th parallel north 41st parallel north Baseline Geological Exploration of the Fortieth Parallel
40th parallel north
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Survey marker on the Kansas/Nebraska state line
42.
Northern Hemisphere
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The Northern Hemisphere is the half of Earth that is north of the equator. For other planets in the Solar System, north is defined as being in the celestial hemisphere relative to the invariable plane of the solar system as Earths North pole. Due to the Earths axial tilt, winter in the Northern Hemisphere lasts from the December solstice to the March Equinox, the dates vary each year due to the difference between the calendar year and the astronomical year. Its surface is 60. 7% water, compared with 80. 9% water in the case of the Southern Hemisphere, the Arctic is the region north of the Arctic Circle. Its climate is characterized by cold winters and cool summers, precipitation mostly comes in the form of snow. The Arctic experiences some days in summer when the Sun never sets, the duration of these phases varies from one day for locations right on the Arctic Circle to several months near the North Pole, which is the middle of the Northern Hemisphere. Between the Arctic Circle and the Tropic of Cancer lies the Northern Temperate Zone, the changes in these regions between summer and winter are generally mild, rather than extreme hot or cold. However, a temperate climate can have very unpredictable weather, tropical regions are generally hot all year round and tend to experience a rainy season during the summer months, and a dry season during the winter months. In the Northern Hemisphere, objects moving across or above the surface of the Earth tend to turn to the right because of the coriolis effect, as a result, large-scale horizontal flows of air or water tend to form clockwise-turning gyres. These are best seen in circulation patterns in the North Atlantic. For the same reason, flows of air down toward the surface of the Earth tend to spread across the surface in a clockwise pattern. Thus, clockwise air circulation is characteristic of high pressure weather cells in the Northern Hemisphere, conversely, air rising from the northern surface of the Earth tends to draw air toward it in a counterclockwise pattern. Hurricanes and tropical storms spin counter-clockwise in the Northern Hemisphere, the shadow of a sundial moves clockwise in the Northern Hemisphere. When viewed from the Northern Hemisphere, the Moon appears inverted compared to a view from the Southern Hemisphere, the North Pole faces away from the galactic center of the Milky Way. The Northern Hemisphere is home to approximately 6.57 billion people which is around 90% of the total human population of 7.3 billion people
Northern Hemisphere
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Northern Hemisphere highlighted in blue
43.
45th parallel north
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The 45th parallel north is a circle of latitude that is 45 degrees north of the Earths equatorial plane. It crosses Europe, Asia, the Pacific Ocean, North America, at this latitude the sun is visible for 15 hours,37 minutes during the summer solstice and 8 hours,46 minutes during the winter solstice. The midday sun stands 21.6 degrees above the horizon at the December solstice,68.4 degrees at the June solstice. Lawrence and Connecticut rivers, where the parallel is called the Canada line. The actual boundary of Vermont lies approximately 1 kilometre north of the due to an error in the 1772 survey. The boundary here intersects Lake Champlain, which is shared by the two nations, with most of the lying in the United States. The 45th parallel makes up most of the boundary between Montana and Wyoming, the parallel roughly bisects mainland Nova Scotia. Halifax is approximately 40 km south of the parallel, all of mainland New Brunswick lies north of the 45th parallel. The southernmost point in mainland New Brunswick, just north of the 45th parallel, is Greens Point, approximately two-thirds of Deer Island, plus all of Campobello and Grand Manan islands, are south of the 45th parallel. In Michigan, the Old Mission Peninsula in Grand Traverse Bay ends just shy of the 45th parallel, many guidebooks and signs at the Mission Point Lighthouse describe it as being halfway between the equator and north pole. When the Grand Traverse Bay recedes below normal level, it is possible to walk out to the exact line, farther west, the line roughly bisects the metropolitan area of Minneapolis-St. Paul. In Minneapolis there is a marker in Theodore Wirth Park, in the Western United States, the parallel passes through the Great Plains and Rocky Mountains, intersecting the Pacific coast in Oregon. Throughout the United States the parallel is marked in places on highways by a sign proclaiming that the location is halfway between the North Pole and the Equator. It continues through the part of the Sea of Japan, entering the Asian mainland on the coast of Primorsky Krai in Russia. At Khanka Lake it enters northeast China, cutting across Heilongjiang and continuing through part of Jilin, transecting southern Mongolia it passes through the provinces of Sükhbaatar, Dornogovi, Dundgovi, Övörkhangai, Bayankhongor, Govi-Altai, and Khovd. In northwest China it passes through the Ili Kazakh Autonomous Prefecture in Xinjiang, the parallel passes through southern Kazakhstan, intersecting the city of Burylbaytal at the southern tip of Lake Balkhash and the city of Qyzylorda further west. At the border with Uzbekistan it bisects the Aral Sea and its toxic Vozrozhdeniya Island peninsula and it skirts the northern edge of the Ustyurt Plateau, entering back into Kazakhstan before cutting across the northern tip of the Caspian Sea and into Europe and Russia. In Europe the 45th parallel stretches between the Caspian Sea coast of the Russian Caucasus in the east and Bay of Biscay coast of France in the west, in Ukraine it crosses the Crimea and its capital Simferopol
45th parallel north
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Marker in Theodore Wirth Park, Golden Valley, Minnesota.
45th parallel north
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Granite marker in Richford, Vermont.
45th parallel north
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Marker on Interstate 5 near Keizer, Oregon.
