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Journal for Geometry and Graphics 10 (2006), No. 1, 063--071
Copyright Heldermann Verlag 2006

On a Possible Constructive Geometrical Derivation of Mercator's Conformal Cylindrical Map Projection Based on Some Historical Facts

Branislav Popkonstantinovic
Dept. of Machine Theory and Mechanisms, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia

Aleksandar Cucakovic
Dept. Descriptive Geometry, Faculty of Civil Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Servia

In modern cartography, Mercator's conformal cylindrical map projection is mathematically described by equations which involve logarithmic and trigonometric functions. It is evident that calculus and differential geometry are necessary for the derivation of these equations. The very fact that Mercator's map was published in 1569, long before logarithms and calculus were invented, confirms that Mercator created his famous map projection somehow directly -- by some simple and plain geometrical constructions. This paper exposes one possible constructive graphical method by which the direct geometrical synthesis of Mercator's conformal cylindrical map projection can be accomplished. We believe that the original inventive process used by Gerhard Kremer Mercator in creation of his famous world map was at least similar or compatible to the method exposed in this paper.

Keywords: Cartography, Mercator, conformal, loxodrome, stereographic projection.

MSC: 51N05; 53-03, 01A40

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