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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.
The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in (3, −10.5). Thus the origin has coordinates (0, 0), and the points on the positive half-axes, one unit away from the origin, have coordinates (1, 0) and (0, 1).
Quadray coordinates, also known as caltrop, tetray or Chakovian coordinates (named for David Chako [1]), were developed by Darrel Jarmusch (in 1981 [2]) and others, as another take on simplicial coordinates, a coordinate system using a simplex or tetrahedron as its basis polyhedron.
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
There are 2 dihedral subgroups: Dih 2, Dih 1, and 3 cyclic subgroups: Z 4, Z 2, and Z 1. A square is a special case of many lower symmetry quadrilaterals: A rectangle with two adjacent equal sides; A quadrilateral with four equal sides and four right angles; A parallelogram with one right angle and two adjacent equal sides; A rhombus with a ...
The slope field can be defined for the following type of differential equations ′ = (,), which can be interpreted geometrically as giving the slope of the tangent to the graph of the differential equation's solution (integral curve) at each point (x, y) as a function of the point coordinates.
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
Kruskal–Szekeres diagram, illustrated for 2GM=1. The quadrants are the black hole interior (II), the white hole interior (IV) and the two exterior regions (I and III). The dotted 45° lines, which separate these four regions, are the event horizons. The darker hyperbolas which bound the top and bottom of the diagram are the physical ...