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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.
A straight line on the Mercator map at angle α to the meridians is a rhumb line. When α = π / 2 or 3 π / 2 the rhumb corresponds to one of the parallels; only one, the equator, is a great circle. When α = 0 or π it corresponds to a meridian great circle (if continued around the Earth).
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.
All points along a given azimuth will project along a straight line from the center, and the angle θ that the line subtends from the vertical is the azimuth angle. The distance from the center point to another projected point ρ is the arc length along a great circle between them on the globe.
Has straight parallels symmetrically placed about the equator; Has parallels constrained to where they fall when light shines through the globe onto the cylinder, with the light source someplace along the line formed by the intersection of the prime meridian with the equator, and the center of the sphere.
The 1878 edition of The Globe Encyclopaedia of Universal Information describes a loxodrome line as: [3] Loxodrom′ic Line is a curve which cuts every member of a system of lines of curvature of a given surface at the same angle. A ship sailing towards the same point of the compass describes such a line which cuts all the meridians at the same ...
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 ...
Since the meridians have converged a little the line will bend up a little generating a rhumb which describes a spiral on the sphere. The latitude and longitude of selected points on the rhumb could have then been transferred to the chart and the latitude scale of the chart adjusted so that the rhumb becomes a straight line.
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