Henri Brocard
Encyclopedia
Pierre René Jean Baptiste Henri Brocard (12 May 1845 – 16 January 1922) was a French
meteorologist and mathematician
, in particular a geometer. His best-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.
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 is listed as an Emeritus at the International Academy of Science, 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.
), Meuse
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.
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.
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. Brocard also visited Oran
while in northern Africa, which was occupied by the French in 1831.
, and the Brocard circle
, all of which today bear his name.
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) Courbes géométriques 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 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
.
Brocard's most well-known contributions to mathematics are the Brocard point
s, 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. 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
.
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.
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.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
meteorologist and mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, in particular a geometer. His best-known achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle
Brocard circle
In geometry, the Brocard circle for a triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. The Brocard circle is named for Henri Brocard....
, and the Brocard triangle
Brocard triangle
In geometry, 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...
, all bearing his name.
Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg
Joseph Jean Baptiste Neuberg
Joseph Jean Baptiste Neuberg was a Luxembourger mathematician who worked primarily in geometry.-Biography:Neuberg was born on 30 October 1840 in Luxembourg City, Luxembourg. He first studied at a local school, the Athénée de Luxembourg, then progressed to Ghent University, studying at the École...
, was one of the three co-founders of modern triangle geometry. He is listed as an Emeritus at the International Academy of Science, was awarded the Ordre des Palmes Académiques, and was an officer of the Légion d'honneur
Légion d'honneur
The Legion of Honour, or in full the National Order of the Legion of Honour is a French order established by Napoleon Bonaparte, First Consul of the Consulat which succeeded to the First Republic, on 19 May 1802...
.
He spent most of his life studying meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
as an officer in the French Navy
French Navy
The French Navy, officially the Marine nationale and often called La Royale is the maritime arm of the French military. It includes a full range of fighting vessels, from patrol boats to a nuclear powered aircraft carrier and 10 nuclear-powered submarines, four of which are capable of launching...
, but seems to have made no notable original contributions to the subject.
Early years
Pierre René Jean Baptiste Henri Brocard was born on 12 May 1845, in Vignot (a part of CommercyCommercy
Commercy is a commune in the Meuse department in Lorraine in north-eastern France.It is the home of the madeleines referred to by Marcel Proust in A la Recherche du Temps Perdu.-History:...
), Meuse
Meuse
Meuse is a department in northeast France, named after the River Meuse.-History:Meuse is one of the original 83 departments created during the French Revolution on March 4, 1790...
to Elizabeth Auguste Liouville and Jean Sebastien Brocard. He attended the Lycée in Marseilles as a young child, and then the Lycée in Strasbourg
Strasbourg
Strasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
. After graduating from the Lycée he entered the Academy
Academy
An academy is an institution of higher learning, research, or honorary membership.The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. In the western world academia is the...
in Strasbourg
Strasbourg
Strasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
where he was prepared for the examination for entrance to the prestigious École Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, to which he was accepted in 1865.
École Polytechnique and military years
As was the norm at the time, he, after graduation, became a technical officer
Officer (armed forces)
An officer is a member of an armed force or uniformed service who holds a position of authority. Commissioned officers derive authority directly from a sovereign power and, as such, hold a commission charging them with the duties and responsibilities of a specific office or position...
in the French military, which had been reorganized in 1866. He acted as a meteorologist in the French navy
French Navy
The French Navy, officially the Marine nationale and often called La Royale is the maritime arm of the French military. It includes a full range of fighting vessels, from patrol boats to a nuclear powered aircraft carrier and 10 nuclear-powered submarines, four of which are capable of launching...
, and general technician as well. Brocard taught briefly in Montpellier
Montpellier
-Neighbourhoods:Since 2001, Montpellier has been divided into seven official neighbourhoods, themselves divided into sub-neighbourhoods. Each of them possesses a neighbourhood council....
.
