Definition of Polar coordinates. Meaning of Polar coordinates. Synonyms of Polar coordinates

Here you will find one or more explanations in English for the word Polar coordinates. Also in the bottom left of the page several parts of wikipedia pages related to the word Polar coordinates and, of course, Polar coordinates synonyms and on the right images related to the word Polar coordinates.

Definition of Polar coordinates

Polar coordinates
Note: Co["o]rdinates are of several kinds, consisting in some of the different cases, of the following elements, namely: (a) (Geom. of Two Dimensions) The abscissa and ordinate of any point, taken together; as the abscissa PY and ordinate PX of the point P (Fig. 2, referred to the co["o]rdinate axes AY and AX. (b) Any radius vector PA (Fig. 1), together with its angle of inclination to a fixed line, APX, by which any point A in the same plane is referred to that fixed line, and a fixed point in it, called the pole, P. (c) (Geom. of Three Dimensions) Any three lines, or distances, PB, PC, PD (Fig. 3), taken parallel to three co["o]rdinate axes, AX, AY, AZ, and measured from the corresponding co["o]rdinate fixed planes, YAZ, XAZ, XAY, to any point in space, P, whose position is thereby determined with respect to these planes and axes. (d) A radius vector, the angle which it makes with a fixed plane, and the angle which its projection on the plane makes with a fixed line line in the plane, by which means any point in space at the free extremity of the radius vector is referred to that fixed plane and fixed line, and a fixed point in that line, the pole of the radius vector. Cartesian co["o]rdinates. See under Cartesian. Geographical co["o]rdinates, the latitude and longitude of a place, by which its relative situation on the globe is known. The height of the above the sea level constitutes a third co["o]rdinate. Polar co["o]rdinates, co["o]rdinates made up of a radius vector and its angle of inclination to another line, or a line and plane; as those defined in (b) and (d) above. Rectangular co["o]rdinates, co["o]rdinates the axes of which intersect at right angles. Rectilinear co["o]rdinates, co["o]rdinates made up of right lines. Those defined in (a) and (c) above are called also Cartesian co["o]rdinates. Trigonometrical or Spherical co["o]rdinates, elements of reference, by means of which the position of a point on the surface of a sphere may be determined with respect to two great circles of the sphere. Trilinear co["o]rdinates, co["o]rdinates of a point in a plane, consisting of the three ratios which the three distances of the point from three fixed lines have one to another.

Meaning of Polar coordinates from wikipedia

- as its three coordinates. These are the radial distance r along the line connecting the point to a fixed point called the origin; the polar angle θ between...
- mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are the point's...
- In mathematics, log-polar coordinates (or logarithmic polar coordinates) is a coordinate system in two dimensions, where a point is identified by two...
- meaning as in Cartesian coordinates is added to the r and θ polar coordinates giving a triple (r, θ, z). Spherical coordinates take this a step further...
- radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional polar coordinate system in the plane through the...
- semi-axes are given by the denominators in the canonical form. In polar coordinates, a conic section with one focus at the origin and, if any, the other...
- (x,y)} be the standard Cartesian coordinates, and ( r , θ ) {\displaystyle (r,\theta )} the standard polar coordinates. x = r cos ⁡ θ y = r sin ⁡ θ ∂ (...
- point at right angles. Geodesic polar coordinates are obtained by combining the exponential map with polar coordinates on tangent vectors at the base point...
- the transform to polar coordinates (r dr dθ is the standard measure on the plane, expressed in polar coordinates Wikibooks:Calculus/Polar Integration#Generalization)...
- the introduction of a system of spherical coordinates, known as polar coordinates. These are the coordinates on M obtained by introducing the standard...