"calculated from the width ""W"" of the map by ""R"" = . For example, on a map with ""R"" = 1 the values of ""y"" = 0, 1, 2, 3 correspond to latitudes of ""φ"" = 0°, 50°, 75°, 84° and therefore the successive intervals of 1 cm on the map correspond to latitude intervals on the globe of 50°, 25°, 9° and distances of 5,560 km, 2,780 km, and 1,000 km on the Earth. A straight line on the Mercator map at angle ""α"" to the meridians is a rhumb line. When ""α"" = or the rhumb corresponds to"
"Mercator projection The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical navigation because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians. Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects (making it a conformal map projection), the Mercator projection distorts the size of objects as the latitude increases from the Equator to"
"Because of its very common usage, it has been supposed to have influenced on people's view of the world, and 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. As a result of these criticisms, most modern atlases no longer use the Mercator projection for world maps or for areas distant from the equator, preferring other cylindrical projections, or forms of equal-area projection. The Mercator projection is still commonly used for areas near the equator, however,"
"distances whose determination requires more sophisticated calculations. Mercator projection The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569. It became the standard map projection for nautical navigation because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians. Although the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects (making it a conformal map projection), the Mercator projection distorts the size of objects as"
"on all map projections, shapes or sizes are distortions of the true layout of the Earth's surface. The Mercator projection exaggerates areas far from the equator. For example: The Mercator projection is still used commonly for navigation. On the other hand, because of great land area distortions, it is not well suited for general world maps. Therefore, Mercator himself used the equal-area sinusoidal projection to show relative areas. However, despite such distortions, Mercator projection was, especially in the late 19th and early 20th centuries, perhaps the most common projection used in world maps, despite being much criticized for this use."
"map projection known as the Mercator projection. It was a large planisphere measuring , printed in eighteen separate sheets. While the linear scale is constant in all directions around any point, thus preserving the angles and the shapes of small objects (which makes the projection conformal), the Mercator projection distorts the size and shape of large objects, as the scale increases from the Equator to the poles, where it becomes infinite. The title (""Nova et Aucta Orbis Terrae Descriptio ad Usum Navigatium Emendate"": ""new and augmented description of Earth corrected for the use of navigation"") and the map legends show"
"Transverse Mercator projection The transverse Mercator map projection is an adaptation of the standard Mercator projection. The transverse version is widely used in national and international mapping systems around the world, including the UTM. When paired with a suitable geodetic datum, the transverse Mercator delivers high accuracy in zones less than a few degrees in east-west extent. The transverse Mercator projection is the transverse aspect of the standard (or ""Normal"") Mercator projection. They share the same underlying mathematical construction and consequently the transverse Mercator inherits many traits from the normal Mercator: Since the central meridian of the transverse Mercator can"
"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: 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. Several authors are associated with the development of Mercator projection: As"
"Web Mercator projection Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 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 Google Maps adopted it in 2005. It is used by virtually all major online map providers, including Google Maps, Mapbox, Bing Maps, OpenStreetMap, Mapquest, Esri, and many others. Its official EPSG identifier is EPSG:3857, although others have been used historically. Web Mercator is a slight variant of the Mercator projection, one used primarily in Web-based mapping programs. It uses the same"
"where distortion is minimal. Arno Peters stirred controversy when he proposed what is now usually called the Gall–Peters projection as ""the"" alternative to the Mercator. The projection he promoted is a specific parameterization of the cylindrical equal-area projection. In response, a 1989 resolution by seven North American geographical groups deprecated the use of cylindrical projections for general purpose world maps, which would include both the Mercator and the Gall–Peters. Many major online street mapping services (Bing Maps, OpenStreetMap, Google Maps, MapQuest, Yahoo! Maps, and others) use a variant of the Mercator projection for their map images called Web Mercator or"
"land use, shifting power from peasants to colonial institutions. In 1569, Gerardus Mercator introduced a map projection of the Earth which is now known as the Mercator projection. This projection maintained equally spaced longitudinal lines but spaced out the latitudinal lines. These lines were spaced farther apart as their distance from the Equator increased. This means that areas farther away from the Equator seam to be disproportionately large. Greenland, for example, appears to be larger than the continent of Africa. In reality, Africa’s area is 14 times greater than that of Greenland. Due to its common usage, the Mercator had"
"£1M worth of damage was caused to the barge and delayed work on the installation of a tidal energy generator prototype. As stated in the Mariners Handbook and subsequent accident report: ""No chart is infallible. Every chart is liable to be incomplete"". The Mercator projection is used on the vast majority of nautical charts. Since the Mercator projection is conformal, that is, bearings in the chart are identical to the corresponding angles in nature, courses plotted on the chart may be used directly as the course-to-steer at the helm. The gnomonic projection is used for charts intended for plotting of"
