cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A348668 Decimal expansion of the probability that a triangle formed by three points uniformly and independently chosen at random in a rectangle with dimensions 1 X 2 is obtuse.

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%I A348668 #11 Oct 29 2021 09:05:20
%S A348668 7,9,8,3,7,4,2,8,5,1,2,6,9,2,1,0,6,0,3,8,5,1,0,4,7,9,4,1,8,7,3,5,8,7,
%T A348668 5,2,2,8,6,3,1,6,5,8,3,0,2,0,5,0,9,4,1,1,0,1,8,9,2,4,4,6,9,7,0,2,8,8,
%U A348668 4,0,5,3,9,5,2,8,3,8,7,3,1,3,8,5,4,2,8,9,5,8,3,6,8,1,6,1,4,1,5,7,2,7,1,0,2
%N A348668 Decimal expansion of the probability that a triangle formed by three points uniformly and independently chosen at random in a rectangle with dimensions 1 X 2 is obtuse.
%C A348668 The problem of calculating this probability was proposed by Hawthorne (1955) and solved by Langford (1969, 1970). It was mentioned as an unsolved problem in Ogilvy (1962).
%D A348668 A. M. Mathai, An introduction to geometrical probability: distributional aspects with applications, Amsterdam: Gordon and Breach, 1999, pp. 250-253.
%D A348668 Paul J. Nahin, Digital Dice: Computational Solutions to Practical Probability Problems, Princeton University Press, 2008, pp. 8-11.
%D A348668 Luis A. Santaló, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, pp. 21-22.
%D A348668 C. Stanley Ogilvy, Tomorrow's Math: Unsolved Problems for the Amateur, Oxford University Press, New York, 1962, p. 114.
%H A348668 Frank Hawthorne, <a href="http://www.jstor.org/stable/2308020">Problem E1150</a>, The American Mathematical Monthly, Vol. 62, No. 1 (1955), p. 40; <a href="https://www.jstor.org/stable/2316915">Obtuse triangle within a rectangle</a>, Solution to Problem E1150, ibid., Vol. 78, No. 4 (1971), p. 405.
%H A348668 Eric Langford, <a href="https://doi.org/10.1093/biomet/56.3.689">The probability that a random triangle is obtuse</a>, Biometrika, Vol. 56, No. 3 (1969), p. 689.
%H A348668 Eric Langford, <a href="https://www.jstor.org/stable/2688737">A problem in geometric probability</a>, Mathematics Magazine, Vol 43, No. 5 (1970), pp. 237-244.
%F A348668 Equals 1199/1200 + 13*Pi/128 - 3*log(2)/4.
%e A348668 0.79837428512692106038510479418735875228631658302050...
%t A348668 RealDigits[1199/1200 + 13*Pi/128 - 3*Log[2]/4, 10, 100][[1]]
%o A348668 (PARI) 1199/1200 + 13*Pi/128 - 3*log(2)/4 \\ _Michel Marcus_, Oct 29 2021
%Y A348668 Cf. A093072, A341942.
%K A348668 nonn,cons
%O A348668 0,1
%A A348668 _Amiram Eldar_, Oct 29 2021