Henri Brocard

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Pierre René Jean Baptiste Henri Brocard (12 May 1845 – 16 January 1922) was a French meteorologist and mathematician, best known for his work in triangle geometry. He introduced the Brocard points, the Brocard circle, and the Brocard triangle, and he is regarded as a key figure in modern triangle geometry alongside Émile Lemoine and Joseph Neuberg.

Brocard was born in Vignot, Meuse. He studied at the École Polytechnique (1865–1867) and then served as a military engineer and meteorologist in the French navy. He fought in the Franco-Prussian War, was captured at the Battle of Sedan, and was later released. After the war, he continued his mathematical work and began publishing in popular journals.

In 1873 he joined the Société Mathématique de France, and in 1875 he was elected to the French Association for the Advancement of Science. While posted in Algiers, he founded the Meteorological Institute of Algiers and published his early papers on the Brocard concepts. His famous paper, presented at a meeting of the French Association for the Advancement of Science, introduced the ideas behind the Brocard points, the Brocard triangle, and the Brocard circle.

Brocard returned to France in 1884 and worked in Montpellier, Grenoble, and Bar-le-Duc. He retired from the military in 1910 as a lieutenant-colonel. He attended several International Congresses of Mathematicians (Zurich 1897, Paris 1900, Heidelberg 1904, Rome 1908, Cambridge 1912, Strasbourg 1920). He spent his final years in Bar-le-Duc and died in Kensington, London, in 1922.

In mathematics, Brocard’s lasting legacy is the trio of concepts named after him: the Brocard points (the interior point of a triangle where the connecting angles to the vertices are equal), the Brocard circle (a circle associated with the triangle that contains the Brocard points), and the Brocard triangle (a triangle formed by lines through the vertices and their Brocard points). He also explored many geometric curves and posed the famous unsolved Brocard’s problem.

Although his meteorology work was substantial in scope—founding the Meteorological Institute of Algiers and serving as a meteorology technician in the navy—his most enduring fame comes from his geometric discoveries. He received honors such as the Ordre des Palmes Académiques and the rank of Officer of the Légion d’Honneur.