an:01769278
Zbl 1104.01305
Hlawka, Edmund
The idea of ``arbitrary'' functions of Poincar?? in the course of a century
DE
Beck, Hanno (ed.) et al., Nature, mathematics and history. Research on Alexander von Humboldt and on mathematical historiography. Halle/Saale: Deutsche Akademie der Naturforscher Leopoldina (ISBN 3-335-00510-4/pbk). Acta Hist. Leopold. 27, 189-200 (1997).
1997
a
01A60
The author discusses Poincar??'s use in probability theory of the ``method of arbitrary functions'' in two known physical problems: (A) the distribution of the small planets and (B) the probability of hitting red or black in roulette [see \textit{H. Poincar??}, La science et l'hypoth??se, Flammarion, Paris (1902; JFM 34.0080.12) (Chapter 11, pp. 227 (A), 233--235 (B))]. A number of famous comments about problems (A) and (B) are mentioned, especially in connection with ergodic theory. Finally he gives some modern versions of uniform distribution results stated by Poincar?? in more literary terms depending on the Erd??s-Tur??n formula and the works of the author.
For the entire collection see [Zbl 0988.00020].
Olaf Ninnemann (Berlin)
JFM 34.0080.12