44.
Arctic Ocean
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The Arctic Ocean is the smallest and shallowest of the worlds five major oceans. Alternatively, the Arctic Ocean can be seen as the northernmost part of the all-encompassing World Ocean, located mostly in the Arctic north polar region in the middle of the Northern Hemisphere, the Arctic Ocean is almost completely surrounded by Eurasia and North America. It is partly covered by sea ice throughout the year and almost completely in winter, the summer shrinking of the ice has been quoted at 50%. The US National Snow and Ice Data Center uses satellite data to provide a record of Arctic sea ice cover. The Arctic may become ice free for the first time in human history within a few years or by 2040, for much of European history, the north polar regions remained largely unexplored and their geography conjectural. He was probably describing loose sea ice known today as growlers or bergy bits, his Thule was probably Norway, early cartographers were unsure whether to draw the region around the North Pole as land or water. The makers of navigational charts, more conservative than some of the more fanciful cartographers, tended to leave the region blank and this lack of knowledge of what lay north of the shifting barrier of ice gave rise to a number of conjectures. In England and other European nations, the myth of an Open Polar Sea was persistent, john Barrow, longtime Second Secretary of the British Admiralty, promoted exploration of the region from 1818 to 1845 in search of this. In the United States in the 1850s and 1860s, the explorers Elisha Kane, even quite late in the century, the eminent authority Matthew Fontaine Maury included a description of the Open Polar Sea in his textbook The Physical Geography of the Sea. Nevertheless, as all the explorers who travelled closer and closer to the reported, the polar ice cap is quite thick. Fridtjof Nansen was the first to make a crossing of the Arctic Ocean. The first surface crossing of the ocean was led by Wally Herbert in 1969, in a dog sled expedition from Alaska to Svalbard, with air support. The first nautical transit of the pole was made in 1958 by the submarine USS Nautilus. Since 1937, Soviet and Russian manned drifting ice stations have extensively monitored the Arctic Ocean, scientific settlements were established on the drift ice and carried thousands of kilometres by ice floes. In World War II, the European region of the Arctic Ocean was heavily contested, the Arctic Ocean occupies a roughly circular basin and covers an area of about 14,056,000 km2, almost the size of Antarctica. The coastline is 45,390 km long and it is surrounded by the land masses of Eurasia, North America, Greenland, and by several islands. It is connected to the Pacific Ocean by the Bering Strait and to the Atlantic Ocean through the Greenland Sea, countries bordering the Arctic Ocean are, Russia, Norway, Iceland, Greenland, Canada and the United States. There are several ports and harbours around the Arctic Ocean In Alaska, in Canada, ships may anchor at Churchill in Manitoba, Nanisivik in Nunavut, Tuktoyaktuk or Inuvik in the Northwest territories
Arctic Ocean
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A bathymetric / topographic of the Arctic Ocean and the surrounding lands.
Arctic Ocean
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Emanuel Bowen 's 1780s map of the Arctic features a "Northern Ocean".
Arctic Ocean
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Sea cover in the Arctic Ocean, showing the median, 2005 and 2007 coverage
Arctic Ocean
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Three polar bears approach USS Honolulu near the North Pole.
45.
Central cylindrical projection
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The Central cylindrical projection is a perspective cylindrical map projection. It corresponds to projecting the Earths surface onto a tangent to the equator as if from a light source at Earths center. The cylinder is cut along one of the projected meridians. Distortion increases so rapidly away from the equator that the central cylindrical is only used as an easily understood illustration of projection and its vertical stretching is even worse than that of the Mercator projection, whose construction method is sometimes erroneously described equivalently to central cylindricals. As with any cylindrical projection, the construction can be generalized by positioning the cylinder to be tangent to a circle of the globe that is not the equator. This projection has prominent use in photography where it is usually called “cylindrical projection”. X = R, y = R tan φ R denotes the radius of the globe, φ is the latitude, λ is the longitude, λ₀ is the longitude of the central meridian. Gnomonic projection Map projection List of map projections
Central cylindrical projection
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The central cylindrical projection with a 15° graticule, approximately to latitude ±72°. The distortion is noticeably worse than the Mercator projection.
46.
