Datums tend to be of two types. One of them specifies a mathematical surface (the "ellipsoid") to approximate the earth's surface and adds information to situate that surface on the earth, such as the difference between the surface's center and the earth's center and how the surface is rotated (and perhaps rescaled) with respect to a standard earth datum. (Notice that up to seven independent numbers are involved in this description: three for the displacement, three for the rotation, and one more for the rescaling.) Another type of datum consists of a grid or network of points covering an area of interest (such as a country or continent) and specific assignments of latitude, longitude (and even altitude) at each of those points. Coordinates of other points are determined by interpolation. The North American Datum of 1927 (NAD 27) exemplifies the latter type.
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