Geodesic
Flattening the Earth: Mathematical and historical aspects of Mercator projection
Antiquitates Mathematicae, Tome 13 (2019), pp. 235-255.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

When projecting the globe on a plane surface it is not possible to satisfy more than one of the following three criteria: conformity of angles, equidistance and equivalence of areas. Mercator's solution for the use in navigation was to use a cylindrical projection with increasing distances between parallels so that the rhumb lines became straight lines. We present the derivation of the meridional stretching in this projection that requires a unique stretching factor, conformal map that preserves angles. It has been recognized that mathematical methods were used to solve the problems of cartography. We emphasize the fact that the cartographers were using applied mathematics and, in particular, numerical methods. In the literature there exist conflicting tables of results attributed to Wright. We investigate the original Wright’s paper (1599) to find out that his values are in historical nautical miles and not in degrees of latitude. We also present a brief survey of the works of Dutch cartographers of the XVI century.
DOI : 10.14708/am.v13i1.6530
Classification : 91D20, 53A15
Mots-clés : plane surface, conformity of angles, equidistance, equivalence of areas 
@article{ANM_2019_13_a8,
     author = {Wlodek Proskurowski},
     title = {Flattening the {Earth:} {Mathematical} and historical aspects of {Mercator} projection},
     journal = {Antiquitates Mathematicae},
     pages = { 235--255},
     publisher = {mathdoc},
     volume = {13},
     year = {2019},
     doi = {10.14708/am.v13i1.6530},
     url = {https://geodesic-test.mathdoc.fr/articles/10.14708/am.v13i1.6530/}
}
TY  - JOUR
AU  - Wlodek Proskurowski
TI  - Flattening the Earth: Mathematical and historical aspects of Mercator projection
JO  - Antiquitates Mathematicae
PY  - 2019
SP  -  235
EP  - 255
VL  - 13
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.14708/am.v13i1.6530/
DO  - 10.14708/am.v13i1.6530
ID  - ANM_2019_13_a8
ER  - 
%0 Journal Article
%A Wlodek Proskurowski
%T Flattening the Earth: Mathematical and historical aspects of Mercator projection
%J Antiquitates Mathematicae
%D 2019
%P  235-255
%V 13
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.14708/am.v13i1.6530/
%R 10.14708/am.v13i1.6530
%F ANM_2019_13_a8
Wlodek Proskurowski. Flattening the Earth: Mathematical and historical aspects of Mercator projection. Antiquitates Mathematicae, Tome 13 (2019), pp.  235-255. doi : 10.14708/am.v13i1.6530. https://geodesic-test.mathdoc.fr/articles/10.14708/am.v13i1.6530/

Cité par Sources :