Why is extrapolation called extrapolation?

Question

In interpolation we find a polynomial that passes through the points $x_0<x_1<\cdots<x_n$ and estimates $x\in[x_0,x_n]$, so we say the interpolation polynomial interpolates the points. But as far as I know extrapolation doesn't extrapolate but increase the accuracy of a formula that has the error term $$ M = N(h) + K_1 h + K_2 h^2 + K_3 h^3 +\cdots $$ where the $N(h)$ is our formula and $M$ is the exact solution and $K_i$'s are some constants. Why is extrapolation called extrapolation in spite of there seems be no connection between the method and its name?

Answer 1

Because you aren't familiar with enough uses of "extrapolate"? See

• http://en.wikipedia.org/wiki/Extrapolation
• http://www.thefreedictionary.com/extrapolate

Interpolate: to infer values between given values

Extrapolate: to infer values outside the range of given values