# Person: Brocard, Pierre René Jean Baptiste Henri

Henri Brocard was a French mathematician best known for his discovery of the so-called Brocard points of a triangle.

### Mathematical Profile (Excerpt):

• Brocard studied at the École Polytechnique from 1865 to 1867.
• Most graduates at this time became technical officers in the military forces and indeed that is exactly the route which Brocard took, joining the Engineering Corps in the French Army.
• Brocard taught for a short while in Montpellier.
• Brocard was with the 120,000 French troops under Marshal MacMahon accompanied by Napoleon III.
• Brocard was one of 83,000 French soldiers taken as prisoners of war at Sedan.
• After Brocard was released he returned to his army life of teaching and research.
• The French Mathematical Society, Société Mathématique de France, was founded in 1872 and Brocard joined the Society in the year after it was founded.
• Brocard took part in the scientific life of Algiers, being a cofounder of the Meteorological Institute there, and a member of the local committee of the meeting of the French Association for the Advancement of Science in Algiers in 1881.
• At this meeting Brocard delivered a paper Études d'un nouveau cercle du plan du triangle Ⓣ(Studies of a new circle related to the triangle) which contains what is known today as the 'Brocard circle' (see below).
• During his ten years in North Africa, Brocard also spent time in Oran, which was occupied by the French in 1831 and turned by them into a modern port and major naval base.
• In 1884 Brocard returned to France where he served with the Meteorological Commission in Montpellier, Genoble and Bar-le-duc.
• Let us look at the triangle for which Brocard is famed.
• The Brocard points of a triangle ABCABCABC are V,WV, WV,W where VAB,VAB,VAB, VBCVBCVBC and VCAVCAVCA and the angles WBAWBAWBA, WCBWCBWCB and WACWACWAC are equal.
• The Brocard circle is that drawn on a diameter, the end points of which are the circumcentre and symmedian point of the triangle.
• It passes through the Brocard points.
• Although best known through this work on the triangle, Brocard also made other contributions which have proved important.
• In 1880 Brocard showed that each dog's pursuit curve would be that of a logarithmic spiral and that the dogs would meet at a common point.
• This point is now known as the Brocard point of the triangle.
• Brocard spent the last years of his life in Bar-le-Duc as a somewhat solitary figure.

Born 12 May 1845, Vignot (part of Commercy), France. Died 16 January 1922, Bar-le-Duc, France.

View full biography at MacTutor

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Thank you to the contributors under CC BY-SA 4.0!

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### References

#### Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive