Henri Brocard

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Pierre René Jean Baptiste Henri Brocard (born May 12, 1845 in Vignot , Canton Commercy , † January 16, 1922 in Bar-le-Duc ) was a French mathematician and officer.

Brocard attended high schools (lyceums) in Marseille and Strasbourg and studied at the École polytechnique from 1865 to 1867 . He then served as an engineer officer and meteorologist in the French army. In the 1870s war he took part in the Battle of Sedan , where he was captured. Later he was stationed in Algiers and from 1884 worked again in France as a meteorologist in Montpellier , Grenoble and Bar-le-Duc. In 1910 he retired as a lieutenant colonel and lived alone and in seclusion in Bar-le-Duc, where he was the librarian of the Society for Literature, Arts and Sciences. He declined the proposed presidency of the Society. In retirement he also devoted himself to astronomical observations.

Immediately after it was founded in 1873, he joined the French Mathematical Society and had been a member of the Association Française pour l'Avancement des Sciences (Afas) since 1875. Brocard has regularly attended the International Congress of Mathematicians since Zurich in 1897.

Brocard is known for investigations into the geometry of triangles, among other things Brocard points are named after him, about which he published. Brocard points were introduced in Germany in 1817 by August Leopold Crelle , but this was forgotten. Berkhan and Wilhelm Franz Meyer date the resurgence of interest in triangular geometry in the second half of the 19th century in a task by Brocard in 1875 and in a lecture by Émile Lemoine before Afas in 1873. Brocard circles, Brocard diameters, Brocard angle (the uniquely determined angle in the construction of the Brocard point).

He is also known for various conjectures and problems in number theory. The Brocard's problem (Brocard 1876, 1885) is to find n numbers for m natural with a number. Only the solutions n = 4,5,7 are known and it is assumed that there are no more ( Paul Erdős ). The Brocardsche guess is the Legendre conjecture related: The time between the squares of consecutive primes at least four primes. Brocard's problem and conjecture remain unsolved to this day.

Handwritten entry at the Portuguese Academy of Sciences

Brocard was an officer in the Legion of Honor.

Fonts

  • Etudes d'un nouveau cercle du plan du triangle. Assoc. Français pour l'Avancement des Sciences, Congrés d'Alger, Volume 10, 1881, pp. 138-159.
  • Notices sur les titres et travaux scientifique. Bar le Duc 1895.
  • Notes de bibliographie des courbes géométriques. Bar le Duc, 1897, 1899, 2 volumes. The book was only published in around 50 copies and contains information on around 1000 curves.
  • with T. Lemoyne: Courbes géométriques remarquables. 2 volumes, Paris, Volume 1, 1920, 1967 (new edition), Volume 2, 1967.
  • Continuation with E. Vigarié of the historical-bibliographical report on triangular geometry by E. Lemoine, Reports (Compte rendu) der Afas, 1885, 1889, 1895, 1906.

literature

  • Laura Guggenbuhl: Henri Brocard and the geometry of the triangle. In: Mathematical Gazette. Volume 37, 1953, No. 322, p. 241 (and Proc. Internat. Congress Mathem. 1954).
  • Laura Guggenbuhl: Henri Brocard. Article in Dictionary of Scientific Biography , Online.
  • A. Emmerich: Brocard's angles of the triangle. A historical study. Program of the Realgymnasium Mülheim an der Ruhr. 1889.
  • A. Emmerich: The Brocardschen formations and their relations to the related strange points and circles of the triangle. Berlin, Reimer, 1891.

Individual evidence

  1. ↑ Newer triangle geometry. Encyclopedia of Mathematical Sciences , III AB 10, p. 1180.
  2. ↑ Nouv. Annales Mathem. (2), 1875, 14
  3. ↑ Compte rendu Afas 2, 1873, 90.
  4. ^ Math World, Brocard Circle
  5. ↑ Brocard's problem Mathworld
  6. ↑ Brocard's Conjecture, Mathworld
personal data
SURNAME Brocard, Henri
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH May 12, 1845
PLACE OF BIRTH Vignot
DATE OF DEATH January 16, 1922
Place of death Bar-le-Duc