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75-758: The 38th parallel north is a circle of latitude that is 38 degrees north of the Earth's equatorial plane . It crosses Europe , the Mediterranean Sea , Asia , the Pacific Ocean , North America , and the Atlantic Ocean . The 38th parallel north formed the border between North and South Korea prior to the Korean War . At this latitude, the Sun is visible for 14 hours, 48 minutes during
150-435: A compass rose or protractor, and the corresponding directions are easily transferred from point to point, on the map, e.g. with the help of a parallel ruler . Because the linear scale of a Mercator map in normal aspect increases with latitude, it distorts the size of geographical objects far from the equator and conveys a distorted perception of the overall geometry of the planet. At latitudes greater than 70° north or south,
225-442: A Mercator map printed in a book might have an equatorial width of 13.4 cm corresponding to a globe radius of 2.13 cm and an RF of approximately 1 / 300M (M is used as an abbreviation for 1,000,000 in writing an RF) whereas Mercator's original 1569 map has a width of 198 cm corresponding to a globe radius of 31.5 cm and an RF of about 1 / 20M . A cylindrical map projection
300-720: A circle of latitude is given by its longitude . Circles of latitude are unlike circles of longitude, which are all great circles with the centre of Earth in the middle, as the circles of latitude get smaller as the distance from the Equator increases. Their length can be calculated by a common sine or cosine function. For example, the 60th parallel north or south is half as long as the Equator (disregarding Earth's minor flattening by 0.335%), stemming from cos ( 60 ∘ ) = 0.5 {\displaystyle \cos(60^{\circ })=0.5} . On
375-491: A different relationship that does not diverge at φ = ±90°. A transverse Mercator projection tilts the cylinder axis so that it is perpendicular to Earth's axis. The tangent standard line then coincides with a meridian and its opposite meridian, giving a constant scale factor along those meridians and making the projection useful for mapping regions that are predominately north–south in extent. In its more complex ellipsoidal form, most national grid systems around
450-464: A map in Mercator projection that correctly showed those two coordinates. Many major online street mapping services ( Bing Maps , Google Maps , Mapbox , MapQuest , OpenStreetMap , Yahoo! Maps , and others) use a variant of the Mercator projection for their map images called Web Mercator or Google Web Mercator. Despite its obvious scale variation at the world level (small scales), the projection
525-447: A map, the circles of latitude may or may not be parallel, and their spacing may vary, depending on which projection is used to map the surface of the Earth onto a plane. On an equirectangular projection , centered on the equator, the circles of latitude are horizontal, parallel, and equally spaced. On other cylindrical and pseudocylindrical projections, the circles of latitude are horizontal and parallel, but may be spaced unevenly to give
600-401: A median latitude, hk = 11.7. For Australia, taking 25° as a median latitude, hk = 1.2. For Great Britain, taking 55° as a median latitude, hk = 3.04. The variation with latitude is sometimes indicated by multiple bar scales as shown below. The classic way of showing the distortion inherent in a projection is to use Tissot's indicatrix . Nicolas Tissot noted that the scale factors at
675-510: A point on a map projection, specified by the numbers h and k , define an ellipse at that point. For cylindrical projections, the axes of the ellipse are aligned to the meridians and parallels. For the Mercator projection, h = k , so the ellipses degenerate into circles with radius proportional to the value of the scale factor for that latitude. These circles are rendered on the projected map with extreme variation in size, indicative of Mercator's scale variations. As discussed above,
750-418: A small portion of the spherical surface without otherwise distorting it, preserving angles between intersecting curves. Afterward, this cylinder is unrolled onto a flat plane to make a map. In this interpretation, the scale of the surface is preserved exactly along the circle where the cylinder touches the sphere, but increases nonlinearly for points further from the contact circle. However, by uniformly shrinking
825-452: A straight segment. Such a course, known as a rhumb (alternately called a rhumb line or loxodrome) is preferred in marine navigation because ships can sail in a constant compass direction. This reduces the difficult, error-prone course corrections that otherwise would be necessary when sailing a different course. For small distances (compared to the radius of the Earth), the difference between
