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Sophie Germain pp 73–93Cite as

Germain and Her Biharmonic Equation

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Abstract

What prompted Sophie Germain to enter the prize competition to derive a theory for vibrating surfaces? Did she see the contest as a source of mathematical knowledge and sought to advance her own intellectual development?

Toute équation est une égalité. Que sont les propriétés d’une courbe? une égalité entre les produits, au les combinaisons de certaines lignes droites renfermées et bornées par cette courbe. [“Every equation is an equality. What are the properties of a curve? an equality between the products, to the combinations of certain straight lines enclosed and bounded by this curve.”]

—SOPHIE GERMAIN

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Notes

  1. 1.

    Grey (2006), p. 6.

  2. 2.

    Ibid., p. 10.

  3. 3.

    Germain (1821), p. v.

  4. 4.

    Stupuy (1896), p. 291.

  5. 5.

    Germain (1821), p. vi.

  6. 6.

    Stupuy (1896), p. 298.

  7. 7.

    Ibid.

  8. 8.

    Love (1906), p. 6.

  9. 9.

    Ibid., p. 300.

  10. 10.

    Euler (1761).

  11. 11.

    Euler (1760).

  12. 12.

    Stupuy (1896), p. 300.

  13. 13.

    Note in the Annales de Chimie, Vol. 39, 1828, p. 149, part of Navier’s remarks regarding an article published by Poisson.

  14. 14.

    Letter from Legendre to Germain dated 4 Dec 1811. In Stupuy (1896), p. 302.

  15. 15.

    Institut de France. Procès-verbaux. Tome II, p. 169.

  16. 16.

    Euler (1760).

  17. 17.

    Germain (1821), p. vi.

  18. 18.

    Lodder (2003).

  19. 19.

    Stupuy (1896), p. 305.

  20. 20.

    Poisson (1814).

  21. 21.

    Adèle d’Osmond, Comtesse de Boigne, Memoirs of the Comtesse de Boigne, Volume 1, 1781–1815, Helen Marx Books; 2 edition (April 2000), p. 123. She was a writer known for her memoirs describing life under the July Monarchy.

  22. 22.

    Poisson (1814).

  23. 23.

    Institut de France. Procès-verbaux. Tome V, p. 595.

  24. 24.

    A graduate of the École, Jean Jacques Emmanuel Sédillot (1777–1832) was an astronomer at the Bureau des Longitudes, where he assisted Delambre and Laplace in their research.

  25. 25.

    Bugge (2003), p. 89.

  26. 26.

    Journal des Débats, Mardi 9 janvier 1816, p. 2.

  27. 27.

    J.-Noël Hallé (1754–1822) was a medical doctor, perhaps a friend of Sophie Germain’s family. He was a member of the Institut de France since 1795.

  28. 28.

    Stupuy (1896), pp. 307–308.

  29. 29.

    Ibid., p. 310.

  30. 30.

    Bulletin des Sciences par la Société Philomatique de Paris (1818).

  31. 31.

    Germain (1821), p. v.

  32. 32.

    Ibid.

  33. 33.

    Ibid., p. vi.

  34. 34.

    Ibid., pp. viii–ix.

  35. 35.

    Stupuy (1896), p. 314. Legendre’s wrote: «vous proposez votre opinion de la manière la plus modeste et, si l’on avait quelque chose à vous reprocher, ce serait les compliments dont en quelque sorte vous accablez le géomètre dont vous combattez l’opinion. Puisse-t-il répondre dignement à cet assaut de civilité; c’est ce que je désire plus que je n’espère.»

  36. 36.

    Stupuy (1896), pp. 315–317. French text: “qu’il le mérite un écrit aussi remarquable, que bien peu d’hommes peuvent lire, et qu’une seule femme pouvait faire.”

  37. 37.

    Correspondance de Sophie GERMAIN. p. 27.

  38. 38.

    Germain (1824).

  39. 39.

    Effets dus à l’épaisseur plus ou moins grande des plaques élastiques.

  40. 40.

    Stupuy (1896), pp. 320–322.

  41. 41.

    Jean Léopold Nicolas Frédéric or Georges Cuvier (1769–1832) was a French naturalist and zoologist. Cuvier was Permanent Secretary of Physical Sciences of the Academy since 1803.

  42. 42.

    Institut de France. Procès-verbaux. Tome VIII, p. 35.

  43. 43.

    Timoshenko (1983).

  44. 44.

    Germain (1821).

  45. 45.

    Germain (1880), p. 16.

  46. 46.

    Germain (1880).

  47. 47.

    Correspondance de Sophie GERMAIN. The same letters reproduced by Stupuy (pp. 326–328) give the year as 1823 instead of 1826.

  48. 48.

    For the modern derivation of the biharmonic equation governing elastic thin plates, we consulted Selvadurai (2000). He refers to the biharmonic equation governing flexure of thin plates as the “Germain-Poisson-Kirchhoff thin plate equation.”

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  1. University of Texas at Arlington, Arlington, TX, USA

    Dora Musielak

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Musielak, D. (2020). Germain and Her Biharmonic Equation. In: Sophie Germain. Springer Biographies. Springer, Cham. https://doi.org/10.1007/978-3-030-38375-6_6

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