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Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. One problem is the variation of scale with latitude, and another is that straight lines on the map (rhumb lines), other than the meridians or the equator, do not correspond to great circles.
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.
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 ...
A rhumb line appears as a straight line on a Mercator projection map. [ 1 ] The name is derived from Old French or Spanish respectively: "rumb" or "rumbo", a line on the chart which intersects all meridians at the same angle. [ 1 ] On a plane surface this would be the shortest distance between two points.
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).
The distance between two points in physical space is the length of a straight line between them, which is the shortest possible path. This is the usual meaning of distance in classical physics, including Newtonian mechanics. Straight-line distance is formalized mathematically as the Euclidean distance in two-and three-dimensional space.
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