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Ludwig Schläfli – an ingenious Swiss mathematician. (Ludwig Schläfli – ein genialer Schweizer Mathematiker.) (German) Zbl 1209.52001

The author gives a nicely written overview on the main mathematical activities of the famous Swiss mathematician Ludwig Schläfli (1814–1895). The reader, being not familiar with Schläfli’s life and contributions to different mathematical fields, such as Algebraic Geometry, \(n\)-dimensional geometry (here also the classification of the \(n\)-dimensional regular polytopes), Differential Geometry, Number Theory, Analysis, Mechanics etc., is surprised regarding the versatility of this ingenious mathematician! And also examples of his very wide correspondence with famous colleagues (J. Steiner, A. Cayley etc.) are discussed. Also singular observations and results are surprising, such as the remark that Schläfli was most likely the first who discovered the fact that the projective plane cannot be oriented, what he also wrote to F. Klein. Basic notions and methods related to Schläfli’s approach to the class of regular polytopes (like Schläfli’s differential form, his reduction formula and the rational simplex conjecture) are presented in a more detailed way.

MSC:

52-03 History of convex and discrete geometry
01A55 History of mathematics in the 19th century

Biographic References:

Schläfli, Ludwig
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References:

[1] Burckhardt, J.J.: Ludwig Schläfli. Beiheft 4 zu Elem. Math. , Basel 1948. · Zbl 0033.00301
[2] Coxeter, H.S.M.: Star polytopes and the Schläfli function f (\alpha , \beta , \gamma ). Elem. Math. 44 (1989), 25-56. · Zbl 0711.51009
[3] Graf, J.H.: Ludwig Schläfli. Mitteilungen der Naturforschenden Gesellschaft in Bern (1896), 118-203.
[4] Graf, J.H.: Die Exhumirung Jakob Steiner’s und die Einweihung des Grabdenkmals Ludwig Schläfli’s. Mitteilungen der Naturforschenden Gesellschaft in Bern (1897), 6-24. · JFM 28.0016.02
[5] Kellerhals, R.: Der Mathematiker Ludwig Schläfli (15.01.1814-20.03.1895). DMV-Mitteilungen 4 (1996), 35-43.
[6] Rytz, W.: Prof. Ludwig Schläfli als Botaniker. Mitteilungen der Naturforschenden Gesellschaft in Bern (1919), 213-220.
[7] Schlaginhaufen, O.: Der Schädel des Mathematikers Ludwig Schläfli. Mitteilungen der Naturforschenden Gesellschaft in Bern (1931), 35-66.
[8] Schläfli, L.: Gesammelte Mathematische Abhandlungen . 3 Bände, Birkhäuser, Basel 1950-1956.
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