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 The Pas-de-Calais (, ' strait of Calais'; ; ) 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 of France, with 890, and is the ...

, in the north of

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

. 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 ...

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

. He entered the

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

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 probability theory, 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 th ...

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

Nice Nice ( ; ) is a city in and the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly one million Paris Observatory The Paris Observatory (, ), a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centres in the world. Its historic building is on the Left Ban ...

. 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 whose work emphasized number theory, differential geometry, probability theory, economics and thermodynamics. Biography Joseph Bertrand was the son of ...

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 as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

, 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 throug ...

. He was given the Francoeur Prize for his mathematical research by the

French Academy of Sciences The French Academy of 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 method, scientific research. It was at the forefron ...

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

Loire The Loire ( , , ; ; ; ; ) 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. It rises in the so ...

References

{{DEFAULTSORT:Barbier, Joseph-Emile 1839 births 1889 deaths 19th-century French astronomers 19th-century French mathematicians People from Pas-de-Calais