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Polar coordinates

Source : Webster's Revised Unabridged Dictionary (1913)

Polar \Po"lar\, a. [Cf. F. polaire. See {Pole} of the earth.]
   1. Of or pertaining to one of the poles of the earth, or of a
      sphere; situated near, or proceeding from, one of the
      poles; as, polar regions; polar seas; polar winds.

   2. Of or pertaining to the magnetic pole, or to the point to
      which the magnetic needle is directed.

   3. (Geom.) Pertaining to, reckoned from, or having a common
      radiating point; as, polar co["o]rdinates.

   {Polar axis}, that axis of an astronomical instrument, as an
      equatorial, which is parallel to the earths axis.

   {Polar bear} (Zo["o]l.), a large bear ({Ursus, or Thalarctos,
      maritimus}) inhabiting the arctic regions. It sometimes
      measures nearly nine feet in length and weighs 1,600
      pounds. It is partially amphibious, very powerful, and the
      most carnivorous of all the bears. The fur is white,
      tinged with yellow. Called also {White bear}. See {Bear}.
      

   {Polar body}, {cell}, or {globule} (Biol.), a minute cell
      which separates by karyokinesis from the ovum during its
      maturation. In the maturation of ordinary ova two polar
      bodies are formed, but in parthogenetic ova only one. The
      first polar body formed is usually larger than the second
      one, and often divides into two after its separation from
      the ovum. Each of the polar bodies removes maternal
      chromatin from the ovum to make room for the chromatin of
      the fertilizing spermatozo["o]n; but their functions are
      not fully understood.

   {Polar circles} (Astron. & Geog.), two circles, each at a
      distance from a pole of the earth equal to the obliquity
      of the ecliptic, or about 23[deg] 28', the northern called
      the arctic circle, and the southern the antarctic circle.
      

   {Polar clock}, a tube, containing a polarizing apparatus,
      turning on an axis parallel to that of the earth, and
      indicating the hour of the day on an hour circle, by being
      turned toward the plane of maximum polarization of the
      light of the sky, which is always 90[deg] from the sun.

   {Polar co["o]rdinates}. See under 3d {Co["o]rdinate}.

   {Polar dial}, a dial whose plane is parallel to a great
      circle passing through the poles of the earth. --Math.
      Dict.

   {Polar distance}, the angular distance of any point on a
      sphere from one of its poles, particularly of a heavenly
      body from the north pole of the heavens.

   {Polar equation of a line} or {surface}, an equation which
      expresses the relation between the polar co["o]rdinates of
      every point of the line or surface.

   {Polar forces} (Physics), forces that are developed and act
      in pairs, with opposite tendencies or properties in the
      two elements, as magnetism, electricity, etc.

   {Polar hare} (Zo["o]l.), a large hare of Arctic America
      ({Lepus arcticus}), which turns pure white in winter. It
      is probably a variety of the common European hare ({L.
      timidus}).

   {Polar lights}, the aurora borealis or australis.

   {Polar}, or {Polaric}, {opposition} or {contrast} (Logic), an
      opposition or contrast made by the existence of two
      opposite conceptions which are the extremes in a species,
      as white and black in colors; hence, as great an
      opposition or contrast as possible.

   {Polar projection}. See under {Projection}.

   {Polar spherical triangle} (Spherics), a spherical triangle
      whose three angular points are poles of the sides of a
      given triangle. See 4th {Pole}, 2.

   {Polar whale} (Zo["o]l.), the right whale, or bowhead. See
      {Whale}.



   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.
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