curvilinear$503207$ - traduzione in greco
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curvilinear$503207$ - traduzione in greco

COORDINATE SYSTEM WHOSE DIRECTIONS VARY IN SPACE
Curvilinear; Parametric coordinates; Parametric coordinate; Parametric coord; Lamé coefficients; Curvilinear coordinate system; Curvalinear coordinate systems; Orthogonal curvilinear coordinates; Curvilinear coordinate; Lamé coefficients (curvilinear coordinates)
  • <span style="color:black">'''Cartesian'''</span>]] (left) coordinates in two-dimensional space
  • Fig. 1 - Coordinate surfaces, coordinate lines, and coordinate axes of general curvilinear coordinates.
  • Fig. 3 – Transformation of local covariant basis in the case of general curvilinear coordinates
  • Fig. 2 - Coordinate surfaces, coordinate lines, and coordinate axes of spherical coordinates. '''Surfaces:''' ''r'' - spheres, θ - cones, φ - half-planes; '''Lines:''' ''r'' - straight beams, θ - vertical semicircles, φ - horizontal circles;

'''Axes:''' ''r'' - straight beams, θ - tangents to vertical semicircles, φ - tangents to horizontal circles
  • isbn=0-7167-0344-0}}</ref>

curvilinear      
adj. καμπυλόγραμμος
obtuse angle         
  • Angles ''A'' and ''B'' are adjacent.
  • ''r''}} radians}}.
  • The angles <var>a</var> and <var>b</var> are ''supplementary'' angles.
  • The ''complementary'' angles <var>a</var> and <var>b</var> (<var>b</var> is the ''complement'' of <var>a</var>, and <var>a</var> is the complement of <var>b</var>).
  • The angle between the two curves at ''P'' is defined as the angle between the tangents <var>A</var> and <var>B</var> at <var>P</var>.
  • Internal and external angles.
  • Coterminal Angles
  • Sum of two ''explementary'' angles is a ''complete'' angle.
  • Hatch marks]] are used here to show angle equality.
SOMETHING THAT IS FORMED WHEN TWO RAYS MEET AT A SINGLE OR SAME POINT
Angular measurement; Angular measure; Plane angle measure; Angle measure; Supplementary angles; Complementary angles; Straight angle; Acute angle; Obtuse angle; Angle (geometry); Positive angle; Negative angle; Angulate; Complementary angle; Vertical angles; Acute Angle; Reflex angle; Complementary Angles; Adjacent Angles; Adjacent angles; Theta angle; Vertical angle; Supplementary angle; Supplemental angle; Coterminal angles; Vertical Angles; Bow tie angle; ∠; ∡; ∢; Bow Tie angle; Plane angle; Oblique angle; Complamentary angle; Types of angles; Opposite angles; Suplementary angles; Ajacent angels; Vertical (angles); Vertically opposite angles; Vertically opposite angle; Angle of rotation; Angles of rotation; Vert. opp. ∠s; Vert. opp. ∠; Adj. ∠s on st. line; Complementary ∠; Supplementary ∠; Supplementary ∠s; Supp. ∠s; Complementary ∠s; Supp. ∠; Nonadjacent angle; Adjacent angle pairs; Adjacent angle pair; Anggulo; Linear pair of angles; ⦛; ⦞; ⦟; ⦢; ⦣; ⦦; ⦧; ⦨; ⦩; ⦪; ⦫; ⦬; ⦭; ⦮; ⦯; Adjacent angle; ⦤; ⦥; Corner angle; Planar angle; Planar angles; Intersecting angle pairs; Co-angle; Explementary angle; Explementary angles; Conjugate angles; Rotation angle; Angular unit; Draft:Unit of angle; Angle addition postulate; Angular units; Units of angle measure; Perigon angle; Measuring angles; Measurement of angles; User:Kat098643234567/sandbox/angles; Multiples of π; Factors of π; Factor of π; MULπ; MOπ; Multiples of pi; Factors of pi; Factor of pi; Fraction of pi; Fraction of π; Curvilinear angle; Mixed angle; Right-angled; Oblique-angled; Complement angle
αμβλεία γωνία
vertical angle         
  • Angles ''A'' and ''B'' are adjacent.
  • ''r''}} radians}}.
  • The angles <var>a</var> and <var>b</var> are ''supplementary'' angles.
  • The ''complementary'' angles <var>a</var> and <var>b</var> (<var>b</var> is the ''complement'' of <var>a</var>, and <var>a</var> is the complement of <var>b</var>).
  • The angle between the two curves at ''P'' is defined as the angle between the tangents <var>A</var> and <var>B</var> at <var>P</var>.
  • Internal and external angles.
  • Coterminal Angles
  • Sum of two ''explementary'' angles is a ''complete'' angle.
  • Hatch marks]] are used here to show angle equality.
SOMETHING THAT IS FORMED WHEN TWO RAYS MEET AT A SINGLE OR SAME POINT
Angular measurement; Angular measure; Plane angle measure; Angle measure; Supplementary angles; Complementary angles; Straight angle; Acute angle; Obtuse angle; Angle (geometry); Positive angle; Negative angle; Angulate; Complementary angle; Vertical angles; Acute Angle; Reflex angle; Complementary Angles; Adjacent Angles; Adjacent angles; Theta angle; Vertical angle; Supplementary angle; Supplemental angle; Coterminal angles; Vertical Angles; Bow tie angle; ∠; ∡; ∢; Bow Tie angle; Plane angle; Oblique angle; Complamentary angle; Types of angles; Opposite angles; Suplementary angles; Ajacent angels; Vertical (angles); Vertically opposite angles; Vertically opposite angle; Angle of rotation; Angles of rotation; Vert. opp. ∠s; Vert. opp. ∠; Adj. ∠s on st. line; Complementary ∠; Supplementary ∠; Supplementary ∠s; Supp. ∠s; Complementary ∠s; Supp. ∠; Nonadjacent angle; Adjacent angle pairs; Adjacent angle pair; Anggulo; Linear pair of angles; ⦛; ⦞; ⦟; ⦢; ⦣; ⦦; ⦧; ⦨; ⦩; ⦪; ⦫; ⦬; ⦭; ⦮; ⦯; Adjacent angle; ⦤; ⦥; Corner angle; Planar angle; Planar angles; Intersecting angle pairs; Co-angle; Explementary angle; Explementary angles; Conjugate angles; Rotation angle; Angular unit; Draft:Unit of angle; Angle addition postulate; Angular units; Units of angle measure; Perigon angle; Measuring angles; Measurement of angles; User:Kat098643234567/sandbox/angles; Multiples of π; Factors of π; Factor of π; MULπ; MOπ; Multiples of pi; Factors of pi; Factor of pi; Fraction of pi; Fraction of π; Curvilinear angle; Mixed angle; Right-angled; Oblique-angled; Complement angle
καθετή γωνία

