Joseph-Émile Barbier (1839–1889) was a French astronomer and mathematician, known for Barbier's theorem on the perimeter of curves of constant width. Barbier was born on 18 March 1839 in Saint-Hilaire-Cottes,

Pas-de-Calais Pas-de-Calais (, " strait of Calais"; pcd, Pas-Calés; also nl, Nauw van Kales) is a department in northern France named after the French designation of the Strait of Dover, which it borders. It has the most communes of all the departments ...

, in the north of

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan ar ...

. He studied at the College of Saint-Omer, also in Pas-de-Calais, and then at the

Lycée Henri-IV The Lycée Henri-IV is a public secondary school located in Paris. Along with the Lycée Louis-le-Grand, it is widely regarded as one of the most prestigious and demanding sixth-form colleges ('' lycées'') in France. The school educates more th ...

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. ...

. He entered the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education Secondary education or post-primary education covers two phases on the International Standard Classification of Education sca ...

in 1857, and finished his studies there in 1860, the same year in which he published the paper containing his theorem on constant-width curves. In this paper he also presented a solution to

Buffon's needle problem In mathematics, Buffon's needle problem is a question first posed in the 18th century by Georges-Louis Leclerc, Comte de Buffon: :Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floo ...

, known as Buffon's noodle, that avoided the use of integrals. He began teaching at a lycée in

Nice Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative c ...

, but it was not a success, and he soon moved to a position as an assistant astronomer at the

Paris Observatory The Paris Observatory (french: Observatoire de Paris ), a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centers in the world. Its hist ...

. He left there in 1865, and in 1880

Joseph Louis François Bertrand Joseph Louis François Bertrand (; 11 March 1822 – 5 April 1900) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, economics and thermodynamics. Biography Joseph Bertrand was the ...

found him in the

Charenton asylum Charenton was a lunatic asylum, founded in 1645 by the Frères de la Charité or Brothers of Charity in Charenton-Saint-Maurice, now Saint-Maurice, Val-de-Marne, France. Charenton was first under monastic rule, then Sisters of Charity of S ...

. Bertrand arranged for Barbier's support and encouraged him to return to mathematical publication. In this later period of his work, he published ten more papers. He contributed to Bertrand's studies of

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

, and announced a generalization of Bertrand's ballot theorem. He was given the Francoeur Prize for his mathematical research by the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at th ...

in multiple years.. Barbier died on 28 January 1889 in Saint-Genest,

Loire The Loire (, also ; ; oc, Léger, ; la, Liger) is the longest river in France and the 171st longest in the world. With a length of , it drains , more than a fifth of France's land, while its average discharge is only half that of the Rhôn ...

References

1839 births 1889 deaths 19th-century French astronomers 19th-century French mathematicians People from Pas-de-Calais {{France-astronomer-stub