Definition of Interpolate

Date: 10/27/95 at 5:56:19
From: Anonymous
Subject: Interpolate

Could you please define interpolate and give me an example?

I have looked in "The Book of Answers" and it defines interpolate:

Determination of an intermediary value of a function by means of a
sequence of known values of the function.

Please help!

                                              Mark

Date: 11/7/95 at 13:0:8
From: Doctor Steve
Subject: Re: Interpolate

Hi Mark,

In more informal language, interpolate means to guess at what happens 
between two values you already know.  If I gave you a sequence of 
numbers and asked you to fill in the missing number you would be 
interpolating:

0,1,2, ... ,6

But, since you don't know the rule I'm using, you're only making a 
guess.  It often happens, for instance in economics, that you know the 
data but you don't know what the formula is that explains why something 
happened that way or what the next value will be. I might calculate the 
national debt every three months and that might enable me to make a good 
guess what it was the two months in between.

Usually when you make an interpolation you are making an assumption 
that the behavior you're looking at is predictable or that the amount of 
error in your guess can't be enough to prevent you from using it.

In the sequence I gave above you might interpolate a value of 4 and have 
some confidence that you wouldn't be more than one off.  

So interpolation relies on some assumptions about the behavior of 
whatever you're investigating that make it possible for you to guess 
values for which you only have information about what happened 
"before" and "after".

- Doctor Steve,  The Geometry Forum