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{{about||Dava Sobel's book about John Harrison|Longitude (book)|the adaptation of Sobel's book| Longitude (TV series)}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
{{refimprove|date=May 2011}}
{{longlat}}


'''Longitude''' ({{IPAc-en|icon|ˈ|l|ɒ|n|dʒ|ɨ|tj|uː|d}} or {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ɨ|tj|uː|d}}),<ref>Oxford English Dictionary</ref> is a [[Geographic coordinate system|geographic coordinate]] that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in [[Degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] (λ). Points with the same longitude lie in lines running from the North Pole to the South Pole. By convention, one of these, the [[Prime Meridian]], which passes through the [[Royal Observatory, Greenwich]], England, establishes the position of zero degrees longitude. The longitude of other places is measured as an angle east or west from the Prime Meridian, ranging from 0° at the Prime Meridian to +180° eastward and &minus;180° westward. Specifically, it is the angle between a plane containing the Prime Meridian and a plane containing the North Pole, South Pole and the location in question. This forms a [[right hand rule|right-handed]] [[right-handed coordinate system|coordinate system]] with the ''z'' axis (right hand thumb) pointing from the Earth's center toward the North Pole and the ''x'' axis (right hand index finger) extending from Earth's center through the equator at the Prime Meridian.  
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A location's north-south position along a meridian is given by its [[latitude]], which is (not quite exactly) the angle between the local vertical and the plane of the Equator.
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If the Earth were perfectly spherical and homogeneous, then longitude at a point would just be the angle between a vertical north-south plane through that point and the plane of the Greenwich meridian. Everywhere on Earth the vertical north-south plane would contain the Earth's axis. But the Earth is not homogenous, and has mountains—which have gravity and so can shift the vertical plane away from the Earth's axis. The vertical north-south plane still intersects the plane of the Greenwich meridian at some angle; that angle is astronomical longitude, the longitude you calculate from star observations. The longitude shown on maps and GPS devices is the angle between the Greenwich plane and a not-quite-vertical plane through the point; the not-quite-vertical plane is perpendicular to the surface of the spheroid chosen to approximate the Earth's sea-level surface, rather than perpendicular to the sea-level surface itself.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


==History==
<!--'''PNG'''  (currently default in production)
{{Main|History of longitude}}
:<math forcemathmode="png">E=mc^2</math>
[[File:Longitude Vespucci.png|thumb|left|Amerigo Vespucci's means of determining longitude]]
The measurement of longitude is important both to [[cartography]] and to provide safe ocean [[navigation]]. [[Mariner]]s and [[explorer]]s for most of history struggled to determine precise longitude. Finding a method of determining exact longitude took centuries, resulting in the [[history of longitude]] recording the effort of some of the greatest scientific minds.


Latitude was calculated by observing with [[Quadrant (instrument)|quadrant]] or [[astrolabe]] the inclination of the sun or of charted stars, but longitude presented no such manifest means of study.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


[[Amerigo Vespucci]] was perhaps the first European to proffer a solution, after devoting a great deal of time and energy studying the problem during his sojourns in the [[New World]]:
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
<blockquote>''As to longitude, I declare that I found so much difficulty in determining it that I was put to great pains to ascertain the east-west distance I had covered. The final result of my labours was that I found nothing better to do than to watch for and take observations at night of the conjunction of one planet with another, and especially of the conjunction of the moon with the other planets, because the moon is swifter in her course than any other planet. I compared my observations with an almanac. After I had made experiments many nights, one night, the twenty-third of August 1499, there was a conjunction of the moon with Mars, which according to the almanac was to occur at midnight or a half hour before. I found that...at midnight Mars's position was three and a half degrees to the east.<ref>Vespucci, Amerigo. "Letter from Seville to Lorenzo di Pier Francesco de' Medici, 1500." Pohl, Frederick J. '''Amerigo Vespucci: Pilot Major'''. New York: Columbia University Press, 1945. 76-90. Page 80.</ref>''</blockquote>[[File:John Harrison Uhrmacher.jpg|thumb|upright|left|John Harrison solved the greatest problem of his day.<ref name="Harrison"/>]]
By comparing the relative positions of the moon and Mars with their anticipated positions, Vespucci was able to crudely deduce his longitude. But this method had several limitations: First, it required the occurrence of a specific astronomical event (in this case, Mars passing through the same [[right ascension]] as the moon), and the observer needed to anticipate this event via an astronomical [[almanac]]. One needed also to know the precise time, which was difficult to ascertain in foreign lands. Finally, it required a stable viewing platform, rendering the technique useless on the rolling deck of a ship at sea. See [[Lunar distance (navigation)]].


