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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 ...
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
The formula states that if γ is a parametrization of a great circle then (()) (()) =, where ρ(P) is the distance from a point P on the great circle to the z-axis, and ψ(P) is the angle between the great circle and the meridian through the point P.
Construct the great circle from A that is normal to the side BC at the point D. Use Napier's rules to solve the triangle ABD: use c and B to find the sides AD and BD and the angle ∠BAD. Then use Napier's rules to solve the triangle ACD: that is use AD and b to find the side DC and the angles C and ∠DAC. The angle A and side a follow by ...
The disk bounded by a great circle is called a great disk: it is the intersection of a ball and a plane passing through its center. In higher dimensions, the great circles on the n-sphere are the intersection of the n-sphere with 2-planes that pass through the origin in the Euclidean space R n + 1. Half of a great circle may be called a great ...
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 ...
The great thing about trifles is they wow twice. First, it's hard to miss the towering layers of spice cake, whipped pumpkin and cream cheese filling, crunchy gingersnap cookies, and whipped cream.
They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such as great-circle distance. The first (direct) method computes the location of a point that is a given distance and azimuth (direction) from another point. The second (inverse) method ...
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