1880, Werke, Vierter band, herausgegebenen von der Königlichen Gesellschaft der Wissenschaften zu Göttingen 1979, 150 Years after Gauss’ Disquisitiones generales circa superficies curvas, astérisque, 62 (with the original text of Gauss and an English translation by A. 1977, Gauss as a geometer, Historia Mathematica 4.4, 379–396.ĭombrowski, P. 1984 Gauss’s Geodesy and the Axiom of Parallels, Archive for History of Exact Sciences 29 273–289Ĭoxeter, H.S.M. Enriques, Open Court, Chicago, Dover reprint, New York, 1955īreitenberger, E. 1912, History of non-Euclidean geometry, tr, H.S. 1906, La geometria non-Euclidea, Zanichelli, Bolognaīonola, R. Akadémia Kiadó, Budapest, 1987, and North-Holland, Amsterdam, North-Holland Mathematics Studies. Ferenc Kárteszi, Doctor of the Mathematical Sciences. Halsted, Science Absolute of Space, Appendix in Bonola, János Bolyai Appendix: The theory of space, with introduction, comments, and addenda. Battaglini, Sulla scienza della spazio assolutamente vera, Giornale di matematiche 6 1868, 97–115, tr. Houël, La Science Absolue de l’Espace, Mémoires de la Société des Sciences physiques et naturelles de Bordeaux 5, 1867, 189–248, tr. 1832, Appendix scientiam spatii absolute veram exhibens, in Bolyai, F. 1832, 1833 Tentamen juventutem studiosam in Elementa Matheosis purae, etc. This process is experimental and the keywords may be updated as the learning algorithm improves.īolyai, F. These keywords were added by machine and not by the authors. The grounds for his conviction are greater, but still insubstantial, because he lacks almost entirely the substantial body of argument that gives Bolyai and Lobachevskii their genuine claim to be the discoverers of non-Euclidean geometry. Gauss, by contrast, possessed a scientist’s conviction in the possibility of a non-Euclidean geometry which was no less, and no greater, than that of Schweikart or Bessel. In particular, there is no three-dimensional differential geometry leading to an account of non-Euclidean space. This is a long way from saying, what enthusiasts for Gauss’s grasp of non-Euclidean geometry suggest, that this is the Lobachevskian horosphere, a surface in non-Euclidean three-dimensional Space on which the induced geometry is Euclidean. The only hint that he explored the non-Euclidean three-dimensional case is the remark by Wachter, but what Wachter said was not encouraging: “Now the inconvenience arises that the parts of this surface are merely symmetrical, not, as in the plane, congruent or, that the radius on one side is infinite and on the other imaginary” and more of the same. It becomes clear that a mathematician persuaded of the truth of non-Euclidean geometry and seeking to convince others is almost driven to start by looking for, or creating, non-Euclidean three-dimensional Space, and to derive a rich theory of non-Euclidean two-dimensional Space from it - as Bolyai and Lobachevskii did, but not Gauss.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |