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The value of parallel coordinates is that certain geometrical properties in high dimensions transform into easily seen 2D patterns. For example, a set of points on a line in n-space transforms to a set of polylines in parallel coordinates all intersecting at n − 1 points.
The distance between two parallel lines in the plane is the minimum distance between any two points. ... to get the coordinates of the intersection points. The ...
The star plot can be used to answer the following questions: [5] Which observations are most similar, i.e., are there clusters of observations? (Radar charts are used to examine the relative values for a single data point (e.g., point 3 is large for variables 2 and 4, small for variables 1, 3, 5, and 6) and to locate similar points or ...
For two points, A and B, separated by 10° of longitude on the parallel at 60° the distance along the parallel is approximately 0.5 km greater than the great circle distance. (The distance AB along the parallel is (a cos φ) λ. The length of the chord AB is 2(a cos φ) sin λ / 2 .
For an xyz-Cartesian coordinate system in three dimensions, suppose that a second Cartesian coordinate system is introduced, with axes x', y' and z' so located that the x' axis is parallel to the x axis and h units from it, the y' axis is parallel to the y axis and k units from it, and the z' axis is parallel to the z axis and l units from it.
This is a fundamental result in absolute geometry because its proof does not depend upon the parallel postulate. In several high school treatments of geometry, the term "exterior angle theorem" has been applied to a different result, [ 1 ] namely the portion of Proposition 1.32 which states that the measure of an exterior angle of a triangle is ...
These lines are parallel to the desired tangent lines, because the situation corresponds to shrinking both circles C 1 and C 2 by a constant amount, r 2, which shrinks C 2 to a point. Two radial lines may be drawn from the center O 1 through the tangent points on C 3; these intersect C 1 at the desired tangent points. The desired external ...
At noon of January 1st 2000 AD, the mean value of the tilt was 23° 26′ 21.406″ (according to IAU 2006, theory P03), the corresponding value being 23° 26′ 10.633" at noon of January 1st 2023 AD. The main long-term cycle causes the axial tilt to fluctuate between about 22.1° and 24.5° with a period of 41,000 years.