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#1732776341104900-412: Is R cos φ , the corresponding parallel on the map must have been stretched by a factor of 1 / cos φ = sec φ . This scale factor on the parallel is conventionally denoted by k and the corresponding scale factor on the meridian is denoted by h . The Mercator projection is conformal . One implication of that is the "isotropy of scale factors", which means that
975-520: Is a conformal cylindrical map projection first presented by Flemish geographer and mapmaker Gerardus Mercator in 1569. In the 18th century, it became the standard map projection for navigation due to its property of representing rhumb lines as straight lines. When applied to world maps, the Mercator projection inflates the size of lands the further they are from the equator . Therefore, landmasses such as Greenland and Antarctica appear far larger than they actually are relative to landmasses near
1050-474: Is a specific parameterization of the cylindrical equal-area projection . In response, a 1989 resolution by seven North American geographical groups disparaged using cylindrical projections for general-purpose world maps, which would include both the Mercator and the Gall–Peters. Practically every marine chart in print is based on the Mercator projection due to its uniquely favorable properties for navigation. It
1125-468: Is also commonly used by street map services hosted on the Internet, due to its uniquely favorable properties for local-area maps computed on demand. Mercator projections were also important in the mathematical development of plate tectonics in the 1960s. The Mercator projection was designed for use in marine navigation because of its unique property of representing any course of constant bearing as
1200-516: Is drawn as a "line on a map", which was made in massive scale during the 1884 Berlin Conference , regarding huge parts of the African continent. North American nations and states have also mostly been created by straight lines, which are often parts of circles of latitudes. For instance, the northern border of Colorado is at 41° N while the southern border is at 37° N . Roughly half
1275-474: Is equal to the Earth's axial tilt. By definition, the positions of the Tropic of Cancer , Tropic of Capricorn , Arctic Circle and Antarctic Circle all depend on the tilt of the Earth's axis relative to the plane of its orbit around the Sun (the "obliquity of the ecliptic"). If the Earth were "upright" (its axis at right angles to the orbital plane) there would be no Arctic, Antarctic, or Tropical circles: at
1350-481: Is specified by formulae linking the geographic coordinates of latitude φ and longitude λ to Cartesian coordinates on the map with origin on the equator and x -axis along the equator. By construction, all points on the same meridian lie on the same generator of the cylinder at a constant value of x , but the distance y along the generator (measured from the equator) is an arbitrary function of latitude, y ( φ ). In general this function does not describe
1425-463: Is the longest circle of latitude and is the only circle of latitude which also is a great circle. As such, it is perpendicular to all meridians. There are 89 integral (whole degree ) circles of latitude between the Equator and the poles in each hemisphere , but these can be divided into more precise measurements of latitude, and are often represented as a decimal degree (e.g. 34.637° N) or with minutes and seconds (e.g. 22°14'26" S). On
1500-494: Is well-suited as an interactive world map that can be zoomed seamlessly to local (large-scale) maps, where there is relatively little distortion due to the variant projection's near- conformality . The major online street mapping services' tiling systems display most of the world at the lowest zoom level as a single square image, excluding the polar regions by truncation at latitudes of φ max = ±85.05113°. (See below .) Latitude values outside this range are mapped using
1575-658: The Mercator projection or on the Gall-Peters projection , a circle of latitude is perpendicular to all meridians . On the ellipsoid or on spherical projection, all circles of latitude are rhumb lines , except the Equator. The latitude of the circle is approximately the angle between the Equator and the circle, with the angle's vertex at Earth's centre. The Equator is at 0°, and the North Pole and South Pole are at 90° north and 90° south, respectively. The Equator
