Henri Brocard

Infobox_Scientist
name = Pierre René Jean Baptiste Henri Brocard

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image_width = 250px
caption = The first page of Henri Brocard's "Notes de bibliographie des courbes géométriques".
birth_date = birth date|1845|5|12|df=y
birth_place = Vignot, France
residence = France
nationality =

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Pierre René Jean Baptiste Henri Brocard (12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, in particular a geometer.cite web|url=http://mundomatematico.webcindario.com/proyecto_mactutor/biografias/b/bio_brocard.html|title=Pierre René Jean Baptiste Henri Brocard] His most well-known achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle, and the Brocard triangle, all bearing his name.mathworld|urlname=BrocardPoints|title=Brocard Points]

Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg, was one of the three co-founders of modern triangle geometry.cite web|url=http://faculty.evansville.edu/ck6/bstud/tg.html|title=Triangle Geometers] He is listed as an Emeritus at the International Academy of Science,cite web|title=International Academy of Science Fellows|url=http://www.science.edu/Membership/Fellows/Fellows.htm] was awarded the Ordre des Palmes Académiques, and was an officer of the Légion d'honneur. [ Cite web | url=http://name.umdl.umich.edu/ABE2896 | title="Courbes géométriques remarquables (courbes spéciales) planes et gauches" | author=Henri Brocard | coauthors=T. Lemoyne | editor=éd. Vuibert, Paris | year=1919, rééd. 1967 ]

He spent most of his life studying meteorology as an officer in the French Navy, but seems to have made no notable original contributions to the subject.cite web|url=http://mundomatematico.webcindario.com/proyecto_mactutor/biografias/b/bio_brocard.html|title=Pierre René Jean Baptiste Henri Brocard]

Biography

Early years

Pierre René Jean Baptiste Henri Brocard was born on 12 May 1845, in Vignot (a part of Commercy), France to Elizabeth Auguste Liouville and Jean Sebastien Brocard. He attended the Lycée in Marseilles as a young child, and then the Lycée in Strasbourg. After graduating from the Lycée he entered the Academy in Strasbourg where he was prepared for the examination for entrance to the prestigious École Polytechnique in Paris, to which he was accepted in 1865.cite web|url=http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Brocard.html|title=Henri Brocard Biography]

École Polytechnique and military years

Brocard attended the École Polytechnique from 1865 to 1867.

As was the norm at the time, he, after graduation, became a technical officer in the French military, which had been reorganized in 1866. He acted as a meteorologist in the French navy, and general technician as well. Brocard taught briefly in Montpellier.

Brocard soon saw active service, as Napoleon III declared war upon Prussia. Brocard was one of the 120,000 men under Marshal MacMahon led to Metz to free the French army of the Rhine. The French army, however, was defeated on 31 August at the Battle of Sedan, and was taken prisoner along with approximately 83,000 other combatants.cite web|url=http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Brocard.html|title=Henri Brocard Biography]

Middle years

After Brocard was freed, he returned to his military position and continued teaching, publishing his mathematical articles in the most popular mathematical journal of that time, "Nouvelles Correspondances Mathématiques" (also called "Nouvelles annales mathématiques"). [cite web|url=http://hdl.handle.net/2027/mdp.39015065163720 |title="Notes de bibliographie des courbes géométriques" T. 1 |author=Henri Brocard | editor=impr. et lith. Comte-Jacquet, Bar Le Duc | year=1897 ] [ Cite web | url=http://name.umdl.umich.edu/ABQ9972 | title="Notes de bibliographie des courbes géométriques" T. 2 | author=Henri Brocard | editor=impr. et lith. Comte-Jacquet, Bar Le Duc | year=1899 ] He joined the Société Mathématique de France in 1873, just a year after its founding. In 1875 he was inducted into the French Association for the Advancement of Scienc] as well as the French Meteorological Society. He was shortly after sent to northern Africa, where he served as a military technician for the French forces stationed in Algiers, the seat of French Africa. While in Algiers, Brocard founded the Meteorological Institute of Algiers. [cite web|title=Albert Camus|url=http://www.imagi-nation.com/moonstruck/clsc40.html (3rd paragraph, reference to institute mentioned)]

Discovery of Brocard points

During a meeting of the French Association for the Advancement of Science, Brocard presented a self-written article entitled "Etudes d'un nouveau cercle du plan du triangle", his first paper on the Brocard points, the Brocard triangle, and the Brocard circle, all of which today bear his name. [cite web|url=http://links.jstor.org/sici?sici=0025-5572(195312)2%3A37%3A322%3C241%3AHBATGO%3E2.0.CO%3B2-8|title=Henri Brocard and the Geometry of the Triangle] [citeweb|title=CIM Bulletin 2004|url=http://at.yorku.ca/i/a/a/h/61.dir/number16.htm] Brocard also visited Oran while in northern Africa, which was occupied by the French in 1831. [cite|title=Encyclopaedia of Mathematics|year=1994|publisher=Springer|author=Michiel Hazewinkel|date=1 January]

Later years

In 1884 Brocard returned to France. He served with the Meteorological Commission in Montpellier before moving to Genoble and lastly Bar-le-duc. He honorably retired from the French military in 1910 as a lieutenant colonel. His remaining two major publications were "Notes de bibliographie des corbes géométriques" (1897, 1899, published in two volumes) and the "Courbes géométriques remarkables" (1920, posthumous 1967, also published in two volumes) "Courbes géométriques remarkables" was written in collaboration with Lemoyne.

