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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.
Given a point P on the unit circle, draw a line from P to the point N = (0, 1) (the north pole). The point P ′ where the line intersects the x -axis is the stereographic projection of P . Inversely, starting with a point P ′ on the x -axis, and drawing a line from P ′ to N , the inverse stereographic projection is the point P where the ...
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). 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 ...
When the rays are lines of sight from an observer to two points in space, it is known as the apparent distance or apparent separation. Angular distance appears in mathematics (in particular geometry and trigonometry ) and all natural sciences (e.g., kinematics , astronomy , and geophysics ).
Points with equal power, isolines of (), are circles concentric to circle . Steiner used the power of a point for proofs of several statements on circles, for example: Determination of a circle, that intersects four circles by the same angle. [2] Solving the Problem of Apollonius
If the outcome values are (seemingly) perfectly determined by the predictor (e.g., y = 0 when x ≤ 2) then the condition "complete separation" is said to occur. If instead there is some overlap (e.g., y = 0 when x < 2, but y has observed values of 0 and 1 when x = 2) then "quasi-complete
One approach to cross ratio interprets it as a homography that takes three designated points to 0, 1, and ∞. Under restrictions having to do with inverses, it is possible to generate such a mapping with ring operations in the projective line over a ring. The cross ratio of four points is the evaluation of this homography at the fourth point.
In coordinate geometry, the Section formula is a formula used to find the ratio in which a line segment is divided by a point internally or externally. [1] It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc. [2] [3] [4] [5]