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#17327763411041650-516: The equator ; the closer to the poles of the Earth, the greater the distortion. Because of great land area distortions, critics like George Kellaway and Irving Fisher consider the projection unsuitable for general world maps. It has been conjectured to have influenced people's views of the world: because it shows countries near the Equator as too small when compared to those of Europe and North America, it has been supposed to cause people to consider those countries as less important. Mercator himself used
1725-424: The globe in this section. The globe determines the scale of the map. The various cylindrical projections specify how the geographic detail is transferred from the globe to a cylinder tangential to it at the equator. The cylinder is then unrolled to give the planar map. The fraction R / a is called the representative fraction (RF) or the principal scale of the projection. For example,
1800-407: The integral of the secant function , The function y ( φ ) is plotted alongside φ for the case R = 1: it tends to infinity at the poles. The linear y -axis values are not usually shown on printed maps; instead some maps show the non-linear scale of latitude values on the right. More often than not the maps show only a graticule of selected meridians and parallels. The expression on
1875-664: The summer solstice and 9 hours, 32 minutes during the winter solstice . Starting at the Prime Meridian heading eastward, the 38th parallel north passes through: Japan had ruled the Korean Peninsula between 1910 and 1945. When Japan surrendered in August 1945, the 38th parallel was established as the boundary between Soviet and American occupation zones . This parallel divided the Korean peninsula roughly in
1950-503: The 13th century, the earliest extant portolan charts of the Mediterranean sea, which are generally not believed to be based on any deliberate map projection, included windrose networks of criss-crossing lines which could be used to help set a ship's bearing in sailing between locations on the chart; the region of the Earth covered by such charts was small enough that a course of constant bearing would be approximately straight on
2025-497: The 38th parallel, from the southwest to the northeast. Circle of latitude A circle of latitude or line of latitude on Earth is an abstract east – west small circle connecting all locations around Earth (ignoring elevation ) at a given latitude coordinate line . Circles of latitude are often called parallels because they are parallel to each other; that is, planes that contain any of these circles never intersect each other. A location's position along
2100-553: The Equator, mark the divisions between the five principal geographical zones . The equator is the circle that is equidistant from the North Pole and South Pole . It divides the Earth into the Northern Hemisphere and the Southern Hemisphere . Of the parallels or circles of latitude, it is the longest, and the only ' great circle ' (a circle on the surface of the Earth, centered on Earth's center). All
2175-473: The Mercator projection can be found in many world maps in the centuries following Mercator's first publication. However, it did not begin to dominate world maps until the 19th century, when the problem of position determination had been largely solved. Once the Mercator became the usual projection for commercial and educational maps, it came under persistent criticism from cartographers for its unbalanced representation of landmasses and its inability to usefully show
2250-420: The Mercator projection is practically unusable, because the linear scale becomes infinitely large at the poles. A Mercator map can therefore never fully show the polar areas (but see Uses below for applications of the oblique and transverse Mercator projections). The Mercator projection is often compared to and confused with the central cylindrical projection , which is the result of projecting points from
2325-481: The Mercator projection is the unique projection which balances this East–West stretching by a precisely corresponding North–South stretching, so that at every location the scale is locally uniform and angles are preserved. The Mercator projection in normal aspect maps trajectories of constant bearing (called rhumb lines or loxodromes ) on a sphere to straight lines on the map, and is thus uniquely suited to marine navigation : courses and bearings are measured using
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2400-539: The North and South poles, and the contact circle is the Earth's equator . As for all cylindrical projections in normal aspect, circles of latitude and meridians of longitude are straight and perpendicular to each other on the map, forming a grid of rectangles. While circles of latitude on the Earth are smaller the closer they are to the poles, they are stretched in an East–West direction to have uniform length on any cylindrical map projection. Among cylindrical projections,