"to central cylindrical's. It is not known who first developed the projection, but it appeared with other new cylindrical projections in the 19th century, and regularly finds its way into textbooks, chiefly to illustrate that this is not the way Mercator is constructed. As with any cylindrical projection, the construction can be generalized by positioning the cylinder to be tangent to a great circle of the globe that is not the equator. This projection has prominent use in panoramic photography where it is usually called ""cylindrical projection"". It can present a full 360° panorama and preserves vertical lines. Unlike other"
"augmented description of Earth corrected for the use of sailors"") show that it was expressly conceived for the use of marine navigation. Although the method of construction is not explained by the author, Mercator probably used a graphical method, transferring some rhumb lines previously plotted on a globe to a square graticule (grid formed by lines of latitude and longitude), and then adjusting the spacing between parallels so that those lines became straight, making the same angle with the meridians as in the globe. The development of the Mercator projection represented a major breakthrough in the nautical cartography of the"
"shown in correct proportion. However, representing area ratios correctly necessarily distorts shapes more than many maps that are not equal-area. The Mercator projection, developed for navigational purposes, has often been used in world maps where other projections would have been more appropriate. This problem has long been recognized even outside professional circles. For example, a 1943 ""New York Times"" editorial states: A controversy in the 1980s over the Peters map motivated the American Cartographic Association (now Cartography and Geographic Information Society) to produce a series of booklets (including ""Which Map Is Best"") designed to educate the public about map projections"
"growing after 55 degrees. Miller cylindrical projection The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of , projected according to Mercator, and then the result is multiplied by to retain scale along the equator. Hence: or inversely, where ""λ"" is the longitude from the central meridian of the projection, and ""φ"" is the latitude. Meridians are thus about 0.733 the length of the equator. In GIS applications, this projection is known as: ""ESRI:54003 - World Miller Cylindrical"" Compact Miller projection is similar to Miller but"
"be chosen at will, it may be used to construct highly accurate maps (of narrow width) anywhere on the globe. The secant, ellipsoidal form of the transverse Mercator is the most widely applied of all projections for accurate large-scale maps. In constructing a map on any projection, a sphere is normally chosen to model the Earth when the extent of the mapped region exceeds a few hundred kilometers in length in both dimensions. For maps of smaller regions, an ellipsoidal model must be chosen if greater accuracy is required; see next section. The spherical form of the transverse Mercator projection"
"part in 100. Similarly sec 2.56° = 1.001, so a strip of width 5.12° (centred on the equator) is accurate to within 0.1% or 1 part in 1,000. Therefore, the Mercator projection is adequate for mapping countries close to the equator. In a secant (in the sense of cutting) Mercator projection the globe is projected to a cylinder which cuts the sphere at two parallels with latitudes ±""φ"". The scale is now true at these latitudes whereas parallels between these latitudes are contracted by the projection and their scale factor must be less than one. The result is that ""deviation"""
"Space-oblique Mercator projection Space-oblique Mercator projection is a map projection. The space-oblique Mercator projection (SOM) was developed by John P. Snyder, Alden Partridge Colvocoresses and John L. Junkins in 1976. Snyder had an interest in maps, originating back to his childhood and he regularly attended cartography conferences while on vacation. When the United States Geological Survey (USGS) needed to develop a system for reducing the amount of distortion caused when satellite pictures of the ellipsoidal Earth were printed on a flat page, they appealed for help at one such conference. Snyder worked on the problem armed with his newly purchased"
"Miller cylindrical projection The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of , projected according to Mercator, and then the result is multiplied by to retain scale along the equator. Hence: or inversely, where ""λ"" is the longitude from the central meridian of the projection, and ""φ"" is the latitude. Meridians are thus about 0.733 the length of the equator. In GIS applications, this projection is known as: ""ESRI:54003 - World Miller Cylindrical"" Compact Miller projection is similar to Miller but spacing between parallels stops"
"of wall maps, bound maps, globes and scientific instruments but his greatest legacy was the mathematical projection he devised for his 1569 world map. The Mercator projection is an example of a cylindrical projection in which the meridians are straight and perpendicular to the parallels. As a result, the map has a constant width and the parallels are stretched east-west as the poles are approached. Mercator's insight was to stretch the separation of the parallels in a way which exactly compensates for their increasing length, thus preserving shapes of small regions, albeit at the expense of global distortion. Such a"
"sinusoidal projection and the Bonne projection. The Werner projection places its standard parallel at the North Pole; a sinusoidal projection places its standard parallel at the equator; and the Bonne projection is intermediate between the two. In 1569, mapmaker Gerardus Mercator first published a map based on his Mercator projection, which uses equally-spaced parallel vertical lines of longitude and parallel latitude lines spaced farther apart as they get farther away from the equator. By this construction, courses of constant bearing are conveniently represented as straight lines for navigation. The same property limits its value as a general-purpose world map because"
