1. The problem is to understand the meaning of "interpolate" in mathematics. 2. Interpolation is a method used to estimate unknown values that fall between known data points. 3. The basic idea is to construct a function or curve that passes through the known points and then use it to find intermediate values. 4. A common formula for linear interpolation between two points $(x_0, y_0)$ and $(x_1, y_1)$ is: $$y = y_0 + \frac{(y_1 - y_0)}{(x_1 - x_0)} (x - x_0)$$ 5. This formula calculates the value $y$ at any $x$ between $x_0$ and $x_1$ by assuming the change between points is linear. 6. Interpolation is useful in many fields such as data analysis, computer graphics, and numerical methods to estimate values where direct measurement is not available. 7. In simple terms, interpolation helps you "fill in the gaps" between known data points.