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53-490: LLA may stand for: Latitude, longitude, and altitude, in a geographic coordinate system Irish Land and Labour Association La Liga Argentina de Básquet , 2nd-division Argentinian basketball league Lady Literate in Arts , qualification formerly awarded by St Andrews University, Scotland Licensed Landscape Architect , a postnominal qualification for Landscape Architects in
106-505: A tan ϕ {\displaystyle \textstyle {\tan \beta ={\frac {b}{a}}\tan \phi }\,\!} ; for the GRS 80 and WGS 84 spheroids, b a = 0.99664719 {\textstyle {\tfrac {b}{a}}=0.99664719} . ( β {\displaystyle \textstyle {\beta }\,\!} is known as the reduced (or parametric) latitude ). Aside from rounding, this
159-460: A datum transformation such as a Helmert transformation , although in certain situations a simple translation may be sufficient. Datums may be global, meaning that they represent the whole Earth, or they may be local, meaning that they represent an ellipsoid best-fit to only a portion of the Earth. Examples of global datums include World Geodetic System (WGS 84, also known as EPSG:4326 ),
212-452: A given prime are generated starting from that prime, as a sequence of numbers with the same difference, equal to that prime, between consecutive numbers. This is the sieve's key distinction from using trial division to sequentially test each candidate number for divisibility by each prime. Eratosthenes was one of the most pre-eminent scholarly figures of his time, and produced works covering a vast area of knowledge before and during his time at
265-608: A point on Earth's surface is the angle east or west of a reference meridian to another meridian that passes through that point. All meridians are halves of great ellipses (often called great circles ), which converge at the North and South Poles. The meridian of the British Royal Observatory in Greenwich , in southeast London, England, is the international prime meridian , although some organizations—such as
318-498: A professional association for librarians in Louisiana Luleå/Kallax Airport , Sweden, IATA airport code La Libertad Avanza , a libertarian conservative Argentine political coalition Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title LLA . If an internal link led you here, you may wish to change the link to point directly to
371-473: A region of the surface of the Earth. Some newer datums are bound to the center of mass of the Earth. This combination of mathematical model and physical binding mean that anyone using the same datum will obtain the same location measurement for the same physical location. However, two different datums will usually yield different location measurements for the same physical location, which may appear to differ by as much as several hundred meters; this not because
424-411: Is 6,367,449 m . Since the Earth is an oblate spheroid , not spherical, that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude ϕ {\displaystyle \phi } is where Earth's equatorial radius a {\displaystyle a} equals 6,378,137 m and tan β = b
477-480: Is 110.6 km. The circles of longitude, meridians, meet at the geographical poles, with the west–east width of a second naturally decreasing as latitude increases. On the Equator at sea level, one longitudinal second measures 30.92 m, a longitudinal minute is 1855 m and a longitudinal degree is 111.3 km. At 30° a longitudinal second is 26.76 m, at Greenwich (51°28′38″N) 19.22 m, and at 60° it
530-522: Is 15.42 m. On the WGS 84 spheroid, the length in meters of a degree of latitude at latitude ϕ (that is, the number of meters you would have to travel along a north–south line to move 1 degree in latitude, when at latitude ϕ ), is about The returned measure of meters per degree latitude varies continuously with latitude. Similarly, the length in meters of a degree of longitude can be calculated as (Those coefficients can be improved, but as they stand
583-456: Is known as a graticule . The origin/zero point of this system is located in the Gulf of Guinea about 625 km (390 mi) south of Tema , Ghana , a location often facetiously called Null Island . In order to use the theoretical definitions of latitude, longitude, and height to precisely measure actual locations on the physical earth, a geodetic datum must be used. A horizonal datum
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#1732775885633636-455: Is known in mathematics as the Sieve of Eratosthenes . In mathematics, the sieve of Eratosthenes (Greek: κόσκινον Ἐρατοσθένους), one of a number of prime number sieves , is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite, i.e. , not prime, the multiples of each prime, starting with the multiples of 2. The multiples of
689-816: Is the exact distance along a parallel of latitude; getting the distance along the shortest route will be more work, but those two distances are always within 0.6 m of each other if the two points are one degree of longitude apart. Like any series of multiple-digit numbers, latitude-longitude pairs can be challenging to communicate and remember. Therefore, alternative schemes have been developed for encoding GCS coordinates into alphanumeric strings or words: These are not distinct coordinate systems, only alternative methods for expressing latitude and longitude measurements. Geography (Eratosthenes) Eratosthenes of Cyrene ( / ɛr ə ˈ t ɒ s θ ə n iː z / ; ‹See Tfd› Greek : Ἐρατοσθένης [eratostʰénɛːs] ; c. 276 BC – c. 195/194 BC )
742-409: Is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system , the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface. A full GCS specification, such as those listed in
