(b. Lille, France, 28 November 1845; d. Philippeville [now Skikda], Algeria, 13 September 1893)
Ribaucour was the son of placide Francois Charles Ribaucour, a teacher of mathematics, and Angélique Francoise Devemy. In 1865 he entered the École Polytechnique in paris and in 1867 began studying at the École des Ponts et Chaussées, which he left in 1870 to become an engineer at the Rochefort naval base. At Rochefort he showed an exceptional aptitude for engineering, which also distinguished him after transfer, in 1873, to Draguignan (Var), where from 1874 to 1876 he was in charge of road construction in Var. The bridges that he designed were remarkable because of their combination of maximum strength with minimum material. From 1878 to 1885 he stayed at Aix-en-Provence, where his skills displayed in the construction works on the canal of the Durance earned him a Légion d’Honneur and a gold medal at the Paris Exposition of 1889. Ribaucour’s suspension bridge of Mallemort-sur-Corrége and his construction of the reservoir of Saint-Christophe (near Rognes, Bouches-du-Rhône) were especially praised.
After a short stay at Vesoul (Haute-Saone) in order to receive the title of hcief enginner, Ribaucour was sent to Algeria, where from 1886 until his death he stayed at Philippeville and worked on the construction of railroad and harbor works.
Ribaucour’s mathemetical work—to which he dedicated himself especially under the influence of Mannheim—belonged to his spare time, expect for a short period during 1873 and 1874, when he was répétiteur in geometry at the École Polytechnique. His main field was differential geometry, and his work was distinguished enough to earn him the prix Dalmont in 1877 and a posthumous prix. Petit d’Ormoy in 1895, awarded by the paris Academy. His most elaborate work was a study of minimal surfaces, Étude des élassoides ou surfaces á courbure moyenne nulle, presented to the Belgian Academy of Sciences in 1880 (in Mémoires cournnés et mémoires des savants étrangers. Académie royale des science, des lettres et des beaux-arts de Belgique, 44 ). In the work he explained his method called perimorphie, which utilized a moving trihedron on a surface. The approach to minimal surfaces was to consider them as the envelope of the middle planes of isotropic congruences; this approach led Robaucour to a wealth of results.
Many of Ribaucour’s papers deal with congruences of circle and spheres. Special attention was devoted to those system of circle that are orthogonal to a family of surfaces. Such systems form systémes cycliques, and it is sufficient for the circles to be orthogonal to more than two surfaces for them to be orthogonal to a family. Ribaucour’s research thus led him to envelopes of spheres, to triply orthogonal system, cyclides, and surfaces of constant curvature.
I. Original Works. Ribaucour reported most of his results in Comptes rendus hebdomadaires des séances de l’Acamémie des sciences, 67 (1868), to 113 (1891); also in the Nouvelles annales de mathématiques, 2nd ser., 4 (1865), to 10 (1871); and the Bulletin de la Societe philomathique in Paris (1867–1871). See also “Sur deux phenomenes d’hydrodynamique observes au bassin de Saint Christophe,” in Compte rendu de la 14 session de l’Association francaise pour l’avancement des science, pt. 2 (1885), 252–255; and M. Salva, Notice sur le port de Philippeville (Paris, 1892), esp.chs.5 and 6.
II. Secondary Literature. A good approach to Ribaucour’s work is through Gaston Darboux, Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitesimal, 4 vols. (Paris, 1887–1896); see also L. Bianchi, Lezioni di geometria differenziale, 3rd ed., II (Pisa, 1923), esp. chs. 17, 19 ,20 , 21. Other works include P. Mansion, “Ribaucour,” in Mathésis, 2nd ser., 3 (1893), 270–272; and P. M. d’ocagne, “Un ingénieur et géométre polytechnicien: Albert Ribaucour,” Bulletin de la Société des amis de l’Ecole Polytechnique (July, 1913). (A. Brunot in Paris and E. de Zelicourt in Aix have also provided data for this article.)
D. J. Struik