Schoenflies was born in the small district town of Landsberg an der Warte, then belonging to Brandenburg, now in Polish territory. He began studying mathematics in Berlin just after the war in 1870 and obtained his Ph. D. in March 1877. His main teacher was E. E. Kummer, famous for his research in geometry. The next six years Schoenflies spent as high-school teacher, the first two in Berlin, the others in Colmar in Alsace. He managed to continue research in this period along the lines begun in his thesis, combining in it geometrical inspection methods with those of analytical, synthetic and projective geometry. The success of his work led to his becoming Privatdozent (Lecturer) in 1884 and later (1892) Associate Professor of Applied Mathematics in Göttingen. Here he became interested in the geometrical properties of rigid-body motion which had first been studied in this sense by Camille Jordan nearly twenty years earlier. Two theorems established by Schoenflies will serve to illustrate the kind of properties involved: (i) All points of a rigid system which lie on straight lines in three of its positions belong to a (spatial) curve of the third degree; (ii) there exists a curve of the sixth degree whose points lie on circles in any four different positions of the body.
KeywordsStructure Theory Fundamental Domain Projective Geometry Akademii Nauk SSSR Rigid System
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