center of a curve

center \cen"ter\ (s[e^]n"t[~e]r), n. [F. centre, fr. L. centrum,
   fr. Gr. ke`ntron any sharp point, the point round which a
   circle is described, fr. kentei^n to prick, goad.]
   1. A point equally distant from the extremities of a line,
      figure, or body, or from all parts of the circumference of
      a circle; the middle point or place.
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   2. The middle or central portion of anything.
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   3. A principal or important point of concentration; the
      nucleus around which things are gathered or to which they
      tend; an object of attention, action, or force; as, a
      center of attaction.
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   4. The earth. [Obs.] --Shak.
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   5. Those members of a legislative assembly (as in France) who
      support the existing government. They sit in the middle of
      the legislative chamber, opposite the presiding officer,
      between the conservatives or monarchists, who sit on the
      right of the speaker, and the radicals or advanced
      republicans who occupy the seats on his left, See {Right},
      and {Left}.
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   6. (Arch.) A temporary structure upon which the materials of
      a vault or arch are supported in position until the work
      becomes self-supporting.
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   7. (Mech.)
      (a) One of the two conical steel pins, in a lathe, etc.,
          upon which the work is held, and about which it
          revolves.
      (b) A conical recess, or indentation, in the end of a
          shaft or other work, to receive the point of a center,
          on which the work can turn, as in a lathe.
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   Note: In a lathe the

   {live center} is in the spindle of the head stock; the

   {dead center} is on the tail stock.

   {Planer centers} are stocks carrying centers, when the object
      to be planed must be turned on its axis.
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   {Center of an army}, the body or troops occupying the place
      in the line between the wings.

   {Center of a curve} or {Center of a surface} (Geom.)
      (a) A point such that every line drawn through the point
          and terminated by the curve or surface is bisected at
          the point.
      (b) The fixed point of reference in polar coordinates. See
          {Coordinates}.

   {Center of curvature of a curve} (Geom.), the center of that
      circle which has at any given point of the curve closer
      contact with the curve than has any other circle whatever.
      See {Circle}.

   {Center of a fleet}, the division or column between the van
      and rear, or between the weather division and the lee.

   {Center of gravity} (Mech.), that point of a body about which
      all its parts can be balanced, or which being supported,
      the whole body will remain at rest, though acted upon by
      gravity.

   {Center of gyration} (Mech.), that point in a rotating body
      at which the whole mass might be concentrated
      (theoretically) without altering the resistance of the
      intertia of the body to angular acceleration or
      retardation.

   {Center of inertia} (Mech.), the center of gravity of a body
      or system of bodies.

   {Center of motion}, the point which remains at rest, while
      all the other parts of a body move round it.

   {Center of oscillation}, the point at which, if the whole
      matter of a suspended body were collected, the time of
      oscillation would be the same as it is in the actual form
      and state of the body.

   {Center of percussion}, that point in a body moving about a
      fixed axis at which it may strike an obstacle without
      communicating a shock to the axis.

   {Center of pressure} (Hydros.), that point in a surface
      pressed by a fluid, at which, if a force equal to the
      whole pressure and in the same line be applied in a
      contrary direction, it will balance or counteract the
      whole pressure of the fluid.
      [1913 Webster] Center