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====Definition via Cartesian coordinates==== In terms of [[Cartesian coordinates]] ''x'', ''y'' ascribed to every point of the plane, a line is the set of p

====Definition via Cartesian coordinates==== In terms of [[Cartesian coordinates]] ''x'', ''y'', ''z'' ascribed to every point of the space, a plane is the

====Definition via Cartesian coordinates==== In terms of [[Cartesian coordinates]] ''x'', ''y'', ''z'' ascribed to every point of the space, a plane is the

Its equation in Cartesian coordinates is

...ilon;₁₂₃ = ε_xyz = 1 in [[Cartesian coordinates]].

...lications is the ''z-y&prime;-z&prime;'' convention. Attach a system of [[Cartesian coordinates|Cartesian coordinate]] axes to the body that is to be rotated (the coordina ...es. The first and second column contain by definition expressions for the Cartesian coordinates of <math>\hat{e}_{x'''}</math> and <math>\hat{e}_{y''}</math>, respectively

Let ''x'', ''y'', ''z'' be [[Cartesian coordinates]] of a vector <math>\scriptstyle \vec\mathbf{r}</math> in <math>\scriptsty ...and &phi; of <math>\scriptstyle \vec\mathbf{r}</math> are related to its Cartesian coordinates by

...gian is defined in terms of [[generalized coordinates|generalized]] (non-[[Cartesian coordinates|Cartesian]]) coordinates ''q'' and generalized velocities (time derivatives

# The procedure just sketched applies only to quantities in [[Cartesian coordinates]]. For other coordinate systems, such as [[spherical polar coordinate]]s th ...Because the metric tensor is represented by the unit (identity) matrix in Cartesian coordinates, the latter fact is easily overlooked. One could go through the transforma

The following expresses normalized spherical harmonics in Cartesian coordinates (Condon-Shortley phase):

...solid harmonics]] for closed expressions of regular harmonics expressed in Cartesian coordinates. If one expresses regular solid harmonics in spherical polar coordinates, t

In cartesian coordinates of dimension ''n>3'' it has to be defined in a different way because it is

...oordinates <math>r</math> and <math>\theta</math>, related to conventional Cartesian coordinates by <math>x=r\cos\theta</math> and <math>y=r\sin\theta</math>. In polar coo

...imensional [[integral]]s over [[generalized coordinates]], i.e, over non-[[Cartesian coordinates]].

Let us write '''r''' for the electronic coordinates and '''R''' for the [[Cartesian coordinates|Cartesian]] nuclear coordinates of a molecule. The highly symmetric configu ...s over the ''N''_nuc nuclei of the molecule and &alpha; over the Cartesian coordinates of '''R'''_''A''. The elements of the matrix '''L''' can be dete

The [[Jacobian]] (Jacobi determinant) of this transformation from [[Cartesian coordinates]] to [[spherical polar coordinates]] is where &nabla;² is the [[Laplace operator]] in three-dimensional [[Cartesian coordinates]] and ''r'' is the length of '''''r'''''.

...tant is a [[second rank tensor]], which is represented with respect to a [[Cartesian coordinates|Cartesian coordinate system]] by a 3 &times; 3 matrix

...se two vectors in component form we implicitly assumed the presence of a [[Cartesian coordinates|Cartesian coordinate system]]. The polarizability '''&alpha;''' is express

...ons of relativity.<ref name=Moller>For example, Møller states: "Instead of Cartesian coordinates we can obviously just as well employ general curvilinear coordinates for th where ''x'', ''y'', ''z'', ''etc.'' are the ''n'' Cartesian coordinates of the point. Given these functions, coordinate surfaces are defined by th

...onditions arise in a natural way from a harmonic analysis in mass-weighted Cartesian coordinates. ...ximation to the nuclear motion problem, described in 3''N'' mass-weighted Cartesian coordinates, became standard in [[quantum chemistry]], since the days (1980s-1990s) tha