Pierre RenĂ© Jean Baptiste Henri Brocard  

The first page of Henri Brocard's Notes de bibliographie des courbes gĂ©omĂ©triques.


Born  12 May 1845 Vignot, Meuse 
Died  16 January 1922 (aged 76) Kensington, London, United Kingdom 
Residence  France 
Nationality  French 
Fields  Mathematics, Meteorology 
Institutions  Military engineer, French army 
Alma mater  Ă‰cole Polytechnique 
Known for  Meteorology Brocard points Brocard triangle Brocard circle 
Notable awards  Emeritus at the International Academy of Science Officer of the LĂ©gion d'honneur 
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Pierre RenĂ© Jean Baptiste Henri Brocard (12 May 1845 â€“ 16 January 1922) was a French meteorologist and mathematician, in particular a geometer.^{[1]} His most wellknown achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle, and the Brocard triangle, all bearing his name.^{[2]}
Contemporary mathematician Nathan Court wrote that he, along with Ă‰mile Lemoine and Joseph Neuberg, was one of the three cofounders of modern triangle geometry.^{[3]} He is listed as an Emeritus at the International Academy of Science,^{[4]} was awarded the Ordre des Palmes AcadĂ©miques, and was an officer of the LĂ©gion d'honneur.^{[5]}
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.^{[1]}
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Pierre RenĂ© Jean Baptiste Henri Brocard was born on 12 May 1845, in Vignot (a part of Commercy), Meuse to Elizabeth Auguste Liouville and Jean Sebastien Brocard. He attended the LycĂ©e in Marseilles as a young child, and then the LycĂ©e in Strasbourg. After graduating from the LycĂ©e he entered the Academy in Strasbourg where he was prepared for the examination for entrance to the prestigious Ă‰cole Polytechnique in Paris, to which he was accepted in 1865.^{[6]}
Brocard attended the Ă‰cole 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.^{[6]}
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 MathĂ©matiques (also called Nouvelles annales mathĂ©matiques).^{[7]}^{[8]} He joined the SociĂ©tĂ© MathĂ©matique 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.^{[9]}
During a meeting of the French Association for the Advancement of Science, Brocard presented a selfwritten 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.^{[10]}^{[11]} Brocard also visited Oran while in northern Africa, which was occupied by the French in 1831.^{[12]}
In 1884 Brocard returned to France. He served with the Meteorological Commission in Montpellier before moving to Grenoble and lastly Barleduc. He honorably retired from the French military in 1910 as a lieutenant colonel. His remaining two major publications were Notes de bibliographie des courbes gĂ©omĂ©triques (1897, 1899, published in two volumes) and the Courbes gĂ©omĂ©triques remarquables (1920, posthumous 1967, also published in two volumes) Courbes gĂ©omĂ©triques remarquables 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 years of his life in BarleDuc. He was offered the presidency of BarleDuc'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.^{[6]}
Brocard's most wellknown 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 of the triangle.^{[13]} 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.^{[14]} 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.^{[15]}
Brocard published various other papers on mathematics during his time at Barleduc, none of which became as wellknown 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 Ă©crits de Girard Desargues, he surmised that it stood for Des Argues, Lyonnais, GĂ©ometre, which is the generally accepted title.^{[16]}
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.^{[17]}^{[18]}