Brocard soon saw active service, as Napoleon III declared war
War
War is a state of organized, armed, and often prolonged conflict carried on between states, nations, or other parties typified by extreme aggression, social disruption, and usually high mortality. War should be understood as an actual, intentional and widespread armed conflict between political...
upon Prussia
Prussia
Prussia was a German kingdom and historic state originating out of the Duchy of Prussia and the Margraviate of Brandenburg. For centuries, the House of Hohenzollern ruled Prussia, successfully expanding its size by way of an unusually well-organized and effective army. Prussia shaped the history...
. Brocard was one of the 120,000 men under Marshal MacMahon led to Metz
Metz
Metz is a city in the northeast of France located at the confluence of the Moselle and the Seille rivers.Metz is the capital of the Lorraine region and prefecture of the Moselle department. Located near the tripoint along the junction of France, Germany, and Luxembourg, Metz forms a central place...
to free the French army
French Army
The French Army, officially the Armée de Terre , is the land-based and largest component of the French Armed Forces.As of 2010, the army employs 123,100 regulars, 18,350 part-time reservists and 7,700 Legionnaires. All soldiers are professionals, following the suspension of conscription, voted in...
of the Rhine. The French army, however, was defeated on 31 August at the Battle of Sedan
Battle of Sedan
The Battle of Sedan was fought during the Franco-Prussian War on 1 September 1870. It resulted in the capture of Emperor Napoleon III and large numbers of his troops and for all intents and purposes decided the war in favour of Prussia and its allies, though fighting continued under a new French...
, and was taken prisoner along with approximately 83,000 other combatants.
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, (also called Nouvelles annales mathématiques). He joined the Société Mathématique de FranceSociété Mathématique de France
The Société Mathématique de France is the main professional society of French mathematicians.The society was founded in 1872 by Émile Lemoine and is one of the oldest mathematical societies in existence...
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
Africa
Africa is the world's second largest and second most populous continent, after Asia. At about 30.2 million km² including adjacent islands, it covers 6% of the Earth's total surface area and 20.4% of the total land area...
, where he served as a military technician for the French forces stationed in Algiers
Algiers
' is the capital and largest city of Algeria. According to the 1998 census, the population of the city proper was 1,519,570 and that of the urban agglomeration was 2,135,630. In 2009, the population was about 3,500,000...
, the seat of French Africa. While in Algiers, Brocard founded the Meteorological Institute of Algiers. Brocard also visited Oran
Oran
Oran is a major city on the northwestern Mediterranean coast of Algeria, and the second largest city of the country.It is the capital of the Oran Province . The city has a population of 759,645 , while the metropolitan area has a population of approximately 1,500,000, making it the second largest...
while in northern Africa, which was occupied by the French in 1831.
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 triangleBrocard triangle
In geometry, 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...
, and the Brocard circle
Brocard circle
In geometry, the Brocard circle for a triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. The Brocard circle is named for Henri Brocard....
, all of which today bear his name.
Later years
In 1884 Brocard returned to France. He served with the Meteorological Commission in MontpellierMontpellier
-Neighbourhoods:Since 2001, Montpellier has been divided into seven official neighbourhoods, themselves divided into sub-neighbourhoods. Each of them possesses a neighbourhood council....
before moving to Grenoble
Grenoble
Grenoble is a city in southeastern France, at the foot of the French Alps where the river Drac joins the Isère. Located in the Rhône-Alpes region, Grenoble is the capital of the department of Isère...
and lastly Bar-le-duc
Bar-le-Duc
Bar-le-Duc, formerly known as Bar, is a commune in the Meuse département, of which it is the préfecture . The department is in Lorraine in north-eastern France-Geography:...
. He honorably retired from the French military in 1910 as a lieutenant colonel
Lieutenant colonel
Lieutenant colonel is a rank of commissioned officer in the armies and most marine forces and some air forces of the world, typically ranking above a major and below a colonel. The rank of lieutenant colonel is often shortened to simply "colonel" in conversation and in unofficial correspondence...
