Henri Brocard

Pierre René Jean Baptiste Henri Brocard (; 12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, in particular a geometer.

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. He was awarded the Ordre des Palmes Académiques, and was an officer of the Légion d'honneur.

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.

École Polytechnique and military years

Brocard attended the École Polytechnique from 1865 to 1867. 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 Science 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.

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.

Later years

In 1884 Brocard returned to France. He served with the Meteorological Commission in Montpellier before moving to Grenoble 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 courbes géométriques (1897, 1899, published in two volumes) and the Courbes géométriques remarquables (1920, posthumous 1967, also published in two volumes) which was written in collaboration with Timoléon 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. 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. 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.

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. He also conjured up a famous unsolved problem thought to have no answers other than the three he provided. This problem is called Brocard's Problem. 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.

Meteorology The University of Algiers administrates the Meteorological Society which Brocard founded. 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.