Web Mercator
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Web Mercator, Google Web Mercator, Spherical Mercator, WGS84 Web Mercator or WGS 84/Pseudo-Mercator is a variant of the Mercator projection and is the de facto standard for Web mapping applications. It rose to prominence when used in the first Google Maps in 2005 and it is used by virtually all major online map providers, including Google Maps, Bing Maps, OpenStreetMap, Mapquest, Esri, Mapbox, and many others. Its official EPSG identifier is EPSG,3857, although others have used historically. Web Mercator is a variant of the Mercator projection, one used primarily in Web-based mapping programs. It uses the same formulas as the standard Mercator as used for small-scale maps, however, the Web Mercator uses the spherical formulas at all scales whereas large-scale Mercator maps normally use the ellipsoidal form of the projection. The discrepancy is imperceptible at the scale but causes maps of local areas to deviate slightly from true ellipsoidal Mercator maps at the same scale. This deviation becomes more pronounced further from the equator, and can reach as high as 35 km on the ground, while the Web Mercators formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the WGS84 ellipsoidal datum. This discrepancy causes the projection to be slightly non-conformal, general lack of understanding that the Web Mercator differs from standard Mercator usage has caused considerable confusion and misuse. For all these reasons, the United States Department of Defense through the National Geospatial-Intelligence Agency has declared this map projection to be unacceptable for any official use, because the Mercator projects the poles at infinity, Google Maps cannot show the poles. Instead it cuts off coverage at 85. 051129° north and south and this is not considered a limitation, given the purpose of the service. The value 85. 051129° is the latitude at which the map becomes a square. EPSGs definition says the projection uses spherical development of ellipsoidal coordinates, alastair Aitchison says the underlying geographic coordinates are defined using WGS84, but projected as if they were defined on a sphere. Unlike the ellipsoidal Mercator and spherical Mercator, the Web Mercator is not quite conformal due to its use of ellipsoidal datum geographical coordinates against a spherical projection, rhumb lines are not straight lines. The benefit is that the form is much simpler to calculate. And believe that it is technically flawed and we will not devalue the EPSG dataset by including such inappropriate geodesy and cartography. The unofficial code 900913 came to be used and it was originally defined by Christopher Schmidt in his Technical Ramblings blog. In 2008, EPSG provided the official identifier EPSG,3785 with the official name Popular Visualisation CRS / Mercator and this definition used a spherical model of the Earth. Later that year, EPSG provided an updated identifier, EPSG,3857 with the official name WGS84 / Pseudo-Mercator, the definition switched to using the WGS84 ellipsoid, rather than the sphere
Web Mercator
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OpenStreetMap, like most web maps, uses the Web Mercator projection.
47.
Eckert VI projection
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The Eckert VI projection is an equal-area pseudocylindrical map projection. The length of line is half that of the equator. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections, in each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert VI is the Eckert V projection, list of map projections Eckert II projection Eckert IV projection Max Eckert-Greifendorff Eckert VI projection at Mathworld
Eckert VI projection
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Eckert VI projection of the world.
48.
Mollweide projection
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The Mollweide projection is an equal-area, pseudocylindrical map projection generally used for global maps of the world or night sky. It is also known as the Babinet projection, homalographic projection, homolographic projection, the projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions. The projection was first published by mathematician and astronomer Karl Brandan Mollweide of Leipzig in 1805 and it was reinvented and popularized in 1857 by Jacques Babinet, who gave it the name homalographic projection. The variation homolographic arose from frequent nineteenth-century usage in star atlases, the Mollweide is a pseudocylindrical projection in which the equator is represented as a straight horizontal line perpendicular to a central meridian one-half its length. The other parallels compress near the poles, while the other meridians are equally spaced at the equator, the meridians at 90 degrees east and west form a perfect circle, and the whole earth is depicted in a proportional 2,1 ellipse. Shape distortion may be diminished by using an interrupted version, a sinusoidal interrupted Mollweide projection discards the central meridian in favor of alternating half-meridians which terminate at right angles to the equator. This has the effect of dividing the globe into lobes, in contrast, a parallel interrupted Mollweide projection uses multiple disjoint central meridians, giving the effect of multiple ellipses joined at the equator. More rarely, the project can be drawn obliquely to shift the areas of distortion to the oceans, the Mollweide, or its properties, has inspired the creation of several other projections, including the Goodes homolosine, van der Grinten and the Boggs eumorphic. The map has area 4πR2, conforming to the area of the generating globe. The x-coordinate has a range of, and the y-coordinate has a range of, if φ = ±π/2, then also θ = ±π/2. In that case the iteration should be bypassed, otherwise, division by zero may result, the inverse transformations allow one to find the latitude and longitude corresponding to the map coordinates x and y. List of map projections Aitoff projection Hammer projection An interactive Java applet to study deformations of the Mollweide Map Projection Mollweide Projection at Mathworld
Mollweide projection
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Mollweide projection of the world.
49.
Lambert conformal conic projection
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A Lambert conformal conic projection is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten, conceptually, the projection seats a cone over the sphere of the Earth and projects the surface conformally onto the cone. The cone is unrolled, and the parallel that was touching the sphere is assigned unit scale and that parallel is called the reference parallel or standard parallel. By scaling the map, two parallels can be assigned unit scale, with scale decreasing between the two parallels and increasing outside them. This gives the map two standard parallels, in this way, deviation from unit scale can be minimized within a region of interest that lies largely between the two standard parallels. Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels. Pilots use aeronautical charts based on LCC because a line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances. The US systems of VFR sectional charts and terminal area charts are drafted on the LCC with standard parallels at 33°N and 45°N. The European Environment Agency and the INSPIRE specification for coordinate systems using this projection for conformal pan-European mapping at scales smaller or equal to 1,500,000. In Metropolitan France, the projection is Lambert-93, a Lambert conic projection using RGF93 geodetic system. The National Spatial Framework for India uses Datum WGS84 with a LCC projection and is a recommended NNRMS standard, each state has its own set of reference parameters given in the standard. The projection as used in CCS83 yields maps in which errors are limited to 1 part in 10,000. The Lambert conformal conic is one of several map projection developed by Johann Heinrich Lambert, an 18th-century Swiss mathematician, physicist, philosopher
Lambert conformal conic projection
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Lambert conformal conic projection with standard parallels at 20°N and 50°N. Projection extends toward infinity southward and so has been cut off at 30°S.
50.
