Advertisement

The Mathematical Intelligencer

, Volume 30, Issue 2, pp 48–56 | Cite as

In Search of the “Birthday” of Elliptic Functions

  • Adrian RiceEmail author
Article

Conclusion

Is it possible to answer the questionWhat is the “birthday” of elliptic functions? Yes, but far from uniquely. But does the overabundance of possible answers occasioned by the inherent näivety of the question mean that such lines of inquiry are pointless for the historian? Can questions regarding the temporal origins of mathematical areas and the research to which they lead ever be useful or instructive?

Keywords

Elliptic Function Theta Function Mathematical Intelligencer Elliptic Integral Addition Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Abel, N. H. (1827) Recherches sur les fonctions élliptiques.Journal fűr die reine und angewandte Mathematik 2, 101–181. In Oeuvrescomplètes, vol. 1, 141–221.CrossRefzbMATHGoogle Scholar
  2. [2]
    Abeles, F. (2005) Lewis Carroll’s formal logic.History and Philosophy of Logic 26, 33–46.CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    Abeles, F. (2007) Lewis Carroll’s visual logic.History and Philosophy of Logic 28, 1–19.CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    Ayoub, R. (1984) The lemniscate and Fagnano’s contributions to elliptic integrals.Archive for History of Exact Sciences 29, 131 -149.zbMATHMathSciNetGoogle Scholar
  5. [5]
    Bartley, W. W., ed. (1977).Lewis Carroll’s Symbolic Logic. Hassocks, Harvester Press.Google Scholar
  6. [6]
    Bernoulli, J. (1694) Curvatura laminae elasticae.Acta Eruditorum 13, 262–276. InOpera, vol. 1, 576–600.Google Scholar
  7. [7]
    Cooke, R. (1994) Elliptic integrals and functions. In I. Grattan-Guinness, ed.,Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, London, Routledge, vol. 1, 529–539.Google Scholar
  8. [8]
    Cooke, R. (2005) C.G.J. Jacobi’s book on elliptic functions (1829). In I. Grattan-Guinness, ed.,Landmark Writings in Western Mathematics 1640–1940, Amsterdam, Elsevier, 412–430.Google Scholar
  9. [9]
    D’Antonio, L. A. (2007) Euler and elliptic integrals. In R. E. Bradley, L. A. D’Antonio, and C. E. Sandifer, eds.,Euler at 300: An Appreciation, Washington DC, Mathematical Association of America, 119–129.Google Scholar
  10. [10]
    Euler, L. (1761a) De integratione aequationis differentialis\({{m dx} \mathord{\left/ {\vphantom {{m dx} {\sqrt {1 - x^4 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - x^4 } }} = {{n dy} \mathord{\left/ {\vphantom {{n dy} {\sqrt {1 - y^4 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - y^4 } }}\).Novi Commentarii Academiae Petropolitanae 6, 37–57. InOpera Omnia, ser. 1, vol. 20, 58–79.Google Scholar
  11. [11]
    Euler, L (1761b) Observationes de comparatione arcuum curvarum irrectificabilium.Novi Commentarii Academiae Petropolitanae 6, 58–84. InOpera Omnia, ser. 1, Vol. 20, 80–107.Google Scholar
  12. [12]
    Euler, L. (1912–1913)Leonhardi Euleri Opera Omnia, ser. 1, vols. 20–21, Leipzig and Berlin, B. G. Teubner.Google Scholar
  13. [13]
    Fagnano, G. C. (1718) Metodo per misurare la lemniscata. InOpere matematiche, vol. 2, 293–313.Google Scholar
  14. [14]
    Fagnano, G. C. (1750).Produzioni matematiche, 2 vols., Pesaro, Gavelliana.Google Scholar
  15. [15]
    Fricke, R. (1913) Elliptische Funktionen. InEncyklopadie dermathematischen Wissenschaften, vol. 2, pt. 2, article II B 3, Leipzig, B. G. Teubner, 177–348.Google Scholar
  16. [16]
    Gauss, C. F. (1863–1929) Werke, 12 vols., Göttingen, Königlichen Gesellschaft der Wissenschaften.Google Scholar
  17. [17]
    Gauss, C. F. (1876a) Elegantiores integralis\({{\smallint dx} \mathord{\left/ {\vphantom {{\smallint dx} {\sqrt {1 - x^4 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - x^4 } }}\) proprieties. InWerke, vol. 3, 404–412.Google Scholar
  18. [18]
    Gauss, C. F. (1876b) De curva lemniscata. InWerke, vol. 3, 413–432.Google Scholar
  19. [19]
    Houzel, C. (1978) Fonctions elliptiques et integrals abéliennes. In J. Dieudonné, ed.,éAbrégéd’histoiredesmathématiques 1700–1900, vol. 2, Paris, Hermann, 1–113.Google Scholar
  20. [20]
    Jacobi, C. G. J. (1829)Fundamenta nova theoriae functionum ellipticarum. Königsberg, Borntraeger. In Gesammelte Werke, vol. 1, 49–239.Google Scholar
  21. [21]
    Legendre, A.-M. (1811–1817)Exercices de calcul intégral, 3 vols., Paris, Courcier.Google Scholar
  22. [22]
    Legendre, A.-M. (1825–1828)Traité des fonctions elliptiques et des integrals Eulériennes, 3 vols., Paris, Huzard-Courcier.Google Scholar
  23. [23]
    Mahoney, M. S. (1984) On differential calculuses.Isis 75, 366–372.CrossRefGoogle Scholar
  24. [24]
    Moktefi, A. (2007) Lewis Carroll’s logic. In D. M. Gabbay and J. Woods, eds.,British Logic in the Nineteenth Century, Vol. 4 of theHandbook of the History of Logic, Elsevier, Amsterdam.Google Scholar
  25. [25]
    Poincaré, H. (1909) L’avenirdes mathématiques. InAttidellVCongresso Internazionale dei Matematici, vol. 1, Rome, Academia dei Lincei, 167–182.Google Scholar
  26. [26]
    Stäckel, P., and Ahrens, W. (1908)Der Briefwechsel zwischen C. G. J. Jacobi und P. H. von Fuss űber die Herausgabe der Werke Leonhard Eulers. Leipzig.Google Scholar
  27. [27]
    Watson, G. N. (1933) The marquis and the land-agent: A tale of the eighteenth century.The Mathematical Gazette 17, 5–17.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Department of MathematicsRandolph-Macon CollegeAshlandUSA

Personalised recommendations