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The four quadrants of a Cartesian coordinate system. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. The axes themselves are, in general, not part of the respective quadrants.
A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system [8]) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning ...
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
The sum of the entries along the main diagonal (the trace), plus one, equals 4 − 4(x 2 + y 2 + z 2), which is 4w 2. Thus we can write the trace itself as 2 w 2 + 2 w 2 − 1 ; and from the previous version of the matrix we see that the diagonal entries themselves have the same form: 2 x 2 + 2 w 2 − 1 , 2 y 2 + 2 w 2 − 1 , and 2 z 2 + 2 w ...
Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple. In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates.
As an example, the distance squared between the points (0,0,0,0) and (1,1,1,0) is 3 in both the Euclidean and Minkowskian 4-spaces, while the distance squared between (0,0,0,0) and (1,1,1,1) is 4 in Euclidean space and 2 in Minkowski space; increasing b 4 decreases the metric distance. This leads to many of the well-known apparent "paradoxes ...
The 5D rotation group SO(5) and all higher rotation groups contain subgroups isomorphic to O(4). Like SO(4), all even-dimensional rotation groups contain isoclinic rotations. But unlike SO(4), in SO(6) and all higher even-dimensional rotation groups any two isoclinic rotations through the same angle are conjugate.
Galactic quadrants (NGQ/SGQ, 1–4) indicated vis-a-vis Galactic poles (NGP/SGP), Galactic Plane (containing galactic centre) and Galactic Coordinates Plane (containing our sun) Constellations grouped in galactic quadrants (N/S, 1–4) - this image depicts as a hollow concave face Constellations grouped in galactic quadrants (N/S, 1–4) - their approx divisions vis-a-vis celestial quadrants ...