Polyconic projection
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Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American Polyconic. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and this description applies to projections in equatorial aspect. Each parallel is an arc of true scale. The scale is true on the central meridian of the projection. The projection was in use by many map-making agencies of the United States from the time of its proposal by Ferdinand Rudolph Hassler in 1825 until the middle of the 20th century. To avoid division by zero, the formulas above are extended so that if φ =0 then x = λ − λ0, list of map projections Weisstein, Eric W. Polyconic projection. Table of examples and properties of all projections, from radicalcartography. net An interactive Java Applet to study the metric deformations of the Polyconic Projection
Polyconic projection
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American polyconic projection of the world
51.
Werner projection
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The Werner projection is a pseudoconic equal-area map projection sometimes called the Stab-Werner or Stabius-Werner projection. Like other heart-shaped projections, it is categorized as cordiform. Stab-Werner refers to two originators, Johannes Werner, a parish priest in Nuremberg, refined and promoted this projection that had developed earlier by Johannes Stabius of Vienna around 1500. The projection is a form of the Bonne projection, having its standard parallel at one of the poles. Distances along each parallel and along the meridian are correct. List of map projections Media related to Maps with Stab-Werner projection at Wikimedia Commons Table of examples and properties of all common projections, Radical Cartography
Werner projection
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Werner projection of the world
Werner projection
52.
General Perspective projection
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The General Perspective Projection is a map projection of cartography. When the Earth is photographed from space, the records the view as a perspective projection. If the camera precisely faces the center of the Earth, the projection is Vertical Perspective, otherwise, a Tilted Perspective projection is obtained. The Vertical Perspective is related to the Stereographic projection, Gnomonic projection and these are all true perspective projections, and are also azimuthal. The point of perspective for the General Perspective Projection is a finite distance and it depicts the earth as it appears from some relatively short distance above the surface, typically a few hundred to a few tens of thousands of kilometers. Tilted Perspective projections are not azimuthal, directions are not true from the point. Some forms of the projection were known to the Greeks and Egyptians 2,000 years ago and it was studied by several French and British scientists in the 18th and 19th centuries. But the projection had little value, computationally simpler nonperspective azimuthal projections could be used instead. Space exploration led to a renewed interest in the perspective projection, now the concern was for a pictorial view from space, not for minimal distortion. A picture taken with a camera from the window of a spacecraft has a tilted vertical perspective, so the manned Gemini. Some prominent Internet mapping tools also use the tilted perspective projection, for example, Google Earth and NASA World Wind show the globe as it appears from space. List of map projections Map projection
General Perspective projection
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Vertical perspective from an altitude of 35,786 km over (0°, 90°W), corresponding to a view from geostationary orbit. 10° graticule.
General Perspective projection
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Geometric projection of the parallels of the polar Perspective projections, Vertical and Tilted.
53.
Gnomonic projection
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This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane. No distortion occurs at the tangent point, but distortion increases rapidly away from it, less than half of the sphere can be projected onto a finite map. Consequently, a photographic lens, which is based on the gnomonic principle. The gnomonic projection is said to be the oldest map projection, the path of the shadow-tip or light-spot in a nodus-based sundial traces out the same hyperbolae formed by parallels on a gnomonic map. Since meridians and the equator are great circles, they are shown as straight lines on a gnomonic map. If the tangent point is one of the then the meridians are radial. The equator is at infinity in all directions, other parallels are depicted as concentric circles. If the tangent point is not on a pole or the equator, then the meridians are radially outward straight lines from a Pole, the equator is a straight line that is perpendicular to only one meridian, indicating that the projection is not conformal. Other parallels are depicted as conic sections, if the tangent point is on the equator then the meridians are parallel but not equally spaced. The equator is a line perpendicular to the meridians. Other parallels are depicted as hyperbolae, as with all azimuthal projections, angles from the tangent point are preserved. The map distance from that point is an r of the true distance d. The radial scale is r ′ =1 cos 2 d R and the transverse scale 1 cos d R so the scale increases outwardly. Gnomonic projections are used in work because seismic waves tend to travel along great circles. They are also used by navies in plotting direction finding bearings, meteors also travel along great circles, with the Gnomonic Atlas Brno 2000.0 being the IMOs recommended set of star charts for visual meteor observations. Aircraft and ship pilots use the projection to find the shortest route between start and destination, the gnomonic projection is used extensively in photography, where it is called rectilinear projection. The gnomonic projection is used in astronomy where the tangent point is centered on the object of interest, the sphere being projected in this case is the celestial sphere, R =1, and not the surface of the Earth. List of map projections Beltrami–Klein model, the mapping of the hyperbolic plane Snyder
Gnomonic projection
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Gnomonic projection of a portion of the north hemisphere centered on the geographic North Pole
Gnomonic projection
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Great circles transform to straight lines via gnomonic projection
54.
