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The coordinates of a point p are obtained by drawing a line through p perpendicular to each coordinate axis, and reading the points where these lines meet the axes as three numbers of these number lines.
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coordinates and point
In the f-plane the coordinates of the corresponding point are Af.
A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation.
In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates.
This system can also be used for three-dimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates ( x, y, z ).
On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ.
The two integers a and b are coprime if and only if the point with coordinates ( a, b ) in a Cartesian coordinate system is " visible " from the origin ( 0, 0 ), in the sense that there is no point with integer coordinates between the origin and ( a, b ).
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.
The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.
One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes ( or, equivalently, by its perpendicular projection onto three mutually perpendicular lines ).
In general, one can specify a point in a space of any dimension n by use of n Cartesian coordinates, the signed distances from n mutually perpendicular hyperplanes.
The black dot shows the point with coordinates X = 2, Y = 3, and Z = 4, or ( 2, 3, 4 ).
Alternatively, the coordinates of a point p can also be taken as the ( signed ) distances from p to the three planes defined by the three axes.
The three surfaces intersect at the point P ( shown as a black sphere ) with the Cartesian coordinates ( 1, − 1, 1 ).
Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers ( a, b ) to the Cartesian coordinates of every point in the set.
That is, if the original coordinates of a point are ( x, y ), after the translation they will be
To rotate a figure counterclockwise around the origin by some angle is equivalent to replacing every point with coordinates ( x, y ) by the point with coordinates ( x < nowiki >'</ nowiki >, y < nowiki >'</ nowiki >), where
If ( x, y ) are the Cartesian coordinates of a point, then (− x, y ) are the coordinates of its reflection across the second coordinate axis ( the Y axis ), as if that line were a mirror.
coordinates and p
The distance is to be taken with the + or − sign, depending on which of the two half-spaces separated by that plane contains p. The y and z coordinates can be obtained in the same way from the ( x, z ) and ( x, y ) planes, respectively.
The field is defined by p in the prime case and the pair of m and f An additional speed-up is possible if mixed coordinates are used.
In terms of Cartesian coordinates p, the distance from the minor axis, and z, the distance above the equatorial plane, the equation of the ellipse is
The space-time coordinates of an event, as measured by each observer in their inertial reference frame ( in standard configuration ) are shown in the speech bubbles .< p > Top: frame F ' moves at velocity v along the x-axis of frame F .< p > Bottom: frame F moves at velocity − v along the x '- axis of frame F '.
A product of more than one non-zero rings always has zero divisors: if x is an element of the product all of whose coordinates are zero except p < sub > i </ sub >( x ), and y is an element of the product with all coordinates zero except p < sub > j </ sub >( y ) ( with i ≠ j ), then xy
It can be alternatively stated as: if the span of n vectors has dimension p, then p of these vectors span the space and there is a set of p coordinates on which they are linearly independent.
Introduce spherical coordinates so that p coincides with the north pole.
In Cartesian coordinates, if p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >,..., p < sub > n </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >,..., q < sub > n </ sub >) are two points in Euclidean n-space, then the distance from p to q, or from q to p is given by:
Alternatively, it follows from () that if the polar coordinates of the point p are ( r < sub > 1 </ sub >, θ < sub > 1 </ sub >) and those of q are ( r < sub > 2 </ sub >, θ < sub > 2 </ sub >), then the distance between the points is
These coordinates are just as canonical as x, p, but the orbits are now lines of constant J instead of nested ovoids in x-p space.
coordinates and are
The data presented are derived almost entirely from X-ray diffraction measurements and include atomic coordinates, cell dimensions, and atomic and ionic radii.
Time coordinates on the TAI scales are conventionally specified using traditional means of specifying days, carried over from non-uniform time standards based on the rotation of the Earth.
Although digital setting circles can be used to display a telescope's RA and Dec coordinates, they are not simply a digital read-out of what can be seen on the telescope's analog setting circles.
These are graphs of ψ ( x, y, z ) functions which depend on the coordinates of one electron.
Alternatively, atomic orbitals refer to functions that depend on the coordinates of one electron ( i. e. orbitals ) but are used as starting points for approximating wave functions that depend on the simultaneous coordinates of all the electrons in an atom or molecule.
The coordinate systems chosen for atomic orbitals are usually spherical coordinates ( r, θ, φ ) in atoms and cartesians ( x, y, z ) in poly-atomic molecules.
In terms of components, these three equations for the conservation of momentum in cylindrical coordinates are
Unlike McCaffrey's black crystal transceivers, Le Guin's ansibles are not mated pairs: it is possible for an ansible's coordinates to be set to any known location of a receiving ansible.
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.
The coordinates of the points on the curve are of the form ( x, 1 / x ) where x is a number other than 0.
The British Virgin Islands are located in the Caribbean, between the Caribbean Sea and the North Atlantic Ocean, east of Puerto Rico. Its geographic coordinates are.
Its geographical coordinates are.
Informally basis vectors are like " building blocks of a vector ", they are added together to make a vector, and the coordinates are the number of basis vectors in each direction.
The coordinates of the vector are equal to the projections of the vector ( yellow ) onto the x-component basis vector ( green )-using the dot product ( a special case of an inner product, see below ).
respectively, where e < sub > x </ sub >, e < sub > y </ sub >, e < sub > z </ sub > denotes the cartesian basis vectors ( all are orthogonal unit vectors ) and A < sub > x </ sub >, A < sub > y </ sub >, A < sub > z </ sub > are the corresponding coordinates, in the x, y, z directions.
though the coordinates and vectors are now all complex-valued.
The coordinates of the vector are equal to the projections of the vector ( yellow ) onto the x-component basis vector ( green )-using the inner product ( see below ).
Bessel functions are also known as cylinder functions or cylindrical harmonics because they are found in the solution to Laplace's equation in cylindrical coordinates.
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