Flattening the Earth: Mathematical and historical aspects of Mercator projection

Wlodek Proskurowski. "Flattening the Earth: Mathematical and historical aspects of Mercator projection." Antiquitates Mathematicae 13 (2019): null. <http://eudml.org/doc/295119>.

@article{WlodekProskurowski2019,
abstract = {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.},
author = {Wlodek Proskurowski},
journal = {Antiquitates Mathematicae},
keywords = {plane surface; conformity of angles, equidistance; equivalence of areas},
language = {eng},
pages = {null},
title = {Flattening the Earth: Mathematical and historical aspects of Mercator projection},
url = {http://eudml.org/doc/295119},
volume = {13},
year = {2019},
}

TY - JOUR
AU - Wlodek Proskurowski
TI - Flattening the Earth: Mathematical and historical aspects of Mercator projection
JO - Antiquitates Mathematicae
PY - 2019
VL - 13
SP - null
AB - 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.
LA - eng
KW - plane surface; conformity of angles, equidistance; equivalence of areas
UR - http://eudml.org/doc/295119
ER -