795-465: Is used to precisely measure latitude and longitude, while a vertical datum is used to measure elevation or altitude. Both types of datum bind a mathematical model of the shape of the earth (usually a reference ellipsoid for a horizontal datum, and a more precise geoid for a vertical datum) to the earth. Traditionally, this binding was created by a network of control points , surveyed locations at which monuments are installed, and were only accurate for
848-750: The EPSG and ISO 19111 standards, also includes a choice of geodetic datum (including an Earth ellipsoid ), as different datums will yield different latitude and longitude values for the same location. The invention of a geographic coordinate system is generally credited to Eratosthenes of Cyrene , who composed his now-lost Geography at the Library of Alexandria in the 3rd century BC. A century later, Hipparchus of Nicaea improved on this system by determining latitude from stellar measurements rather than solar altitude and determining longitude by timings of lunar eclipses , rather than dead reckoning . In
901-481: The International Date Line , which diverges from it in several places for political and convenience reasons, including between far eastern Russia and the far western Aleutian Islands . The combination of these two components specifies the position of any location on the surface of Earth, without consideration of altitude or depth. The visual grid on a map formed by lines of latitude and longitude
954-471: The Library of Pergamum . Eratosthenes created a whole section devoted to the examination of Homer , and acquired original works of great tragic dramas of Aeschylus , Sophocles and Euripides . Eratosthenes made several important contributions to mathematics and science , and was a friend of Archimedes . Around 255 BC, he invented the armillary sphere . In On the Circular Motions of
1007-583: The Trojan War . This work was highly esteemed for its accuracy. George Syncellus was later able to preserve from Chronographies a list of 38 kings of the Egyptian Thebes . Eratosthenes also wrote Olympic Victors , a chronology of the winners of the Olympic Games . It is not known when he wrote his works, but they highlighted his abilities. These works and his great poetic abilities led
1060-526: The 1st or 2nd century, Marinus of Tyre compiled an extensive gazetteer and mathematically plotted world map using coordinates measured east from a prime meridian at the westernmost known land, designated the Fortunate Isles , off the coast of western Africa around the Canary or Cape Verde Islands , and measured north or south of the island of Rhodes off Asia Minor . Ptolemy credited him with
1113-624: The Celestial Bodies , Cleomedes credited him with having calculated the Earth's circumference around 240 BC, with high accuracy. Eratosthenes believed there was both good and bad in every nation and criticized Aristotle for arguing that humanity was divided into Greeks and barbarians , as well as for arguing that the Greeks should keep themselves racially pure. As he aged, he contracted ophthalmia , becoming blind around 195 BC. Losing
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#17327758856331166-476: The Earth , which he did by using the extensive survey results he could access in his role at the Library. His calculation was remarkably accurate (his error margin turned out to be less than 1%). He was also the first person to calculate Earth's axial tilt , which similarly proved to have remarkable accuracy. He created the first global projection of the world, incorporating parallels and meridians based on
1219-416: The Earth is the distance between the two cities divided by the difference in shadow angles expressed as a fraction of one turn . Eratosthenes now continued from his knowledge about the Earth. Using his discoveries and knowledge of its size and shape, he began to sketch it. In the Library of Alexandria he had access to various travel books, which contained various items of information and representations of
1272-506: The Earth's surface move relative to each other due to continental plate motion, subsidence, and diurnal Earth tidal movement caused by the Moon and the Sun. This daily movement can be as much as a meter. Continental movement can be up to 10 cm a year, or 10 m in a century. A weather system high-pressure area can cause a sinking of 5 mm . Scandinavia is rising by 1 cm a year as a result of
1325-729: The European ED50 , and the British OSGB36 . Given a location, the datum provides the latitude ϕ {\displaystyle \phi } and longitude λ {\displaystyle \lambda } . In the United Kingdom there are three common latitude, longitude, and height systems in use. WGS 84 differs at Greenwich from the one used on published maps OSGB36 by approximately 112 m. The military system ED50 , used by NATO , differs from about 120 m to 180 m. Points on
1378-536: The French Institut national de l'information géographique et forestière —continue to use other meridians for internal purposes. The prime meridian determines the proper Eastern and Western Hemispheres , although maps often divide these hemispheres further west in order to keep the Old World on a single side. The antipodal meridian of Greenwich is both 180°W and 180°E. This is not to be conflated with
1431-634: The USA Liga Latinoamérica , a professional esports league for the MOBA PC game League of Legends Link-local address , a type of computer network address Llanaber railway station , Gwynedd, Wales (National Rail station code) Löfbergs Lila Arena, former name of Löfbergs Arena Loma Linda Academy , school in California, USA London Luton Airport , also known as Luton Airport, England Louisiana Library Association ,