Stereographic projection
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In geometry, the stereographic projection is a particular mapping that projects a sphere onto a plane. The projection is defined on the sphere, except at one point. Where it is defined, the mapping is smooth and bijective and it is conformal, meaning that it preserves angles. It is neither isometric nor area-preserving, that is, it preserves neither distances nor the areas of figures, intuitively, then, the stereographic projection is a way of picturing the sphere as the plane, with some inevitable compromises. In practice, the projection is carried out by computer or by using a special kind of graph paper called a stereographic net, shortened to stereonet. The stereographic projection was known to Hipparchus, Ptolemy and probably earlier to the Egyptians and it was originally known as the planisphere projection. Planisphaerium by Ptolemy is the oldest surviving document that describes it, one of its most important uses was the representation of celestial charts. The term planisphere is still used to refer to such charts, in the 16th and 17th century, the equatorial aspect of the stereographic projection was commonly used for maps of the Eastern and Western Hemispheres. It is believed that already the map created in 1507 by Gualterius Lud was in stereographic projection, as were later the maps of Jean Roze, Rumold Mercator, in star charts, even this equatorial aspect had been utilised already by the ancient astronomers like Ptolemy. François dAguilon gave the stereographic projection its current name in his 1613 work Opticorum libri sex philosophis juxta ac mathematicis utiles, in 1695, Edmond Halley, motivated by his interest in star charts, published the first mathematical proof that this map is conformal. He used the recently established tools of calculus, invented by his friend Isaac Newton and this section focuses on the projection of the unit sphere from the north pole onto the plane through the equator. Other formulations are treated in later sections, the unit sphere in three-dimensional space R3 is the set of points such that x2 + y2 + z2 =1. Let N = be the pole, and let M be the rest of the sphere. The plane z =0 runs through the center of the sphere, for any point P on M, there is a unique line through N and P, and this line intersects the plane z =0 in exactly one point P′. Define the stereographic projection of P to be this point P′ in the plane, in Cartesian coordinates on the sphere and on the plane, the projection and its inverse are given by the formulas =, =. In spherical coordinates on the sphere and polar coordinates on the plane, here, φ is understood to have value π when R =0. Also, there are ways to rewrite these formulas using trigonometric identities. In cylindrical coordinates on the sphere and polar coordinates on the plane, the projection is not defined at the projection point N =
Stereographic projection
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Illustration by Rubens for "Opticorum libri sex philosophis juxta ac mathematicis utiles", by François d'Aiguillon. It demonstrates how the projection is computed.
Stereographic projection
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The sphere, with various loxodromes shown in distinct colors
Stereographic projection
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Two points P 1 and P 2 are drawn on a transparent sheet tacked at the origin of a Wulff net.
55.
Azimuthal equidistant projection
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The azimuthal equidistant projection is an azimuthal map projection. A useful application for this type of projection is a projection which shows all meridians as straight. The flag of the United Nations contains an example of an azimuthal equidistant projection. It is useful for showing airline distances from center point of projection and for seismic, while it may have been used by ancient Egyptians for star maps in some holy books, the earliest text describing the azimuthal equidistant projection is an 11th-century work by al-Biruni. The projection appears in many Renaissance maps, and Gerardus Mercator used it for an inset of the polar regions in sheet 13. In France and Russia this projection is named Postel projection after Guillaume Postel, many modern star chart planispheres use the polar azimuthal equidistant projection. A point on the globe is chosen to be special in the sense that mapped distances and that point, will project to the center of a circular projection, with φ referring to latitude and λ referring to longitude. All points along a given azimuth will project along a line from the center. The distance from the point to another projected point is given as ρ. An operator can point the antenna, usually by an electric rotator, simply locating the target in the map, the map should be centered as nearly as possible to the actual antenna location. GeographicLib provides a class for performing azimuthal equidistant projections centered at any point on the ellipsoid, animated US National Weather Service Wind Data for Azimuthal equidistant projection
Azimuthal equidistant projection
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Polar azimuthal equidistant projection
56.
Lambert azimuthal equal-area projection
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The Lambert azimuthal equal-area projection is a particular mapping from a sphere to a disk. It accurately represents area in all regions of the sphere, and it is named for the Swiss mathematician Johann Heinrich Lambert, who announced it in 1772. Zenithal being synonymous with azimuthal, the projection is known as the Lambert zenithal equal-area projection. The Lambert azimuthal projection is used as a map projection in cartography and it is also used in scientific disciplines such as geology for plotting the orientations of lines in three-dimensional space. This plotting is aided by a kind of graph paper called a Schmidt net. To define the Lambert azimuthal projection, imagine a plane set tangent to the sphere at some point S on the sphere, let P be any point on the sphere other than the antipode of S. Let d be the distance between S and P in three-dimensional space, then the projection sends P to a point P′ on the plane that is a distance d from S. To make this precise, there is a unique circle centered at S, passing through P. It intersects the plane in two points, let P′ be the one that is closer to P, the antipode of S is excluded from the projection because the required circle is not unique. The case of S is degenerate, S is projected to itself, explicit formulas are required for carrying out the projection on a computer. Consider the projection centered at S = on the unit sphere, in Cartesian coordinates on the sphere and on the plane, the projection and its inverse are then described by =, =. In spherical coordinates on the sphere and polar coordinates on the disk, in cylindrical coordinates on the sphere and polar coordinates on the plane, the map and its inverse are given by =, =. The projection can be centered at other points, and defined on spheres of other than 1. As defined in the section, the Lambert azimuthal projection of the unit sphere is undefined at. It sends the rest of the sphere to the disk of radius 2 centered at the origin in the plane. It sends the point to, the equator z =0 to the circle of radius √2 centered at, the projection is a diffeomorphism between the sphere and the open disk of radius 2. It is a map, which can be seen by computing the area element of the sphere when parametrized by the inverse of the projection. In Cartesian coordinates it is d A = d X d Y and this means that measuring the area of a region on the sphere is tantamount to measuring the area of the corresponding region on the disk
Lambert azimuthal equal-area projection
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Lambert azimuthal equal-area projection of the world. The center is 0° N 0° E. The antipode is 0° N 180° E, near Kiribati in the Pacific Ocean. That point is represented by the entire circular boundary of the map, and the ocean around that point appears along the entire boundary.
