In mathematics, interpolation is the process of estimating unknown values that fall between known data points. It involves constructing a smooth function—often a polynomial, spline, or other continuous curve—that passes through the given points and can be used to predict intermediate values. Interpolation assumes the trend between known values continues in a predictable way and is commonly used when data is incomplete or irregularly spaced.
The term interpolation comes from the Latin inter, meaning “between,” and polire, meaning “to smooth or polish.” This reflects the idea of “filling in between” known values using a smooth curve. Understanding this root can help distinguish interpolation from extrapolation, which estimates values outside the known range.
For example, a weather station might record temperatures every three hours, but a meteorologist may need to estimate the temperature at a specific time in between recordings. By applying interpolation—such as using a spline function—she can generate a smooth curve through the known temperatures and estimate the temperature at the desired time with reasonable accuracy.
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