Definizione

Curvilinear
·adj Consisting of, or bounded by, curved lines; as, a curvilinear figure.

Wikipedia

Curvilinear coordinates

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.

Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space (R3) are cylindrical and spherical coordinates. A Cartesian coordinate surface in this space is a coordinate plane; for example z = 0 defines the x-y plane. In the same space, the coordinate surface r = 1 in spherical coordinates is the surface of a unit sphere, which is curved. The formalism of curvilinear coordinates provides a unified and general description of the standard coordinate systems.

Curvilinear coordinates are often used to define the location or distribution of physical quantities which may be, for example, scalars, vectors, or tensors. Mathematical expressions involving these quantities in vector calculus and tensor analysis (such as the gradient, divergence, curl, and Laplacian) can be transformed from one coordinate system to another, according to transformation rules for scalars, vectors, and tensors. Such expressions then become valid for any curvilinear coordinate system.

A curvilinear coordinate system may be simpler to use than the Cartesian coordinate system for some applications. The motion of particles under the influence of central forces is usually easier to solve in spherical coordinates than in Cartesian coordinates; this is true of many physical problems with spherical symmetry defined in R3. Equations with boundary conditions that follow coordinate surfaces for a particular curvilinear coordinate system may be easier to solve in that system. While one might describe the motion of a particle in a rectangular box using Cartesian coordinates, it's easier to describe the motion in a sphere with spherical coordinates. Spherical coordinates are the most common curvilinear coordinate systems and are used in Earth sciences, cartography, quantum mechanics, relativity, and engineering.