One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts
Apstrakt
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 di®erential 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.
Ključne reči:
Stereographic / Mercator / Map / Loxodrome / Conformal / CartographyIzvor:
Journal for Geometry and Graphics, 2006, 10, 1, 63-71Izdavač:
- Heldermann Verlag
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Popkonstantinović, Branislav AU - Cučaković, A. PY - 2006 UR - https://machinery.mas.bg.ac.rs/handle/123456789/561 AB - 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 di®erential 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. PB - Heldermann Verlag T2 - Journal for Geometry and Graphics T1 - One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts EP - 71 IS - 1 SP - 63 VL - 10 UR - https://hdl.handle.net/21.15107/rcub_machinery_561 ER -
@article{ author = "Popkonstantinović, Branislav and Cučaković, A.", year = "2006", abstract = "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 di®erential 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.", publisher = "Heldermann Verlag", journal = "Journal for Geometry and Graphics", title = "One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts", pages = "71-63", number = "1", volume = "10", url = "https://hdl.handle.net/21.15107/rcub_machinery_561" }
Popkonstantinović, B.,& Cučaković, A.. (2006). One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts. in Journal for Geometry and Graphics Heldermann Verlag., 10(1), 63-71. https://hdl.handle.net/21.15107/rcub_machinery_561
Popkonstantinović B, Cučaković A. One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts. in Journal for Geometry and Graphics. 2006;10(1):63-71. https://hdl.handle.net/21.15107/rcub_machinery_561 .
Popkonstantinović, Branislav, Cučaković, A., "One a possible constructive geometrical derivation of Mercator's conformal cylindrical map projection based on some historical facts" in Journal for Geometry and Graphics, 10, no. 1 (2006):63-71, https://hdl.handle.net/21.15107/rcub_machinery_561 .