In 1612, [[Galileo Galilei]] proposed that with sufficiently accurate knowledge of the orbits of the moons of Jupiter one could use their positions as a universal clock and this would make possible the determination of longitude, but the practical problems of the method he devised were severe and it was never used at sea. In the early 18th century there were several maritime disasters attributable to serious errors in reckoning position at sea, such as the loss of four ships of the fleet of Sir [[Cloudesley Shovell]] in the [[Scilly naval disaster of 1707]]. Motivated by these disasters, in 1714 the British government established the [[Board of Longitude]]: prizes were to be awarded to the first person to demonstrate a practical method for determining the longitude of a ship at sea. These prizes motivated many to search for a solution.
==Demos==
[[File:Longitude (PSF).png|thumb|Drawing of Earth with Longitudes]]
[[John Harrison]], a self-educated [[England|English]] [[clockmaker]] then invented the [[marine chronometer]], a key piece in solving the problem of accurately establishing longitude at sea, thus revolutionising and extending the possibility of safe long distance sea travel.<ref name="Harrison">"[http://news.bbc.co.uk/2/hi/science/nature/1864737.stm Longitude clock comes alive]". BBC. March 11, 2002.</ref> Though the British rewarded John Harrison for his marine chronometer in 1773, chronometers remained very expensive and the lunar distance method continued to be used for decades. Finally, the combination of the availability of marine chronometers and [[wireless telegraph]] time signals put an end to the use of lunars in the 20th century.


Unlike latitude, which has the equator as a natural starting position, there is no natural starting position for longitude. Therefore, a reference meridian had to be chosen. It was a popular practice to use a nation's capital as the starting point, but other significant locations were also used. While [[Great Britain|British]] cartographers had long used the Greenwich meridian in London, other references were used elsewhere, including: [[El Hierro]], [[Rome]], [[Copenhagen]], [[Jerusalem]], [[Saint Petersburg]], [[Pisa]], [[Paris]], [[Philadelphia, Pennsylvania|Philadelphia]], and [[Washington, DC|Washington]]. In 1884, the [[International Meridian Conference]] adopted the Greenwich meridian as the ''universal Prime Meridian'' or ''zero point of longitude''.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


==Noting and calculating longitude==
Longitude is given as an [[angle|angular measurement]] ranging from 0° at the Prime Meridian to +180° eastward and &minus;180° westward. The Greek letter λ (lambda),<ref>[http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif Coordinate Conversion]</ref><ref>"λ = Longitude east of Greenwich (for longitude west of Greenwich, use a minus sign)."<br>John P. Snyder, ''[http://pubs.er.usgs.gov/usgspubs/pp/pp1395 Map Projections, A Working Manual]'', [[USGS]] Professional Paper 1395, page ix</ref> is used to denote the location of a place on Earth east or west of the Prime Meridian.


