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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.
Distance from the tangent point on the map is proportional to surface distance on the Earth (; for the case where the tangent point is the North Pole, see the flag of the United Nations) Lambert azimuthal equal-area. Distance from the tangent point on the map is proportional to straight-line distance through the Earth: r(d) = c sin d / 2R
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. 200 BC: Stereographic: Azimuthal Conformal Hipparchos* Map is infinite in extent with outer hemisphere inflating severely, so it is often used as two hemispheres.
The accuracy of distance calculations using this approximation become increasingly inaccurate as: The separation between the points becomes greater; The shortest distance between two points in plane is a Cartesian straight line. The Pythagorean theorem is used to calculate the distance
With the circumference of the Earth being approximately 40,000 km (24,855 mi), the maximum distance that can be displayed on an azimuthal equidistant projection map is half the circumference, or about 20,000 km (12,427 mi). For distances less than 10,000 km (6,214 mi) distortions are minimal.
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.
Transverse Mercator projection. A transverse Mercator projection. The transverse Mercator map projection ( TM, TMP) 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 Universal Transverse Mercator.
The Mason–Dixon line, also called the Mason and Dixon line or Mason's and Dixon's line, is a demarcation line separating four U.S. states, constituting parts of the borders of Pennsylvania, Maryland, Delaware, and West Virginia (part of Virginia until 1863). It was surveyed between 1763 and 1767 by Charles Mason and Jeremiah Dixon as part of ...
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