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The straight-line distance between the central point on the map to any other point is the same as the straight-line 3D distance through the globe between the two points. c. 150 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres.
The Mercator projection (/ mərˈkeɪtər /) 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.
Distance from the tangent point on the map is proportional to straight-line distance through the Earth: r(d) = c sin d / 2R [38] Logarithmic azimuthal is constructed so that each point's distance from the center of the map is the logarithm of its distance from the tangent point on the Earth.
An azimuthal equidistant projection about the South Pole extending all the way to the North Pole. Emblem of the United Nations containing a polar azimuthal equidistant projection. The azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances ...
The shortest distance between two points in plane is a Cartesian straight line. The Pythagorean theorem is used to calculate the distance between points in a plane. Even over short distances, the accuracy of geographic distance calculations which assume a flat Earth depend on the method by which the latitude and longitude coordinates have been ...
Distance from a point to a line. The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be ...
On the other hand, the greatest straight line distance that could in theory be covered is a trip exactly on the Equator, a distance of 40,075 kilometres (24,901 mi). The Earth's equatorial bulge makes this slightly longer than a north–south trip around the world along a set of meridian lines, which is a distance of 40,008 kilometres (24,860 mi).
On a north–south passage the rhumb line course coincides with a great circle, as it does on an east–west passage along the equator. On a Mercator projection map, any rhumb line is a straight line; a rhumb line can be drawn on such a map between any two points on Earth without going off the edge of the map. But theoretically a loxodrome can ...
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