Each degree of longitude is sub-divided into 60 [[minute of arc|minutes]], each of which is divided into 60 [[arcsecond|second]]s. A longitude is thus specified in [[sexagesimal]] notation as ''23°&nbsp;27′&nbsp;30"&nbsp;E''. For higher precision, the seconds are specified with a [[Decimal#Decimal fractions|decimal fraction]]. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: ''23°&nbsp;27.500′&nbsp;E''. Degrees may also be expressed as a decimal fraction: ''23.45833°&nbsp;E''. For calculations, the angular measure may be converted to [[radian]]s, so longitude may also be expressed in this manner as a signed fraction of π ([[pi]]), or an unsigned fraction of 2π.
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
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** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
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For calculations, the West/East suffix is replaced by a negative sign in the [[western hemisphere]]. Confusingly, the convention of negative for East is also sometimes seen. The preferred convention—that East be positive—is consistent with a right-handed [[Cartesian coordinate system]], with the North Pole up. A specific longitude may then be combined with a specific latitude (usually positive in the [[northern hemisphere]]) to give a precise position on the Earth's surface.
==Test pages ==


Longitude at a point may be determined by calculating the time difference between that at its location and [[Coordinated Universal Time]] (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360°/24 hours = 15° per hour). So if the [[time zone]] a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word ''near'' was used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, a person needs to have a [[marine chronometer|chronometer]] (watch) set to UTC and needs to determine local time by solar  or astronomical observation. The details are more complex than described here: see the articles on [[Universal Time]] and on the [[equation of time]] for more details.
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
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=== Singularity and discontinuity of longitude ===
*[[Inputtypes|Inputtypes (private Wikis only)]]
Note that the longitude is [[mathematical singularity|singular]] at the [[Geographical pole|Poles]] and calculations that are sufficiently accurate for other positions, may be inaccurate at or near the Poles. Also the [[Discontinuity (mathematics)|discontinuity]] at the ±[[180th meridian|180° meridian]] must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives wrong answer if the two positions are on either side of this meridian. To avoid these complexities, consider replacing latitude and longitude with another [[horizontal position representation]] in calculation.
*[[Url2Image|Url2Image (private Wikis only)]]
 
==Bug reporting==
==Plate movement and longitude== <!-- http://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&oldid=231745680#Plate_movement_and_longitude -->
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
The Earth's various [[plate tectonics|tectonic plates]] move relative to one another in different directions and at different speeds, on the order of 50 to 100mm per year.<ref>{{cite book |author=Read HH, Watson Janet |title=Introduction to Geology |place=New York |publisher=Halsted |year=1975 |pages=13–15}}</ref> <!-- Adapted from http://en.wikipedia.org/w/index.php?title=Plate_tectonics&oldid=226650343 --> As a result, points on the Earth's surface that are located on different plates are always in motion relative to one another over time, for example, the longitudinal difference between a point on the Equator in Uganda, on the [[African Plate]], and a point on the Equator in Ecuador, on the [[South American Plate]], (same latitude) is increasing by about 0.0014 [[Minute of arc#Symbols and abbreviations|arcseconds]] per year.  It should be noted that these relative tectonic movements effect the measurement of latitude similarly.
 
If a global reference frame such as [[WGS84]] is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing exclusively with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as [[NAD83]] for North America or [[ETRS89]] for Europe.
 
==Length of a degree of longitude==
 
The length of a degree of longitude depends only on the radius of a circle of latitude. For a sphere of radius ''a'' the value of the radius at a latitude φ is ''a''cosφ and the length of arc for a one degree (or π/180 radians) increment is
::  <math>
\Delta^1_{\rm LONG}= \frac{\pi}{180}a \cos \phi. \,\!
</math>
 
