Joseph-Émile Barbier

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Joseph-Émile Barbier (1839–1889) was a French astronomer and mathematician best known for Barbier's theorem, which describes the perimeter of curves of constant width. He was born on 18 March 1839 in Saint-Hilaire-Cottes, northern France. He studied at the College of Saint-Omer, then at Lycée Henri-IV in Paris, and entered the École Normale Supérieure in 1857, finishing in 1860—the same year he published his famous paper on constant-width curves. In that work he also gave a simple solution to Buffon’s needle problem, known as Buffon’s noodle, which did not use integrals.

Barbier tried teaching at a high school in Nice but soon moved to the Paris Observatory as an assistant astronomer. He left the observatory in 1865. In 1880, the mathematician Joseph Louis François Bertrand found him in the Charenton asylum, arranged support for him, and encouraged him to return to mathematical research. Barbier then published about ten more papers, contributed to Bertrand’s work on combinatorics, and announced a generalization of Bertrand’s ballot theorem. He won the Francoeur Prize for mathematical research several times. He died on 28 January 1889 in Saint-Genest-Lerpt, Loire, at the age of 49.