2475-475: The North to return its troops to behind the 38th parallel, commencing the Korean War with United Nations troops (mostly American) helping South Korean troops to defend South Korea. After the Armistice agreement was signed on July 27, 1953, a new line was established to separate North Korea and South Korea. This Military Demarcation Line is surrounded by a Demilitarized Zone . The demarcation line crosses
2550-619: The Tropical Circles are drifting towards the equator (and the Polar Circles towards the poles) by 15 m per year, and the area of the Tropics , defined astronomically, is decreasing by 1,100 km (420 sq mi) per year. (However, the tropical belt as defined based on atmospheric conditions is expanding due to global warming . ) The Earth's axial tilt has additional shorter-term variations due to nutation , of which
2625-500: The Tropics and Polar Circles and also on the Equator. Short-term fluctuations over a matter of days do not directly affect the location of the extreme latitudes at which the Sun may appear directly overhead, or at which 24-hour day or night is possible, except when they actually occur at the time of the solstices. Rather, they cause a theoretical shifting of the parallels, that would occur if the given axis tilt were maintained throughout
2700-464: The Web Mercator. The Mercator projection can be visualized as the result of wrapping a cylinder tightly around a sphere, with the two surfaces tangent to (touching) each other along a circle halfway between the poles of their common axis, and then conformally unfolding the surface of the sphere outward onto the cylinder, meaning that at each point the projection uniformly scales the image of
2775-687: The chart. The charts have startling accuracy not found in the maps constructed by contemporary European or Arab scholars, and their construction remains enigmatic; based on cartometric analysis which seems to contradict the scholarly consensus, they have been speculated to have originated in some unknown pre-medieval cartographic tradition, possibly evidence of some ancient understanding of the Mercator projection. German polymath Erhard Etzlaub engraved miniature "compass maps" (about 10×8 cm) of Europe and parts of Africa that spanned latitudes 0°–67° to allow adjustment of his portable pocket-size sundials . The projection found on these maps, dating to 1511,
2850-515: The equal-area sinusoidal projection to show relative areas. However, despite such criticisms, the Mercator projection was, especially in the late 19th and early 20th centuries, perhaps the most common projection used in world maps. Atlases largely stopped using the Mercator projection for world maps or for areas distant from the equator in the 1940s, preferring other cylindrical projections , or forms of equal-area projection . The Mercator projection is, however, still commonly used for areas near
2925-458: The equator where distortion is minimal. It is also frequently found in maps of time zones. Arno Peters stirred controversy beginning in 1972 when he proposed what is now usually called the Gall–Peters projection to remedy the problems of the Mercator, claiming it to be his own original work without referencing prior work by cartographers such as Gall's work from 1855. The projection he promoted
3000-565: The equator. Nowadays the Mercator projection is widely used because, aside from marine navigation, it is well suited for internet web maps . Joseph Needham , a historian of China, speculated that some star charts of the Chinese Song dynasty may have been drafted on the Mercator projection; however, this claim was presented without evidence, and astronomical historian Kazuhiko Miyajima concluded using cartometric analysis that these charts used an equirectangular projection instead. In
3075-567: The form of the Web Mercator projection . Today, the Mercator can be found in marine charts, occasional world maps, and Web mapping services, but commercial atlases have largely abandoned it, and wall maps of the world can be found in many alternative projections. Google Maps , which relied on it since 2005, still uses it for local-area maps but dropped the projection from desktop platforms in 2017 for maps that are zoomed out of local areas. Many other online mapping services still exclusively use
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3150-418: The geometrical projection (as of light rays onto a screen) from the centre of the globe to the cylinder, which is only one of an unlimited number of ways to conceptually project a cylindrical map. Since the cylinder is tangential to the globe at the equator, the scale factor between globe and cylinder is unity on the equator but nowhere else. In particular since the radius of a parallel, or circle of latitude,