When the Earth is modelled by an [[ellipsoid]] this result must be modified to<ref name=osborne>Osborne, P (2008)[http://mercator.myzen.co.uk/mercator.pdf The Mercator Projections](Chapter&nbsp;5)</ref><ref name=rapp>Rapp, Richard H. (1991). ''Geometric Geodesy, Part I'',  Dept. of Geodetic Science and Surveying, Ohio State Univ., Columbus, Ohio.[http://hdl.handle.net/1811/24333](Chapter&nbsp;3)</ref>
::<math>
\Delta^1_{\rm LONG}=
\frac{\pi a\cos\phi}{180(1 - e^2 \sin^2 \phi)^{1/2}}\,,
</math>
where ''e'', the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
{| style="float: right"  border="1" align="right"
!<math>\phi</math>||<math>\Delta^1_{\rm LAT}</math>||<math>\Delta^1_{\rm LONG}</math>
|- style="text-align:right;"
| 0° || 110.574&nbsp;km||  111.320&nbsp;km
|- style="text-align:right;"
| 15° ||  110.649&nbsp;km||  107.551&nbsp;km
|- style="text-align:right;"
| 30° ||  110.852&nbsp;km||  96.486&nbsp;km
|- style="text-align:right;"
| 45° ||  111.132&nbsp;km||  78.847&nbsp;km
|- style="text-align:right;"
| 60° ||  111.412&nbsp;km||  55.800&nbsp;km
|- style="text-align:right;"
| 75° ||  111.618&nbsp;km||  28.902&nbsp;km
|- style="text-align:right;"
| 90° ||  111.694&nbsp;km||  0.000&nbsp;km
|}
::<math>
e^2=\frac{a^2-b^2}{a^2}.
</math>
Cos φ decreases from 1 at the equator to zero at the poles, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a [[Latitude|degree of latitude]]. The table shows values of both for the [[WGS84]] ellipsoid, where ''a''=6,378,137.0&nbsp;m and ''b''=6,356,752.3142&nbsp;m. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is not the shortest ([[geodesic]]) distance between those points; the difference is less than 0.6&nbsp;m.  A calculator for any latitude is provided by the U.S. government's [[National Geospatial-Intelligence Agency]](NGA).<ref>[http://www.nga.mil/MSISiteContent/StaticFiles/Calculators/degree.htmlLengthof degree calculator - National Geospatial-Intelligence Agency]</ref>
 
==Ecliptic latitude and longitude==
 
{{Main|Ecliptic coordinate system}}
[[Ecliptic]] latitude and longitude are defined for the planets, stars, and other celestial bodies in a broadly similar way to that in which terrestrial latitude and longitude are defined, but there is a special difference.
 
The plane of zero latitude for celestial objects is the plane of the ecliptic and is not parallel to the plane of the celestial and terrestrial equator. This is inclined to the Equator by the ''[[obliquity of the ecliptic]]'', which currently has a value of about 23° 26'. The closest celestial counterpart to terrestrial latitude is [[declination]], and the closest celestial counterpart to terrestrial longitude is [[right ascension]]. These celestial coordinates bear the same relationship to the celestial equator as terrestrial latitude and longitude do to the terrestrial equator, and they are also more frequently used in astronomy than celestial longitude and latitude.
 
The polar axis (relative to the celestial equator) is perpendicular to the plane of the Equator, and parallel to the terrestrial polar axis. But the (north) pole of the ecliptic, relevant to the definition of ecliptic latitude, is the normal to the [[ecliptic]] plane nearest to the direction of the celestial north pole of the Equator, i.e. 23° 26' away from it.
 
Ecliptic latitude is measured from 0° to 90° north (+) or south (&minus;) of the ecliptic. [[Ecliptic longitude]] is measured from 0° to 360° eastward (the direction that the Sun appears to move relative to the stars), along the ecliptic from the [[vernal equinox]]. The equinox at a specific date and time is a fixed equinox, such as that in the [[J2000]] reference frame.
 
