Interpolation in mathematics refers to a method of constructing new data points within the range of known or existing data points. This is often done by using a polynomial function or curve to approximate the relationship between the existing data points, allowing values to be approximated or estimated at points in between. Interpolation is commonly used in fields such as engineering, finance, geometry and statistics to estimate missing data or to generate smooth curves that pass through a set of points. The accuracy of the interpolation generally improves as the number of known data points increases.

*Interpolation in geometry refers to the process of finding a point or a set of points that lie within a given geometric shape, such that these points satisfy certain conditions, such as being equidistant from two given vertices or having a specific ratio of distances from the vertices. This process involves constructing new points between known or existing points within the shape, usually by using some form of linear or polynomial interpolation. The resulting interpolated points can be useful for various applications in geometry, such as creating smooth curves or surfaces, or generating new shapes based on existing ones.