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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.
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.
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.
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.
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 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 ...
This straight line diagram illustrates the stops on the Piccadilly Line, part of London's Underground. This is a more accurately rendered map of the Piccadilly Line, showing curvature and the relative distance between stops. It illustrates why straight-line maps are more useful when only the sequence of stops is relevant.
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 ...