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Polar coordinates
(gcide) | 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.
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2. Of or pertaining to the magnetic pole, or to the point to
which the magnetic needle is directed.
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3. (Geom.) Pertaining to, reckoned from, or having a common
radiating point; as, polar coordinates.
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Polar axis, that axis of an astronomical instrument, as an
equatorial, which is parallel to the earths axis.
Polar bear (Zool.), a large bear (Ursus maritimus syn.
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, Polar cell, or Polar 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 spermatozoon; 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 coordinates. See under 3d Coordinate.
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 Polar equation of a surface,
an equation which expresses the relation between the polar
coordinates 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 (Zool.), a large hare of Arctic America ({Lepus
arcticus}), which turns pure white in winter. It is
probably a variety of the common European hare ({Lepus
timidus}).
Polar lights, the aurora borealis or australis.
Polar opposition, or Polaric opposition or {Polar
contrast} or Polaric 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 (Zool.), the right whale, or bowhead. See
Whale.
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Polar coordinates
(gcide) | Coordinate \Co*["o]r"di*nate\, n.
1. A thing of the same rank with another thing; one two or
more persons or things of equal rank, authority, or
importance.
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It has neither coordinate nor analogon; it is
absolutely one. --Coleridge.
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2. pl. (Math.) Lines, or other elements of reference, by
means of which the position of any point, as of a curve,
is defined with respect to certain fixed lines, or planes,
called coordinate axes and coordinate planes. See
Abscissa.
Note: Coordinates 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
coordinate 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 coordinate axes, AX, AY, AZ, and measured from
the corresponding coordinate 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.
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Cartesian coordinates. See under Cartesian.
Geographical coordinates, 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 coordinate.
Polar coordinates, coordinates 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 coordinates, coordinates the axes of which
intersect at right angles.
Rectilinear coordinates, coordinates made up of right
lines. Those defined in
(a) and
(c) above are called also Cartesian coordinates.
Trigonometrical coordinates or Spherical coordinates,
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 coordinates, coordinates 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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