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Some properties related to Mercator projection. (English) Zbl 1004.53001

The author discusses the Mercator projection and gives two remarkable properties of it. First, comparing the Mercator projection with the stereographic one he gets as the relation between these two projections a mapping \(F\) which can now be represented by the complex function \(F(z) = \exp z\). Second, considering the tractrix curve he can show a relationship between Mercator projection and the tractrix. Namely, for a point on the globe with latitude \(\psi\), its vertical position on a Mercator map is identical to the position of the person moving with respect to the tractrix at the time that the angle of the stretched string has become \(\psi\) from the horizontal. To prove these two properties, the author uses the known results in an appropriate form to get the corresponding equations.

MSC:

53A04 Curves in Euclidean and related spaces
53B10 Projective connections
30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)
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