57.
Hammer projection
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The Hammer projection is an equal-area map projection described by Ernst Hammer in 1892. Using the same 2,1 elliptical outer shape as the Mollweide projection, Hammer intended to reduce distortion in the regions of the outer meridians, visually, the Aitoff and Hammer projections are very similar. The Hammer has seen more use because of its equal-area property, the Mollweide projection is another equal-area projection of similar aspect, though with straight parallels of latitude, unlike the Hammers curved parallels. William A. Briesemeister presented a variant of the Hammer in 1953, the purpose is to present the land masses more centrally and with lower distortion. Before projecting to Hammer, John Bartholomew rotated the coordinate system to bring the 45° north parallel to the center and he called this variant the Nordic projection. List of map projections Mollweide projection Aitoff projection Table of common projections An interactive Java Applet to study the metric deformations of the Hammer–Aitoff Projection
Hammer projection
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Hammer projection of the world
58.
Adams hemisphere-in-a-square projection
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The Adams hemisphere-in-a-square is a conformal map projection for a hemisphere. It is a version of the Peirce quincuncial projection, and is named after American cartographer Oscar Sherman Adams. When it is used to represent the entire sphere it is known as the Adams doubly periodic projection, like many conformal projections, conformality fails at certain points, in this case at the four corners. List of map projections Guyou hemisphere-in-a-square projection Doubly periodic function
Adams hemisphere-in-a-square projection
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Adams hemisphere-in-a-square projection. 15° graticule.
59.
Guyou hemisphere-in-a-square projection
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The Guyou hemisphere-in-a-square projection is a conformal map projection for the hemisphere. It is an aspect of the Peirce quincuncial projection. The projection was developed by Émile Guyou of France in 1887, the projection can be computed as an oblique aspect of the Peirce quincuncial projection by rotating the axis 45 degrees. The projection is conformal except for the four corners of each hemisphere’s square, like other conformal polygonal projections, the Guyou is a Schwarz–Christoffel mapping. Its properties are similar to those of the Peirce quincuncial, Each hemisphere is represented as a square. It can be tessellated in all directions, the Adams hemisphere-in-a-square projection and the Peirce quincuncial projection are different aspects of the same underlying Schwarz–Christoffel mapping. Such mappings are transformations of half a stereographic projection
Guyou hemisphere-in-a-square projection
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Guyou doubly periodic projection of the world.
60.
Peirce quincuncial projection
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The Peirce quincuncial projection is a conformal map projection developed by Charles Sanders Peirce in 1879. The projection has the property that it can be tiled ad infinitum on the plane. The projection has seen use in photography for portraying 360° views. The description quincuncial refers to the arrangement of four quadrants of the globe around the hemisphere in an overall square pattern. Typically the projection is oriented such that the north pole lies at the center, the maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane. In effect, the map is a square, inspiring Peirce to call his projection quincuncial. After Peirce presented his projection, two other cartographers developed similar projections of the hemisphere on a square, Guyou in 1887, the three projections are transversal versions of each other. The Peirce quincuncial projection is formed by transforming the stereographic projection with a pole at infinity, the Peirce quincuncial is really a projection of the hemisphere, but its tessellation properties permit its use for the entire sphere. An elliptic integral of the first kind can be used to solve for w, the comma notation used for sd means that 1/√2 is the modulus for the elliptic function ratio, as opposed to the parameter or the amplitude. The mapping has a factor of 1/2 at the center. According to Peirce, his projection has the properties, The sphere is presented in a square. The part where the exaggeration of scale amounts to double that at the centre is only 9% of the area of the sphere, against 13% for the Mercator projection and 50% for the stereographic projection. The curvature of lines representing great circles is, in case, very slight. It is conformal everywhere except at the four corners of the inner hemisphere and these are singularities where differentiability fails. It can be tessellated in all directions, the projection tessellates the plane, i. e. repeated copies can completely cover an arbitrary area, each copys features exactly matching those of its neighbors. Like many other projections based upon complex numbers, the Peirce quincuncial has been used for geographic purposes. One of the few recorded cases is in 1946, when it was used by the U. S. Coast and Geodetic Survey world map of air routes. Its four singularities are at the North Pole, the South Pole, on the equator at 25°W, and on the equator at 155°E, in the Arctic, Atlantic, and Pacific oceans and that great circle divides the traditional Western and Eastern hemispheres
Peirce quincuncial projection
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Peirce quincuncial projection of the world. The red equator is a square whose corners are the only four points on the map which fail to be conformal.
Peirce quincuncial projection
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Tessellated version of the Peirce quincuncial map
Peirce quincuncial projection
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Using the Peirce quincuncial projection to present a spherical panorama.
61.
Hammer retroazimuthal projection
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The Hammer retroazimuthal projection is a modified azimuthal proposed by Ernst Hermann Heinrich Hammer in 1910. As a retroazimuthal projection, azimuths are correct from any point to the center point. Additionally, all distances from the center of the map are proportional to what they are on the globe, in whole-world presentation, the back and front hemispheres overlap, making the projection a non-injective function. Craig retroazimuthal projection List of map projections Description of Hammer Retroazimuthal front hemisphere, Description of Hammer Retroazimuthal back hemisphere
Hammer retroazimuthal projection
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The front hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 90°W.