Brocard attended the International Congress of Mathematicians at Zurich in 1897, Paris in 1900, Heidelberg in 1904, Rome in 1908, Cambridge, England in 1912, and Strasbourg in 1920.

Brocard spent the last several years of his life in Bar-le-Duc. He was offered the presidency of Bar-le-Duc's "Letters, Sciences, and Arts Society", of which he had been a longtime member and correspondent for several foreign academies of, but declined. He died on 16 January 1922 while on a trip to Kensington, London, England.cite web|url=http://www-groups.dcs.st-and.ac.uk/~history/Printonly/Brocard.html|title=Henri Brocard Biography]

Contributions

Brocard triangle, Brocard circle, and Brocard points

Brocard's most well-known contributions to mathematics are the Brocard points, the Brocard circle, and the Brocard triangle. The positive Brocard point (sometimes known as the first Brocard point) of a Euclidean plane triangle is the interior point of the triangle for which the three angles formed by two of the vertices and the point are equal. Their common value is the Brocard angle the triangle. [cite web|title=Math Trek - Brocard points|url=http://www.maa.org/mathland/mathtrek_7_16_01.html] The Brocard circle of the triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. [mathworld|urlname=BrocardCircle|title=Brocard Circle] The Brocard triangle of a triangle is a triangle formed by the intersection of line from a vertex to its corresponding Brocard point and a line from another vertex to its corresponding Brocard point and the other two points constructed using different combinations of vertices and Brocard points. The Brocard triangle is inscribed in the Brocard circle. [mathworld|urlname=FirstBrocardTriangle|title=First Brocard Triangle]

Other mathematical contributions

Brocard published various other papers on mathematics during his time at Bar-le-duc, none of which became as well-known as "Etudes d'un nouveau cercle du plan du triangle". One other achievement of his is guessing at the meaning of the cryptic title of one of Girard Desargues' papers, "DALG". In his paper "Analyse d'autographes et autres écrits de Girard Desargues", he surmised that it stood for "Des Argues, Lyonnais, Géometre", which is the generally accepted title. [cite web|title=Récréations Mathématiques (1624): A Study on its Authorship, Sources and Influence 2004|url=http://logica.rug.ac.be/albrecht/thesis/Etten-intro.pdf|author=Alfred Heefer]

Meteorology

Though Brocard made no major notable original discoveries in meteorology, he founded the Meteorological Institute in Algiers and served as a meteorological technician during his time in the French military. He also published several notable papers on meteorology. [cite web|title=Henri Brocard Biography|url=http://202.38.126.65/navigate/math/history/Mathematicians/Brocard.html] cite web|url=http://links.jstor.org/sici?sici=0002-9890(192208)29%3A7%3C275%3ANAN%3E2.0.CO%3B2-N|title=The American Mathematical Monthly Vol. 29, No. 7]

ee also

*Brocard points
*Brocard triangle
*Brocard circle
*École Polytechnique

Notes

References

*" [http://links.jstor.org/sici?sici=0025-5572(195312)2%3A37%3A322%3C241%3AHBATGO%3E2.0.CO%3B2-8 Henri Brocard and the Geometry of the Triangle by Laura Guggenbuhl]
*"Encyclopaedia of Mathematics: An Updated and Annotated Translation"—Henri Brocard
*Laura Guggenbuhl, "Biography in Dictionary of Scientific Biography" (New York 1970–1990).
*A. Gica and L. Panaitopol, "On a problem of Brocard", Bull. London Math. Soc. 37 (4) (2005), 502–506.
*R. J. Stroeker, "Brocard points, circulant matrices, and Descartes' folium", Math. Mag. 61 (3) (1988), 172–187.

External links

* [http://maa.org/reviews/changingshape.html The Changing Shape of Geometry]

Persondata
NAME = Henri Brocard
ALTERNATIVE NAMES =
SHORT DESCRIPTION = French mathematician (geometer), meteorologist
DATE OF BIRTH = 12 May 1845
PLACE OF BIRTH = Vignot, France
DATE OF DEATH = 16 January 1922
PLACE OF DEATH = London, United Kingdom