However, the equinox moves because it is the intersection of two planes, both of which move. The ecliptic is relatively stationary, wobbling within a 4° diameter circle relative to the fixed stars over millions of years under the gravitational influence of the other planets. The greatest movement is a relatively rapid gyration of Earth's equatorial plane whose pole traces a 47° diameter circle caused by the Moon. This causes the equinox to [[Precession (astronomy)|precess]] westward along the ecliptic about 50" per year. This moving equinox is called the ''equinox of date''. Ecliptic longitude relative to a moving equinox is used whenever the positions of the Sun, Moon, planets, or stars at dates other than that of a fixed equinox is important, as in [[calendar]]s, [[astrology]], or [[celestial mechanics]]. The 'error' of the [[Julian calendar|Julian]] or [[Gregorian calendar]] is always relative to a moving equinox. The years, months, and days of the [[Chinese calendar]] all depend on the ecliptic longitudes ''of date'' of the Sun and Moon. The 30° zodiacal segments used in astrology are also relative to a moving equinox. Celestial mechanics (here restricted to the motion of [[solar system]] bodies) uses both a fixed and moving equinox. Sometimes in the study of [[Milankovitch cycles]], the [[invariable plane]] of the solar system is substituted for the moving ecliptic. Longitude may be denominated from 0 to <math>\begin{matrix}2\pi\end{matrix}</math> radians in either case.
 
==Longitude on bodies other than Earth==<!-- This section is linked from [[Viking 2]] -->
 
[[Planet]]ary co-ordinate systems are defined relative to their mean [[axis of rotation]] and various definitions of longitude depending on the body. The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a [[Impact crater|crater]]. The [[north pole]] is that pole of rotation that lies on the north side of the invariable plane of the solar system (near the [[ecliptic]]). The location of the Prime Meridian as well as the position of body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's Prime Meridian increases with time, the body has a direct (or [[direct motion|prograde]]) rotation; otherwise the rotation is said to be [[retrograde motion|retrograde]].
 
In the absence of other information, the axis of rotation is assumed to be normal to the mean [[Orbital plane (astronomy)|orbital plane]]; [[Mercury (planet)|Mercury]] and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean [[orbital period]]. In the case of the [[gas giant|giant planets]], since their surface features are constantly changing and moving at various rates, the rotation of their [[magnetic field]]s is used as a reference instead. In the case of the [[Sun]], even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
 
For ''planetographic longitude'', west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
 
However, ''planetocentric longitude'' is always measured positively to the east, regardless of which way the planet rotates. ''East'' is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, the following all mean the same thing:
*&minus;91°
*91°W
*+269°
*269°E.
 
The reference surfaces for some planets (such as Earth and [[Mars]]) are [[ellipsoid]]s of revolution for which the equatorial radius is larger than the polar radius; in other words, they are oblate spheroids. Smaller bodies ([[Io (moon)|Io]], [[Mimas (moon)|Mimas]], etc.) tend to be better approximated by triaxial ellipsoids; however, triaxial ellipsoids would render many computations more complicated, especially those related to [[map projection]]s. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
 
The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. The meridian of Mars is located at [[Airy-0]] crater.<ref>[http://www.esa.int/SPECIALS/Mars_Express/SEM0VQV4QWD_0.html Where is zero degrees longitude on Mars?] - Copyright 2000 - 2010 © European Space Agency. All rights reserved.</ref>
 
[[Tidal lock|Tidally-locked]] bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere.<ref>[http://www.cfa.harvard.edu/image_archive/2007/31/lores.jpg First map of extraterrestial planet] - Center of Astrophysics.</ref> However, [[libration]] due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an [[analemma]].
 
==See also==
<div style="-moz-column-count:3; column-count:3;">
*[[American Practical Navigator]]
*[[Cardinal direction]]
*[[Geodesy]]
*[[Geodetic system]]
*[[Geographic coordinate system]]
*[[Geographical distance]]
*[[Geotagging]]
*[[Great-circle distance]]
*[[History of longitude]]
*[[Horse latitudes]]
*[[Latitude]]
*[[List of cities by latitude]]
*[[List of cities by longitude]]
*[[Meridian arc]]
*[[Natural Area Code]]
*[[Navigation]]
*[[Orders of magnitude (length)|Orders of magnitude]]
*[[World Geodetic System]]
</div>
 
