Interpolation \In*ter`po*la"tion\, n. [L. interpolatio an
   alteration made here and there: cf. F. interpolation.]
   1. The act of introducing or inserting anything, especially
      that which is spurious or foreign.
      [1913 Webster]

   2. That which is introduced or inserted, especially something
      foreign or spurious.
      [1913 Webster]

            Bentley wrote a letter . . . . upon the scriptural
            glosses in our present copies of Hesychius, which he
            considered interpolations from a later hand. --De
                                                  Quincey.
      [1913 Webster]

   3. (Math.) The method or operation of finding from a few
      given terms of a series, as of numbers or observations,
      other intermediate terms in conformity with the law of the
      series.
      [1913 Webster]

	

	interpolation
    n 1: a message (spoken or written) that is introduced or
         inserted; "with the help of his friend's interpolations his
         story was eventually told"; "with many insertions in the
         margins" [syn: interpolation, insertion]
    2: (mathematics) calculation of the value of a function between
       the values already known
    3: the action of interjecting or interposing an action or remark
       that interrupts [syn: interjection, interposition,
       interpolation, interpellation]

	

	77 Moby Thesaurus words for "interpolation":
   addition, affix, allonge, appendix, approximation, aside, cadenza,
   coda, codicil, commentary, differentiation, division, embedment,
   enclitic, entrance, envoi, epilogue, episode, equation, evolution,
   extempore, extrapolation, flourish, graft, grafting, hot lick,
   impaction, impactment, implantation, impromptu, improvisation,
   infix, infixion, infusion, injection, inoculation, insert,
   insertion, insinuation, integration, intercalation, interjection,
   interlineation, interlocution, introduction, intromission,
   inversion, involution, lick, marginalia, multiplication, notation,
   note, obiter dictum, parenthesis, penetration, perfusion,
   postscript, practice, prefix, proclitic, proportion, reduction,
   remark, rider, riff, scholia, side remark, subtraction, suffix,
   tail, tessellation, tossing-in, transformation, transplant,
   transplantation, vamp

	

	extrapolation
extrapolate
interpolation

    A mathematical procedure which
   estimates values of a function for certain desired inputs
   given values for known inputs.

   If the desired input is outside the range of the known values
   this is called extrapolation, if it is inside then it is
   called interpolation.

   The method works by fitting a "curve" (i.e. a function) to two
   or more given points and then applying this function to the
   required input.  Example uses are calculating trigonometric
   functions from tables and audio waveform sythesis.

   The simplest form of interpolation is where a function, f(x),
   is estimated by drawing a straight line ("linear
   interpolation") between the nearest given points on either
   side of the required input value:

   	f(x) ~ f(x1) + (f(x2) - f(x1))(x-x1)/(x2 - x1)

   There are many variations using more than two points or higher
   degree polynomial functions.  The technique can also be
   extended to functions of more than one input.

   (2007-06-29)