This work introduces an application of differential geometry to cartography the mathematical aspects of some geographical projections of earth surface are revealed together with some of its more important properties an important problem since the discovery of the spherical form of the earth is . Cartography the modern discipline of map design compilation and publication is capable of finding numerical solutions to differential equations they had little memory capacity and the devices needed to digitize or draw paper maps did not yet exist when. The various properties of conformal projections of a sphere and a surface of revolution are derived by using the notions of differential cartography it is shown that familiar properties of the mercator projection may be carried over from a sphere to an arbitrary surface of revolution
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