"characteristics of the underlying rock, fault lines, and subsurface structures. Maps that depict the surface of the Earth also use a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture. Perhaps the best-known world-map projection is the Mercator projection, originally designed as a form of nautical chart. Aeroplane pilots use aeronautical charts based on a Lambert conformal conic projection, in which a cone is laid over the section of the earth to be mapped. The cone intersects the sphere (the earth) at one or two parallels which are chosen as standard lines. This"
"projection to display information in the online Map Maker application, and the European Environment Agency recommends its usage for European mapping for statistical analysis and display. 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 special 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"
"Mercator projection known as the Web Mercator. The biases formed from the Mercator projection will no longer be due to atlas and textbooks but will come from digital maps and GPS on our phones and computers. The rising popularity of digital mapping systems (such as Google Maps, Apple Maps, and Microsoft Bing Maps) highlights the role of cartography in representing occupied territories. While parts of the occupied territories are labeled on the maps (for example, the West Bank and the Gaza Strip), the name of country associated with these territories is not always labeled on the map. Many critical cartographers"
"First let's compute some intermediate values: The final formulae are: Universal Transverse Mercator coordinate system The Universal Transverse Mercator (UTM) conformal projection uses a 2-dimensional Cartesian coordinate system to give locations on the surface of the Earth. Like the traditional method of latitude and longitude, it is a horizontal position representation, i.e. it is used to identify locations on the Earth independently of vertical position. However, it differs from that method in several respects. The UTM system is not a single map projection. The system instead divides the Earth into sixty zones, each being a six-degree band of longitude, and"
"scale is the same as the north-south scale, making it a conformal map projection. Conformal projections preserve angles around all locations. Because the linear scale of a Mercator map 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 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 (as long as the projection is based on a cylinder"
"the last constraint entirely. Instead the parallels can be placed according to any algorithm the designer has decided suits the needs of the map. The famous Mercator projection is one in which the placement of parallels does not arise by ""projection""; instead parallels are placed how they need to be in order to satisfy the property that a course of constant bearing is always plotted as a straight line. A ""normal cylindrical projection"" is any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude (parallels) are mapped to horizontal lines. The mapping of meridians"
"Europe; the transverse Mercator in the US; or Gauss–Krüger transverse Mercator generally. The projection is conformal with a constant scale on the central meridian. (There are other conformal generalisations of the transverse Mercator from the sphere to the ellipsoid but only Gauss-Krüger has a constant scale on the central meridian.) Throughout the twentieth century the Gauss–Krüger transverse Mercator was adopted, in one form or another, by many nations (and international bodies); in addition it provides the basis for the Universal Transverse Mercator series of projections. The Gauss–Krüger projection is now the most widely used projection in accurate large-scale mapping. The"
"corresponding to formula_80. Since formula_58 attains this value at formula_82 degrees (see figure below, red line). Therefore, the tangent Mercator projection is highly accurate within a strip of width 3.24 degrees centred on the equator. This corresponds to north-south distance of about . Within this strip Mercator is ""very"" good, highly accurate and shape preserving because it is conformal (angle preserving). These observations prompted the development of the transverse Mercator projections in which a meridian is treated 'like an equator' of the projection so that we obtain an accurate map within a narrow distance of that meridian. Such maps are"
"70 years before the projection formula was derived analytically. Wright published a new world map based on the Mercator projection, also in 1599. Slowly, but steadily, charts using the projection appeared throughout the first half of the seventeenth century and by the end of that century chart makers all over the world were using nothing but the Mercator projection, with the aim of showing the oceans and the coastlines in detail without concern for the continental interiors. At some stage the projection made the unfortunate leap to portrayal of the continents and it eventually became the canonical description of the"
"typically employ a transverse Mercator or close variant for large-scale maps in order to preserve conformality and low variation in scale over small areas. For smaller-scale maps, such as those spanning continents or the entire world, many projections are in common use according to their fitness for the purpose, such as Winkel tripel, Robinson and Mollweide. Reference maps of the world often appear on compromise projections. Due to distortions inherent in any map of the world, the choice of projection becomes largely one of aesthetics. Thematic maps normally require an equal area projection so that phenomena per unit area are"
"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 global 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 much as 40 km on the ground. While the Web Mercator's formulas are for the spherical form of the Mercator, geographical coordinates are required to be in the"