1484-484: The ability to read and to observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died in 194 BC at the age of 82 in Alexandria. The measurement of Earth's circumference is the most famous among the results obtained by Eratosthenes, who estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on
1537-452: The available geographic knowledge of his era. Eratosthenes was the founder of scientific chronology ; he used Egyptian and Persian records to estimate the dates of the main events of the Trojan War , dating the sack of Troy to 1183 BC. In number theory , he introduced the sieve of Eratosthenes , an efficient method of identifying prime numbers and composite numbers. He was a figure of influence in many fields who yearned to understand
1590-577: The center of the Earth. Lines joining points of the same latitude trace circles on the surface of Earth called parallels , as they are parallel to the Equator and to each other. The North Pole is 90° N; the South Pole is 90° S. The 0° parallel of latitude is designated the Equator , the fundamental plane of all geographic coordinate systems. The Equator divides the globe into Northern and Southern Hemispheres . The longitude λ of
1643-423: The children of Ptolemy, including Ptolemy IV Philopator who became the fourth Ptolemaic pharaoh. He expanded the library's holdings: in Alexandria all books had to be surrendered for duplication. It was said that these were copied so accurately that it was impossible to tell if the library had returned the original or the copy. He sought to maintain the reputation of the Library of Alexandria against competition from
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1696-527: The complexities of the entire world. His devotees nicknamed him Pentathlos after the Olympians who were well rounded competitors, for he had proven himself to be knowledgeable in every area of learning. Yet, according to an entry in the Suda (a 10th-century encyclopedia), some critics scorned him, calling him Number 2 because he always came in second in all his endeavours. The son of Aglaos, Eratosthenes
1749-649: The default datum used for the Global Positioning System , and the International Terrestrial Reference System and Frame (ITRF), used for estimating continental drift and crustal deformation . The distance to Earth's center can be used both for very deep positions and for positions in space. Local datums chosen by a national cartographical organization include the North American Datum ,
1802-490: The distance they give is correct within a centimeter.) The formulae both return units of meters per degree. An alternative method to estimate the length of a longitudinal degree at latitude ϕ {\displaystyle \phi } is to assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively): where Earth's average meridional radius M r {\displaystyle \textstyle {M_{r}}\,\!}
1855-597: The founder of the Ptolemaic Kingdom . Under Ptolemaic rule the economy prospered, based largely on the export of horses and silphium , a plant used for rich seasoning and medicine. Cyrene became a place of cultivation, where knowledge blossomed. Like any young Greek at the time, Eratosthenes would have studied in the local gymnasium , where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music. Eratosthenes went to Athens to further his studies. There he
1908-474: The full adoption of longitude and latitude, rather than measuring latitude in terms of the length of the midsummer day. Ptolemy's 2nd-century Geography used the same prime meridian but measured latitude from the Equator instead. After their work was translated into Arabic in the 9th century, Al-Khwārizmī 's Book of the Description of the Earth corrected Marinus' and Ptolemy's errors regarding
1961-539: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=LLA&oldid=1219291160 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Geographic coordinate system A geographic coordinate system ( GCS ) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude and longitude . It
2014-418: The king Ptolemy III Euergetes to seek to place him as a librarian at the Library of Alexandria in the year 245 BC. Eratosthenes, then thirty years old, accepted Ptolemy's invitation and traveled to Alexandria, where he lived for the rest of his life. Within about fifty years he became Chief Librarian, a position that the poet Apollonius Rhodius had previously held. As head of the library Eratosthenes tutored
2067-781: The length of the Mediterranean Sea , causing medieval Arabic cartography to use a prime meridian around 10° east of Ptolemy's line. Mathematical cartography resumed in Europe following Maximus Planudes ' recovery of Ptolemy's text a little before 1300; the text was translated into Latin at Florence by Jacopo d'Angelo around 1407. In 1884, the United States hosted the International Meridian Conference , attended by representatives from twenty-five nations. Twenty-two of them agreed to adopt
2120-461: The location has moved, but because the reference system used to measure it has shifted. Because any spatial reference system or map projection is ultimately calculated from latitude and longitude, it is crucial that they clearly state the datum on which they are based. For example, a UTM coordinate based on WGS84 will be different than a UTM coordinate based on NAD27 for the same location. Converting coordinates from one datum to another requires
