MOBIUS, AUGUST FERDINAND

born , Nov. 17, 1790, Schulpforta, Saxony died Sept. 26, 1868, Leipzig German mathematician and theoretical astronomer who is best known for his work in analytic geometry and in topology. In the latter field he is especially remembered as one of the discoverers of the Mbius strip. In 1815 Mbius became professor of astronomy at the University of Leipzig, later being chosen also as director of the university observatory, which was erected (181821) under his supervision. Mbius' reputation as a theoretical astronomer was established with the publication of De Computandis Occultationibus Fixarum per Planetas (1815; Concerning the Calculation of the Occultations of the Planets). Die Hauptstze der Astronomie (1836; The Principles of Astronomy) and Die Elemente der Mechanik des Himmels (1843; The Elements of Celestial Mechanics) are among his other purely astronomical publications. His mathematical papers, appearing mostly in Crelle's Journal (182858), are chiefly geometric, and in many of these papers he developed and applied the methods laid down in his Der barycentrische Calkul (1827; The Calculus of Centres of Gravity). In this work he introduced homogeneous coordinates into analytic geometry and also dealt with geometric transformations, in particular projective transformations. He discussed the configuration known as the Mbius net, which later played an essential part in the systematic development of projective geometry. In the Lehrbuch der Statik (1837; Handbook on Statics) Mbius gave a geometric treatment of statics (a branch of mechanics), leading to the null system of points and planes and to the study of systems of lines in space. Mbius was a pioneer in topology; in a memoir presented to the Academy of Sciences, discovered after his death, he discussed the properties of one-sided surfaces, including the Mbius strip, which was named after him. His Gesammelten Werke, 4 vol. (Collected Works), appeared in 188587.