Hammer retroazimuthal projection
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The back hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 90°W.
62.
Chamberlin trimetric projection
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The Chamberlin trimetric projection is a map projection where three points are fixed on the globe and the points on the sphere are mapped onto a plane by triangulation. It was developed in 1946 by Wellman Chamberlin for the National Geographic Society, Chamberlin was chief cartographer for the Society from 1964 to 1971. The projections principal feature is that it compromises between distortions of area, direction, and distance, a Chamberlin trimetric map therefore gives an excellent overall sense of the region being mapped. Many National Geographic Society maps of single continents use this projection, as originally implemented, the projection algorithm begins with the selection of three points near the outer boundary of the area to be mapped. From these three points, the true distances to a point on the mapping area are calculated. The distances from each of the three points are then drawn on the plane by compass circles. Unlike triangulation on a plane where three such compass circles will intersect at a point, the compass circles from a sphere do not intersect precisely at a point. A small triangle is generated from the intersections, and the center of triangle is calculated as the mapped point. Based on the principles of the projection, precise, but lengthy, the Chamberlin trimetric projection is neither conformal nor equal-area. Rather, the projection was conceived to minimize distortion of distances everywhere with the side-effect of balancing between areal equivalence and conformality and this projection is not appropriate for mapping the entire sphere because the outer boundary would loop and overlap itself in most configurations. Two-point equidistant projection The Chamberlin Trimetric Projection - Implementations of the projection using Matlab scripts, the Chamberlin Trimetric Projection - Notes on the projection from a cartography class at Colorado State University. National Geographic Map Collection - Many examples of National Geographic Society maps employing the Chamberlin Trimetric Projection can be seen here
Chamberlin trimetric projection
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A map of Africa using the Chamberlin trimetric projection. The three red dots indicate the selected "base" locations: (22°N, 0°), (22°N, 45°E), (22°S, 22.5°E). 10° graticule.
63.
Robinson projection
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The Robinson projection is a map projection of a world map which shows the entire world at once. It was specifically created in an attempt to find a compromise to the problem of readily showing the whole globe as a flat image. The Robinson projection was devised by Arthur H. Robinson in 1963 in response to an appeal from the Rand McNally company, Robinson published details of the projections construction in 1974. The National Geographic Society began using the Robinson projection for general world maps in 1988. In 1998 NGS abandoned the Robinson projection for that use in favor of the Winkel tripel projection, the Robinson projection is neither equal-area nor conformal, abandoning both for a compromise. The creator felt this produced an overall view than could be achieved by adhering to either. The meridians curve gently, avoiding extremes, but thereby stretch the poles into long lines instead of leaving them as points, hence, distortion close to the poles is severe, but quickly declines to moderate levels moving away from them. The straight parallels imply severe angular distortion at the high latitudes toward the edges of the map. However, at the time it was developed, the projection effectively met Rand McNallys goal to produce appealing depictions of the entire world, I decided to go about it backwards. … I started with a kind of artistic approach, I visualized the best-looking shapes and sizes. I worked with the variables until it got to the point where, if I changed one of them, then I figured out the mathematical formula to produce that effect. Most mapmakers start with the mathematics, the projection is defined by the table, The table is indexed by latitude at 5 degree intervals, intermediate values are calculated using interpolation. Robinson did not specify any particular method, but it is reported that he used Aitken interpolation himself. The PLEN column is the length of the parallel of latitude, meridians of longitude are equally spaced on each parallel of latitude. List of map projections Winkel Tripel — projection currently used by the National Geographic, a New Map Projection, Its Development and Characteristics. In, National Geographic, December 1988, pp. 911–913, flattening The Earth—2000 Years of Map Projections, The University of Chicago Press. Table of examples and properties of all projections, from radicalcartography. net An interactive Java Applet to study the metric deformations of the Robinson Projection. Numerical evaluation of the Robinson projection, from Cartography and Geographic Information Science, April,2004 by Cengizhan Ipbuker
Robinson projection
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Robinson projection of the world
64.
Van der Grinten projection
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The van der Grinten projection is a compromise map projection, which means that it is neither equal-area nor conformal. Unlike perspective projections, the van der Grinten projection is a geometric construction on the plane. Van der Grinten projects the entire Earth into a circle and it largely preserves the familiar shapes of the Mercator projection while modestly reducing Mercators distortion. Polar regions are subject to extreme distortion, alphons J. van der Grinten invented the projection in 1898 and received US patent #751,226 for it and three others in 1904. The National Geographic Society adopted the projection for their maps of the world in 1922, raising its visibility. In 1988, National Geographic replaced the van der Grinten projection with the Robinson projection, list of map projections Robinson projection Projections by Van der Grinten, and variations
Van der Grinten projection
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Van der Grinten projection of the world.
65.