2173-595: The longitude of the Royal Observatory in Greenwich , England as the zero-reference line. The Dominican Republic voted against the motion, while France and Brazil abstained. France adopted Greenwich Mean Time in place of local determinations by the Paris Observatory in 1911. The latitude ϕ of a point on Earth's surface is the angle between the equatorial plane and the straight line that passes through that point and through (or close to)
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2226-463: The melting of the ice sheets of the last ice age , but neighboring Scotland is rising by only 0.2 cm . These changes are insignificant if a local datum is used, but are statistically significant if a global datum is used. On the GRS 80 or WGS 84 spheroid at sea level at the Equator, one latitudinal second measures 30.715 m , one latitudinal minute is 1843 m and one latitudinal degree
2279-549: The name of the discipline geography . He placed grids of overlapping lines over the surface of the Earth. He used parallels and meridians to link together every place in the world. It was now possible to estimate one's distance from remote locations with this network over the surface of the Earth. In the Geography the names of over 400 cities and their locations were shown, which had never been achieved before. However, his Geography has been lost to history, although fragments of
2332-476: The real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres (509 and 525 ft)). Eratosthenes described his arc measurement technique, in a book entitled On the Measure of the Earth , which has not been preserved. However, a simplified version of the method has been preserved, as described by Cleomedes . The simplified method works by considering two cities along
2385-408: The same meridian and measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (a gnomon ) in each city at noon on the summer solstice . The two cities used were Alexandria and Syene (modern Aswan ), and the distance between the cities was measured by professional bematists . A geometric calculation reveals that the circumference of
2438-547: The work can be pieced together from other great historians like Pliny , Polybius , Strabo , and Marcianus . While this work is the earliest we can trace certain ideas, words, and concepts in the historical record, earlier contributions may have been lost to history. According to Strabo, Eratosthenes argued against the Greek- Barbarian dichotomy. He says Alexander ignored his advisers by his regard for all people with law and government. Strabo says that Eratosthenes
2491-446: The world that needed to be pieced together in some organized format. In his three-volume work Geography ( ‹See Tfd› Greek : Geographika ), he described and mapped his entire known world, even dividing the Earth into five climate zones: two freezing zones around the poles, two temperate zones, and a zone encompassing the equator and the tropics. This book is the first recorded instance of many terms still in use today, including
2544-459: Was a man of many perspectives and investigated the art of poetry under Callimachus . He wrote poems: one in hexameters called Hermes , illustrating the god's life history; and another in elegiacs , called Erigone , describing the suicide of the Athenian maiden Erigone (daughter of Icarius) . He wrote Chronographies , a text that scientifically depicted dates of importance, beginning with
2597-419: Was an Ancient Greek polymath : a mathematician , geographer , poet , astronomer , and music theorist . He was a man of learning, becoming the chief librarian at the Library of Alexandria . His work is comparable to what is now known as the study of geography , and he introduced some of the terminology still used today. He is best known for being the first person known to calculate the circumference of
2650-508: Was born in 276 BC in Cyrene . Now part of modern-day Libya , Cyrene had been founded by Greeks centuries earlier and became the capital of Pentapolis (North Africa) , a country of five cities: Cyrene, Arsinoe , Berenice , Ptolemias , and Apollonia . Alexander the Great conquered Cyrene in 332 BC, and following his death in 323 BC, its rule was given to one of his generals, Ptolemy I Soter ,
2703-435: Was skilled in a variety of things; he was a true polymath. His opponents nicknamed him "Number 2" because he was great at many things and tried to get his hands on every bit of information but never achieved the highest rank in anything; Strabo accounts Eratosthenes as a mathematician among geographers and a geographer among mathematicians. Eratosthenes proposed a simple algorithm for finding prime numbers . This algorithm
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#17327758856332756-578: Was taught Stoicism by its founder, Zeno of Citium , in philosophical lectures on living a virtuous life. He then studied under Aristo of Chios , who led a more cynical school of philosophy. He also studied under the head of the Platonic Academy , who was Arcesilaus of Pitane . His interest in Plato led him to write his first work at a scholarly level, Platonikos , inquiring into the mathematical foundation of Plato's philosophies. Eratosthenes
2809-499: Was wrong to claim that Alexander had disregarded the counsel of his advisers. Strabo argues it was Alexander's interpretation of their "real intent" in recognizing that "in some people there prevail the law-abiding and the political instinct, and the qualities associated with education and powers of speech." Eratosthenes was described by the Suda Lexicon as a Πένταθλος (Pentathlos) which can be translated as "All-Rounded", for he
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