著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.21, no.142, pp.88-97, 1982 (Released:2021-05-13)

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.42, no.228, pp.213-217, 2003 (Released:2021-08-12)

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.33, no.189, pp.1-6, 1994 (Released:2021-03-22)

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.31, no.181, pp.27-42, 1992 (Released:2021-04-07)

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.29, no.175, pp.157-166, 1990 (Released:2021-08-30)

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Among the problems of classical theory of probability, it is problem of the duration that is one of the most difficult problems to solve. Many distinguished mathematicians have grappled with this problem. I.Todhunter detailed the history of this problem in his book, A history of the mathematical theory of probability from the time of Pascal to that of Laplace, But, here is an excellent author that the erudite Todhunter does not discuss with respect to this problem. Andi・ Marie Ampere today is well known as a phisician. The misunderstanding that the name Ampere is not connected with the problem of the duration of play may be that Todhunter does not refer to his study. I examined the contribution of Ampgre to this problem in this article.

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.28, no.169, pp.14-24, 1989 (Released:2021-09-01)

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A history of the strong law of large numbers certainly began with E. Borel. But BoreFs result was motivated or influenced by Bertrand, Poincare, Wiman, and the others. The main results for this law had ended almost with A. Kolmogorov about 1933. The study of this law consists of two aspects of the development. The one aspect was to deepen the study of the relations between measure theory and the theory of denumerable probabilities. The other is as follows: Let p be a point of the interval(0,1)and let p=P1P2P3...... be its binary expansion. Let Xn(p)={+1 if pk=1 {-1 if pk=0 Then Sn=X1+X2+ ……+Xn is the excess frequency of occurrence of the digit 1 among the first n places in the expansion of p. Borel and Cantelli assert almost everywhere Sn = O(n). The enumeration of sharper results indicated the historic development of the problem. In this paper, these two aspects are described historically. For the theorem of the strong law of large numbers is not a mere theorem, but the processes of its studies are just a history of the probability theory in the early 20th century.

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.25, no.158, pp.89-90, 1986 (Released:2021-04-05)

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究 (ISSN:21887535)

巻号頁・発行日

vol.24, no.155, pp.171-173, 1985 (Released:2021-04-07)

著者

長岡 一夫

出版者

現代数学社

雑誌

理系への数学 (ISSN:13441345)

巻号頁・発行日

vol.32, no.8, pp.120-124, 1999-06

著者

長岡 一夫

出版者

日本科学史学会

雑誌

科学史研究. 第II期 (ISSN:00227692)

巻号頁・発行日

vol.36, no.203, pp.169-175, 1997-09-29