3225-431: The geometry of corresponding small elements on the globe and map. The figure below shows a point P at latitude φ and longitude λ on the globe and a nearby point Q at latitude φ + δφ and longitude λ + δλ . The vertical lines PK and MQ are arcs of meridians of length Rδφ . The horizontal lines PM and KQ are arcs of parallels of length R (cos φ ) δλ . The corresponding points on
3300-405: The globe radius R . It is often convenient to work directly with the map width W = 2 π R . For example, the basic transformation equations become The ordinate y of the Mercator projection becomes infinite at the poles and the map must be truncated at some latitude less than ninety degrees. This need not be done symmetrically. Mercator's original map is truncated at 80°N and 66°S with
3375-511: The horizon for 24 hours (at the December and June Solstices respectively). The latitude of the polar circles is equal to 90° minus the Earth's axial tilt . The Tropic of Cancer and Tropic of Capricorn mark the northernmost and southernmost latitudes at which the Sun may be seen directly overhead at the June solstice and December solstice respectively. The latitude of the tropical circles
3450-436: The impossibility of determining the longitude at sea with adequate accuracy and the fact that magnetic directions, instead of geographical directions , were used in navigation. Only in the middle of the 18th century, after the marine chronometer was invented and the spatial distribution of magnetic declination was known, could the Mercator projection be fully adopted by navigators. Despite those position-finding limitations,
3525-451: The isotropy condition implies that h = k = sec φ . Consider a point on the globe of radius R with longitude λ and latitude φ . If φ is increased by an infinitesimal amount, dφ , the point moves R dφ along a meridian of the globe of radius R , so the corresponding change in y , dy , must be hR dφ = R sec φ dφ . Therefore y′ ( φ ) = R sec φ . Similarly, increasing λ by dλ moves
3600-533: The length of the border between the United States and Canada follows 49° N . There are five major circles of latitude, listed below from north to south. The position of the Equator is fixed (90 degrees from Earth's axis of rotation) but the latitudes of the other circles depend on the tilt of this axis relative to the plane of Earth's orbit, and so are not perfectly fixed. The values below are for 22 November 2024: These circles of latitude, excluding
3675-399: The main term, with a period of 18.6 years, has an amplitude of 9.2″ (corresponding to almost 300 m north and south). There are many smaller terms, resulting in varying daily shifts of some metres in any direction. Finally, the Earth's rotational axis is not exactly fixed in the Earth, but undergoes small fluctuations (on the order of 15 m) called polar motion , which have a small effect on
3750-416: The map Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendata : "A new and augmented description of Earth corrected for the use of sailors". This title, along with an elaborate explanation for using the projection that appears as a section of text on the map, shows that Mercator understood exactly what he had achieved and that he intended the projection to aid navigation. Mercator never explained
3825-627: The map useful characteristics. For instance, on a Mercator projection the circles of latitude are more widely spaced near the poles to preserve local scales and shapes, while on a Gall–Peters projection the circles of latitude are spaced more closely near the poles so that comparisons of area will be accurate. On most non-cylindrical and non-pseudocylindrical projections, the circles of latitude are neither straight nor parallel. Arcs of circles of latitude are sometimes used as boundaries between countries or regions where distinctive natural borders are lacking (such as in deserts), or when an artificial border
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#17327763411043900-410: The mathematical principle of the rhumb line or loxodrome, a path with constant bearing as measured relative to true north, which can be used in marine navigation to pick which compass bearing to follow. In 1537, he proposed constructing a nautical atlas composed of several large-scale sheets in the equirectangular projection as a way to minimize distortion of directions. If these sheets were brought to
3975-404: The maximum latitude attained must correspond to y = ± W / 2 , or equivalently y / R = π . Any of the inverse transformation formulae may be used to calculate the corresponding latitudes: The relations between y ( φ ) and properties of the projection, such as the transformation of angles and the variation in scale, follow from
