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A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
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.
With the compasses set at the difference of latitude between the places in question, the number of degrees contained therein being noted, the compasses are run from one place to the other by such number of revolutions as the distance between the two places permits; the distance which may remain and which will be less than the span set on the ...
Given a unit sphere, a "triangle" on the surface of the sphere is defined by the great circles connecting three points u, v, and w on the sphere. If the lengths of these three sides are a (from u to v), b (from u to w), and c (from v to w), and the angle of the corner opposite c is C, then the law of haversines states: [10]
This shows that a great circle is, with respect to distance measurement on the surface of the sphere, a circle: the locus of points all at a specific distance from a center. Each point is associated with a unique great circle, called the polar circle of the point, which is the great circle on the plane through the centre of the sphere and ...
Proposition 1 states that two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line drawn through the centres of the spheres is at right angles to each of the circles in which the surface of the cylinder, or ...
The Bianco map (1436). The Bianco World Map is a map created by Andrea Bianco, a 15th-century Venetian sailor and cartographer who resided on Chios.This map was a large piece of a nautical atlas including ten pages made of vellum (each measuring 26 × 38 cm).
Detail of East and Southeast Asia in Ptolemy's world map. Gulf of the Ganges ( Bay of Bengal ) left, Southeast Asian peninsula in the center, South China Sea right, with "Sinae" (China). The Ptolemy world map is a map of the world known to Greco-Roman societies in the 2nd century.