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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).
Their nonhomogeneous coordinates on the infinity line of the plane z=0 are , , 0, / . (Exchanging I 1 {\displaystyle I_{1}} and I 2 {\displaystyle I_{2}} changes the cross ratio into its inverse, so the formula for ϕ {\displaystyle \phi } gives the same result.)
The spread between two lines is defined in rational geometry as the square of the sine of the angle between the lines. As the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.
For a plane, the two angles are called its strike (angle) and its dip (angle). A strike line is the intersection of a horizontal plane with the observed planar feature (and therefore a horizontal line), and the strike angle is the bearing of this line (that is, relative to geographic north or from magnetic north). The dip is the angle between a ...
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; Construction of the Malfatti circles: [3] For a given triangle determine three circles, which touch each other and two sides of the triangle ...
The sine of the angles between subspaces satisfy the triangle inequality in terms of majorization and thus can be used to define a distance on the set of all subspaces turning the set into a metric space. [6] For example, the sine of the largest angle is known as a gap between subspaces. [9]
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