. 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) Courbes géométriques remarquables was written in collaboration with Lemoyne
Lemoyne
-People:* Charles le Moyne de Longueuil et de Châteauguay , French settler in Canada* Jacques Le Moyne, French artist* Jean-Louis Lemoyne , French sculptor...
.
Brocard attended the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
at Zurich
Zürich
Zurich is the largest city in Switzerland and the capital of the canton of Zurich. It is located in central Switzerland at the northwestern tip of Lake Zurich...
in 1897, Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
in 1900, Heidelberg
Heidelberg
-Early history:Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer. His jaw bone was discovered in 1907; with scientific dating, his remains were determined to be the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of...
in 1904, Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
in 1908, Cambridge, England in 1912, and Strasbourg
Strasbourg
Strasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
in 1920.
Brocard spent the last years of his life in Bar-le-Duc
Bar-le-Duc
Bar-le-Duc, formerly known as Bar, is a commune in the Meuse département, of which it is the préfecture . The department is in Lorraine in north-eastern France-Geography:...
. 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
Kensington
Kensington is a district of west and central London, England within the Royal Borough of Kensington and Chelsea. An affluent and densely-populated area, its commercial heart is Kensington High Street, and it contains the well-known museum district of South Kensington.To the north, Kensington is...
, London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
.
Brocard triangle, Brocard circle, and Brocard points
Brocard's most well-known contributions to mathematics are the Brocard point
Brocard point
In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard , a French mathematician.-Definition:...
s, the Brocard circle
Brocard circle
In geometry, the Brocard circle for a triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. The Brocard circle is named for Henri Brocard....
, and the Brocard triangle
Brocard triangle
In geometry, 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...
. The positive Brocard point (sometimes known as the first Brocard point) of a Euclidean
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
plane triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
is the interior point
Point (geometry)
In geometry, topology and related branches of mathematics a spatial point is a primitive notion upon which other concepts may be defined. In geometry, points are zero-dimensional; i.e., they do not have volume, area, length, or any other higher-dimensional analogue. In branches of mathematics...
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. The Brocard circle of the triangle is a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
having a diameter
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle...
of the line segment
Line segment
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment...
between the circumcenter and symmedian
Symmedian
Symmedians are three particular geometrical lines associated with every triangle. They are constructed by taking a median of the triangle , and reflecting the line over the corresponding angle bisector...
. It contains the Brocard points. The Brocard triangle of a triangle
Triangle
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ....
is a triangle formed by the intersection
Line-line intersection
In Euclidean geometry, the intersection of a line and a line can be the empty set,a point, ora line. Distinguishing these cases, and finding the intersection point have use, for example, in computer graphics, motion planning, and collision detection....
of line
Line (geometry)
The notion of line or straight line was introduced by the ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects...
from a vertex to its corresponding Brocard point
Brocard point
In geometry, Brocard points are special points within a triangle. They are named after Henri Brocard , a French mathematician.-Definition:...
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
Brocard circle
In geometry, the Brocard circle for a triangle is a circle having a diameter of the line segment between the circumcenter and symmedian. It contains the Brocard points. The Brocard circle is named for Henri Brocard....
.
Other mathematical contributions
Brocard published various other papers on mathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
during his time at Bar-le-duc
Bar-le-Duc
Bar-le-Duc, formerly known as Bar, is a commune in the Meuse département, of which it is the préfecture . The department is in Lorraine in north-eastern France-Geography:...
, 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.
Meteorology
Meteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
, he founded the Meteorological Institute in Algiers
Algiers
' is the capital and largest city of Algeria. According to the 1998 census, the population of the city proper was 1,519,570 and that of the urban agglomeration was 2,135,630. In 2009, the population was about 3,500,000...
and served as a meteorological technician during his time in the French military. He also published several notable papers on meteorology.
See also
- Brocard's conjecture
- Brocard points
- Brocard triangleBrocard triangleIn geometry, 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...
- École PolytechniqueÉcole PolytechniqueThe École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...