HEALPix
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HEALPix, an acronym for Hierarchical Equal Area isoLatitude Pixelisation of a 2-sphere, is an algorithm for pixelisation of the 2-sphere, and the associated class of map projections. The HEALPix projection is a class of spherical projections, sharing several key properties. Any of these can be followed by partitioning the region of the 2-plane. The associated software package HEALPix implements the algorithm, the HEALPix projection is represented by the keyword HPX in the FITS standard for writing astronomical data files. It was approved as part of the official FITS World Coordinate System by the IAU FITS Working Group on April 26,2006. As the name indicates, at a level in the hierarchy the pixels are of equal area and their centers lie on a discrete number of circles of latitude. The scheme has a number of properties which make it efficient for certain computations. In the case of the H=4, K=3 projection, the pixels are squares in the plane and every vertex joins four pixels, the pixelisation related to the H=4, K=3 projection has become widely used in cosmology for storing and manipulating maps of the cosmic microwave background. An alternative hierarchical grid is the Hierarchical Triangular Mesh, the pixels at a given level in the hierarchy are of similar but not identical size. The scheme is good at representing complex shapes because the boundaries are all segments of circles of the sphere, another alternative hierarchical grid is the Quadrilateralized Spherical Cube. The 12 base resolution pixels of H=4, K=3 HEALPix projection may be thought of as the facets of a rhombic dodecahedron, the H=6 HEALPix has similarities to another alternative grid based on the icosahedron
HEALPix
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HEALPix H=4, K=3 projection of the world.
66.
Bernard J. S. Cahill
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His Butterfly World Map, like Buckminster Fullers later Dymaxion map of 1943 and 1954, enabled all continents to be uninterrupted, and with reasonable fidelity to a globe. Cahill demonstrated this principle by also inventing a rubber-ball globe which could be flattened under a pane of glass in the Butterfly form, a variant was developed by Gene Keyes in 1975, the Cahill–Keyes projection. World map Waterman butterfly projection Octants projection Cahill–Keyes projection About Cahill Parry, David, Architects Profiles, Bernard J. S. Cahill Collection, ca. J. S. Cahill Butterfly Map Resource Page By Cahill An Account of a New Land Map of the World pp. 449–469 The first publication and exposition of the Butterfly Map, one Base Map in Place of Five Monthly Weather Review, 68/2, 1940-02, p.4,1 illus
Bernard J. S. Cahill
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From cover of 1919 pamphlet by Cahill, "The Butterfly Map", 8 p.
67.
Dymaxion map
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The Dymaxion map or Fuller map is a projection of a world map onto the surface of an icosahedron, which can be unfolded and flattened to two dimensions. The flat map is heavily interrupted in order to preserve shapes and sizes, the projection was invented by Buckminster Fuller. The March 1,1943 edition of Life magazine included an essay titled Life Presents R. Buckminster Fullers Dymaxion World. Fuller applied for a patent in the United States in February 1944, the patent was issued in January 1946. This version depicts the Earths continents as one island, or nearly contiguous land masses, the Dymaxion projection is intended only for representations of the entire globe. It is not a projection, whereby global data expands from the center point of a tangent facet outward to the edges. The name Dymaxion was applied by Fuller to several of his inventions, Fuller claimed that his map had several advantages over other projections for world maps. It has less distortion of size of areas, most notably when compared to the Mercator projection. Other compromise projections attempt a similar trade-off, more unusually, the Dymaxion map does not have any right way up. Fuller argued that in the universe there is no up and down, or north and south, only in, gravitational forces of the stars and planets created in, meaning towards the gravitational center, and out, meaning away from the gravitational center. He attributed the north-up-superior/south-down-inferior presentation of most other world maps to cultural bias, Fuller intended the map to be unfolded in different ways to emphasize different aspects of the world. Peeling the solid apart in a different way presents a view of the world dominated by connected oceans surrounded by land, a 1967 Jasper Johns painting, Map, depicting a Dymaxion map, hangs in the permanent collection of the Museum Ludwig in Cologne. The World Game, a simulation game in which players attempt to solve world problems, is played on a 70-by-35-foot Dymaxion map. The competition received over 300 entries from 42 countries
Dymaxion map
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Example of use illustrating early human migrations according to mitochondrial population genetics (numbers are millennia before present)
Dymaxion map
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Map of the world in a Fuller projection with Tissot's Indicatrix of deformation
68.
Waterman butterfly projection
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The Waterman Butterfly World Map is a map arrangement created by Steve Waterman. Waterman first published a map in this arrangement in 1996, the arrangement is an unfolding of a globe treated as a truncated octahedron, evoking the butterfly map principle first developed by Bernard J. S. Cahill in 1909. Cahill and Waterman maps can be shown in various profiles, typically linked at the north Pacific or north Atlantic oceans, as Cahill was an architect, his approach tended toward forms that could be demonstrated physically, such as by his flattenable rubber-ball map. Waterman, on the hand, derived his design from his work on close-packing of spheres. This involves connecting the sphere centers from cubic closest-packed spheres into a convex hull. These illustrate the W5 sphere cluster, W5 convex hull, to project the polyhedron to the plane, straight lines are used to define each 5 ×5 section onto this convex hull. According to annotations on modern versions of the map, the projection divides the equator equally amongst the meridians, popko notes the projection can be gnomonic too. The two methods yield similar results. Parallels of latitude are drawn as three straight-line sections in each octant, from pole to fold-line, from fold-line to longest line parallel to equator, the longest line parallel to the equator also has equal-length delineations. Waterman chose a specific Waterman polyhedron and central meridian to minimize interrupting major land masses, list of map projections Waterman polyhedron Bernard J. S. Cahill World map Rotating Waterman as globe. Real-time winds and temperature on Waterman projection, interactive Tissot indicatrix of Waterman projection. Description of Waterman polyhedra and projection, explanation of equal-line delineation for projection
Waterman butterfly projection
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Waterman sphere cluster W5
Waterman butterfly projection
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Waterman polyhedron w5
Waterman butterfly projection
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Waterman projection (Pacific centered)