The scale of a map is usually defined as the ratio of a single unit of distance on the map to the corresponding distance on the ground. Although this is true for accurate large scale maps, covering a restricted area, it is not true for map projections[1] of the curved surface of the Earth to the plane. For such projections we must use the concept of a point scale which may vary with position and direction. In the study of point scale it is convenient to define the projection formulae in such a way that the scale is unity, or nearly so, on some lines of the resulting map. Clearly such a map projection must be comparable to the size of the Earth and, in order to represent it on a small sheet of paper, it must be reduced. The ratio defined on the printed map projection is then re-interpreted as the representative fraction, or in short, the RF. Point scale and RF are defined below with examples drawn from simple projections. Tissot's Indicatrix is used to illustrate the variation of point scale in the examples.
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