==References==
{{reflist}}
 
== External links ==
{{sisterlinks}}
* [http://jan.ucc.nau.edu/~cvm/latlon_find_location.html Resources for determining your latitude and longitude]
* [http://www.hnsky.org/iau-iag.htm IAU/IAG Working Group On Cartographic Coordinates and Rotational Elements of the Planets and Satellites]
*[http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/the_tls/article5136819.ece "Longitude forged"]: an essay exposing a hoax solution to the problem of calculating longitude, undetected in Dava Sobel's Longitude, from [http://www.the-tls.co.uk TLS], November 12, 2008.
* [http://www.thegpscoordinates.com Longitude And Latitude Of Points of Interest]
 
{{TimeSig}}
{{Time Topics}}
{{Time measurement and standards}}
 
[[Category:Lines of longitude|*]]
[[Category:Navigation]]
 
[[ar:طول جغرافي]]
[[ast:Llonxitú]]
[[bn:দ্রাঘিমাংশ]]
[[zh-min-nan:Keng-tō͘]]
[[be:Даўгата]]
[[be-x-old:Даўгата]]
[[bg:Географска дължина]]
[[bs:Geografska dužina]]
[[br:Hedred]]
[[ca:Longitud (geografia)]]
[[ceb:Longhitud]]
[[cs:Zeměpisná délka]]
[[sn:Muyeranhambo]]
[[cy:Hydred]]
[[da:Længdekreds]]
[[de:Geographische Länge]]
[[dsb:Geografiska dlinina]]
[[et:Pikkuskraad]]
[[el:Γεωγραφικό μήκος]]
[[es:Longitud (cartografía)]]
[[eo:Longitudo]]
[[fa:طول جغرافیایی]]
[[fr:Longitude]]
[[fy:Lingtegraad]]
[[gl:Lonxitude]]
[[ko:경도]]
[[hi:रेखांश]]
[[hsb:Geografiska dołhosć]]
[[hr:Zemljopisna dužina]]
[[io:Longitudo]]
[[ig:Longitude]]
[[id:Garis bujur]]
[[os:Дæргъад]]
[[is:Lengdargráða]]
[[it:Longitudine]]
[[he:קו אורך]]
[[jv:Garis bujur]]
[[kk:Бойлық]]
[[sw:Longitudo]]
[[ht:Lonjitid]]
[[ku:Hêlîlar]]
[[la:Longitudo geographica]]
[[lv:Ģeogrāfiskais garums]]
[[lb:Geographesch Längt]]
[[lt:Ilguma]]
[[ln:Monkɔlɔ́tɔ molaí]]
[[lmo:Longitüda]]
[[mk:Лонгитуда]]
[[ml:രേഖാംശം]]
[[mr:रेखांश]]
[[nl:Lengtegraad]]
[[nds-nl:Lengtegraod]]
[[ne:देशान्तर]]
[[ja:経度]]
[[nn:Lengdegrad]]
[[mhr:Кутык]]
[[pnb:کھڑی لیک]]
[[pl:Długość geograficzna]]
[[pt:Longitude]]
[[ro:Longitudine]]
[[ru:Долгота]]
[[sq:Gjatësia gjeografike]]
[[scn:Loncitùdini]]
[[sk:Zemepisná dĺžka]]
[[sl:Zemljepisna dolžina]]
[[sr:Географска дужина]]
[[fi:Pituuspiiri]]
[[sv:Longitud]]
[[tl:Longhitud]]
[[ta:நிலநிரைக்கோடு]]
[[te:అక్షాంశం]]
[[th:ลองจิจูด]]
[[uk:Довгота]]
[[ur:طول البلد]]
[[vi:Kinh độ]]
[[vls:Lengtegroad]]
[[wo:Tus-wu-taxaw]]
[[zh:经度]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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