Symmetry And Group

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By I. M. Yaglom

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Extra info for Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century

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He wrote a number of works on practical astronomy, including investigations concerning the improvement of the op­ tical systems of telescopes, and his manuals on astronomical observations were still very popular in Germany in the 1920s (the last edition was dated 1916). As a person, Mobius was the epitome of the absentminded professor. He was shy and unsociable, timid with unfamiliar people, and so absorbed in his thoughts that he was forced to work out a whole system of mnemonic rules (which did not always work) so as not to forget his keys or his inseparable umbrella and handkerchief when he set out from home for a walk or for the university.

The Monge method, now widely used in descriptive geometry, 3. Nineteenth-Century Geometry: Projective Geometry 33 (b) (a) (c) FIGURE 4 consists in replacing the three-dimensional figure F by its orthogonal projec­ tions F1 , F2 , and F3 on three pairwise perpendicular planes. ) Poncelet, on the other hand, was interested in the relationship between a (plane or space) figure F and its central projection F' consisting of the inter­ section points A' of the image plane n with all the lines 0A, where 0 is the fixed center of projection and A E F (Fig.

These outstanding geometers made the strongest impression on the young Lie. Their works led to his first publications, which were followed by a continuous stream of papers, uninterrupted for several decades. To continue his education Lie moved to Berlin in 1 870. There he met and immediately made friends with Klein, who was seven years his junior; the first joint work by Lie and Klein, described below, comes from the same year. The close personal and scientific relationship between Lie and Klein, which began then in Berlin, played a major role in the life of both mathematicians and continued until Lie's death.

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