4050-433: The mean value of the tilt was 23° 26′ 21.406″ (according to IAU 2006, theory P03), the corresponding value being 23° 26′ 10.633" at noon of January 1st 2023 AD. The main long-term cycle causes the axial tilt to fluctuate between about 22.1° and 24.5° with a period of 41,000 years. Currently, the average value of the tilt is decreasing by about 0.468″ per year. As a result (approximately, and on average),
4125-537: The method of construction or how he arrived at it. Various hypotheses have been tendered over the years, but in any case Mercator's friendship with Pedro Nunes and his access to the loxodromic tables Nunes created likely aided his efforts. English mathematician Edward Wright published the first accurate tables for constructing the projection in 1599 and, in more detail, in 1610, calling his treatise "Certaine Errors in Navigation". The first mathematical formulation
4200-796: The middle. In 1948, this parallel became the boundary between the Democratic People's Republic of Korea ( North Korea ) and the Republic of Korea ( South Korea ), both of which claim to be the government of the whole of Korea. On 25 June 1950, after a series of cross-border raids and gunfire from both the Northern and the Southern sides, the North Korean Army crossed the 38th parallel and invaded South Korea. This sparked United Nations Security Council Resolution 82 which called for
4275-487: The northern hemisphere because astronomic latitude can be roughly measured (to within a few tens of metres) by sighting the North Star . Normally the circles of latitude are defined at zero elevation . Elevation has an effect on a location with respect to the plane formed by a circle of latitude. Since (in the geodetic system ) altitude and depth are determined by the normal to the Earth's surface, locations sharing
4350-418: The oblique Mercator in order to keep scale variation low along the surface projection of the cylinder's axis. Although the surface of Earth is best modelled by an oblate ellipsoid of revolution , for small scale maps the ellipsoid is approximated by a sphere of radius a , where a is approximately 6,371 km. This spherical approximation of Earth can be modelled by a smaller sphere of radius R , called
4425-634: The other parallels are smaller and centered only on Earth's axis. The Arctic Circle is the southernmost latitude in the Northern Hemisphere at which the Sun can remain continuously above or below the horizon for 24 hours (at the June and December solstices respectively). Similarly, the Antarctic Circle marks the northernmost latitude in the Southern Hemisphere at which the Sun can remain continuously above or below
4500-435: The point R cos φ dλ along a parallel of the globe, so dx = kR cos φ dλ = R dλ . That is, x′ ( λ ) = R . Integrating the equations with x ( λ 0 ) = 0 and y (0) = 0, gives x(λ) and y(φ) . The value λ 0 is the longitude of an arbitrary central meridian that is usually, but not always, that of Greenwich (i.e., zero). The angles λ and φ are expressed in radians. By
4575-464: The point scale factor is independent of direction, so that small shapes are preserved by the projection. This implies that the vertical scale factor, h , equals the horizontal scale factor, k . Since k = sec φ , so must h . The graph shows the variation of this scale factor with latitude. Some numerical values are listed below. The area scale factor is the product of the parallel and meridian scales hk = sec φ . For Greenland, taking 73° as
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#17327763411044650-428: The polar regions. The criticisms leveled against inappropriate use of the Mercator projection resulted in a flurry of new inventions in the late 19th and early 20th century, often directly touted as alternatives to the Mercator. Due to these pressures, publishers gradually reduced their use of the projection over the course of the 20th century. However, the advent of Web mapping gave the projection an abrupt resurgence in
4725-490: The poles the Sun would always circle along the horizon, and at the equator the Sun would always rise due east, pass directly overhead, and set due west. The positions of the Tropical and Polar Circles are not fixed because the axial tilt changes slowly – a complex motion determined by the superimposition of many different cycles (some of which are described below) with short to very long periods. At noon of January 1st 2000 AD,
4800-409: The result that European countries were moved toward the centre of the map. The aspect ratio of his map is 198 / 120 = 1.65. Even more extreme truncations have been used: a Finnish school atlas was truncated at approximately 76°N and 56°S, an aspect ratio of 1.97. Much Web-based mapping uses a zoomable version of the Mercator projection with an aspect ratio of one. In this case
4875-410: The resulting flat map, as a final step, any pair of circles parallel to and equidistant from the contact circle can be chosen to have their scale preserved, called the standard parallels ; then the region between chosen circles will have its scale smaller than on the sphere, reaching a minimum at the contact circle. This is sometimes visualized as a projection onto a cylinder which is secant to (cuts)
4950-455: The rhumb and the great circle course is negligible. Even for longer distances, the simplicity of the constant bearing makes it attractive. As observed by Mercator, on such a course, the ship would not arrive by the shortest route, but it will surely arrive. Sailing a rhumb meant that all that the sailors had to do was keep a constant course as long as they knew where they were when they started, where they intended to be when they finished, and had
5025-475: The right of the second equation defines the Gudermannian function ; i.e., φ = gd( y / R ): the direct equation may therefore be written as y = R ·gd ( φ ). There are many alternative expressions for y ( φ ), all derived by elementary manipulations. Corresponding inverses are: For angles expressed in degrees: The above formulae are written in terms of
5100-430: The same latitude—but having different elevations (i.e., lying along this normal)—no longer lie within this plane. Rather, all points sharing the same latitude—but of varying elevation and longitude—occupy the surface of a truncated cone formed by the rotation of this normal around the Earth's axis of rotation. Mercator projection The Mercator projection ( / m ər ˈ k eɪ t ər / )
5175-416: The same scale and assembled, they would approximate the Mercator projection. In 1541, Flemish geographer and mapmaker Gerardus Mercator included a network of rhumb lines on a terrestrial globe he made for Nicolas Perrenot . In 1569, Mercator announced a new projection by publishing a large world map measuring 202 by 124 cm (80 by 49 in) and printed in eighteen separate sheets. Mercator titled
5250-431: The sphere onto a tangent cylinder along straight radial lines, as if from a light source placed at the Earth's center. Both have extreme distortion far from the equator and cannot show the poles. However, they are different projections and have different properties. As with all map projections , the shapes or sizes are distortions of the true layout of the Earth's surface. The Mercator projection exaggerates areas far from
5325-405: The sphere, though this picture is misleading insofar as the standard parallels are not spaced the same distance apart on the map as the shortest distance between them through the interior of the sphere. The original and most common aspect of the Mercator projection for maps of the Earth is the normal aspect, for which the axis of the cylinder is the Earth's axis of rotation which passes through
5400-534: The world use the transverse Mercator, as does the Universal Transverse Mercator coordinate system . An oblique Mercator projection tilts the cylinder axis away from the Earth's axis to an angle of one's choosing, so that its tangent or secant lines of contact are circles that are also tilted relative to the Earth's parallels of latitude. Practical uses for the oblique projection, such as national grid systems, use ellipsoidal developments of
5475-445: The year. These circles of latitude can be defined on other planets with axial inclinations relative to their orbital planes. Objects such as Pluto with tilt angles greater than 45 degrees will have the tropic circles closer to the poles and the polar circles closer to the equator. A number of sub-national and international borders were intended to be defined by, or are approximated by, parallels. Parallels make convenient borders in
5550-538: Was publicized around 1645 by a mathematician named Henry Bond ( c. 1600 –1678). However, the mathematics involved were developed but never published by mathematician Thomas Harriot starting around 1589. The development of the Mercator projection represented a major breakthrough in the nautical cartography of the 16th century. However, it was much ahead of its time, since the old navigational and surveying techniques were not compatible with its use in navigation. Two main problems prevented its immediate application:
5625-424: Was stated by John Snyder in 1987 to be the same projection as Mercator's. However, given the geometry of a sundial, these maps may well have been based on the similar central cylindrical projection , a limiting case of the gnomonic projection , which is the basis for a sundial. Snyder amended his assessment to "a similar projection" in 1993. Portuguese mathematician and cosmographer Pedro Nunes first described
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