Joseph-Émile Barbier (1839–1889) was a French astronomer and mathematician, known for

Barbier's theorem In geometry, Barbier's theorem states that every curve of constant width has perimeter times its width, regardless of its precise shape. This theorem was first published by Joseph-Émile Barbier in 1860. Examples The most familiar examples of ...

on the perimeter of

curves of constant width In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body 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 France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...

. 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 than ...

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. S ...

. He entered the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

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 In geometric probability, the problem of Buffon's noodle is a variation on the well-known problem of Buffon's needle, named after Georges-Louis Leclerc, Comte de Buffon who lived in the 18th century. This approach to the problem was published by ...

, 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 histor ...

. 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. 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 appl ...

, and announced a generalization of

Bertrand's ballot theorem In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives ''p'' votes and candidate B receives ''q'' votes with ''p'' > ''q'', what is the probability that A will be strictly ahead of B throu ...

. 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 of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

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 Rhône ...

References

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