Euler and the geometric growth of populations (1748–1761)

  • Nicolas Bacaër


Euler wrote on several occasions on population dynamics. In his 1748 treatise, Introduction to Analysis of the Infinite, the chapter dealing with the exponential function contained four examples on the exponential growth of a population. In 1760 he published an article combining this exponential growth with an age structure for the population. This work is a forerunner of the theory of “stable” populations, which was developed in the twentieth century and plays an important role in demography. In 1761 Euler also helped Süssmilch with the second edition of his treatise on demography. He worked out an interesting model, which is a kind of variant of Fibonacci’s sequence, but did not publish his detailed analysis.


Life Table Geometric Progression Fibonacci Sequence Integral Calculus Decimal Logarithm 
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Further reading

  1. 1.
    Euler, L.: Recherches générales sur la mortalité et la multiplication du genre humain. Hist. Acad. R. Sci. B.-Lett. Berl. 16, 144–164 (1760/1767). Google Scholar
  2. 2.
    Euler, L.: Sur la multiplication du genre humain. In: Leonhardi Euleri Opera omnia, Ser. I, vol. 7, pp. 545–552. Teubner, Leipzig (1923) Google Scholar
  3. 3.
    Euler, L.: Introductio in analysin infinitorum, Tomus primus. Bousquet, Lausanne (1748). Also in: Leonhardi Euleri Opera omnia, Ser. I, vol. 8, Teubner, Leizig (1922). English translation, Springer, New York (1988).
  4. 4.
    Fellmann, E.A.: Leonhard Euler. Birkhäuser, Basel (2007) MATHGoogle Scholar
  5. 5.
    Gumbel, E.J.: Eine Darstellung statistischer Reihen durch Euler. Jahresber. dtsch. Math. Ver. 25, 251–264 (1917). Google Scholar
  6. 6.
    Reimer, K.F.: Johann Peter Süssmilch, seine Abstammung und Biographie. Arch. soz. Hyg. Demogr. 7, 20–28 (1932) Google Scholar
  7. 7.
    Rohrbasser, J.M.: Johann Peter Süssmilch. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 72–76. Springer, New York (2001) Google Scholar
  8. 8.
    Süssmilch, J.P.: Die göttliche Ordnung in den Veränderungen des menschlichen Geschlechts aus der Geburt, dem Tode und der Fortpflanzung desselben. Berlin (1761).
  9. 9.
    Warusfel, A.: Euler, les mathématiques et la vie. Vuibert, Paris (2009) Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRD (Institut de Recherche pour le Développement)BondyFrance

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