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Pafnuty Chebyshev and Geography

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Notes

  1. I also treat this briefly in a forthcoming book that will be published on the occasion of the 2022 ICM in Saint Petersburg [21].

  2. In spherical geometry, the segments are arcs of great circles.

  3. The reader interested in the history of Greek geography and cartography may want to skim the Geographies of both Strabo [25] and Ptolemy [23], two major geographical treatises from antiquity that survive (and exist in several editions).

  4. The book Science in Russian Culture by Alexander Vucinich [26] gives a good account of the very ambitious geographical program of the Russian monarch and, in particular, of the ways in which he managed to attract outstanding Western scientists for the realization of his plans (see, in particular, pp. 59–62).

  5. Pierre Louis Moreau de Maupertuis, famous French mathematician and geographer, was president of the Prussian Academy of Sciences, where Euler worked during his stay in Berlin.

  6. Joseph-Nicolas Delisle, celebrated French astronomer and geographer, was among the first professors hired at the foundation of the Saint Petersburg Academy of Sciences, where Euler spent the largest part of his career. Delisle worked in Saint Petersburg for twenty-two years, and for five years (1735–1740), Euler assisted him.

  7. Translations from the French are mine.

  8. One of the important geographical discoveries of the eighteenth century was that the Earth has the shape of an ellipsoid of revolution (a surface obtained by the rotation of an ellipse around an axis) rather than that of a sphere. This confirmed a theory developed by Newton in the seventeenth century that predicted that the Earth is not spherical but is instead flattened at the poles.

  9. The details and consequences of Lagrange’s work are fascinating. For English translations of his two memoirs, together with extensive historical and mathematical commentaries, see the forthcoming volume [3]. We mention incidentally that the notion of the Schwarzian derivative appears for the first time in one of these memoirs; see the report in [20].

  10. This memoir is reproduced in [4, t. I, pp. 111–143]. We note that Chebyshev sometimes referred to mechanical linkages as parallelograms, because of a famous linkage used by James Watt in his steam engine, which has the form of a parallelogram and which Chebyshev studied extensively.

  11. The verst is an old measure of distances used in Russia, equal to 1066.8 meters.

  12. Euler’s article [10] is in part concerned with area-preserving geographical maps (see §22 ff.).

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Acknowledgments

I would like to thank Karen Parshall, Patrick Popescu-Pampu, and the anonymous referee for several comments and corrections.

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  1. Université de Strasbourg and CNRS, 7 rue René Descartes, 67084, Strasbourg Cedex, France

    Athanase Papadopoulos

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Papadopoulos, A. Pafnuty Chebyshev and Geography. Math Intelligencer 44, 79–86 (2022). https://doi.org/10.1007/s00283-021-10114-5

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