cp's OEIS Frontend

A232717 Decimal expansion of the ratio of the length of the boundary of any arbelos to the length of the boundary of its associated parbelos: Pi / (sqrt(2) + log(1 + sqrt(2))).

%I A232717 #25 Sep 08 2022 08:46:06
%S A232717 1,3,6,8,5,3,5,5,6,3,7,3,1,9,1,4,7,8,8,8,6,0,6,2,6,2,6,5,9,3,2,5,8,8,
%T A232717 1,0,8,4,2,1,4,2,4,8,0,0,1,0,6,2,1,7,3,4,9,0,5,3,9,9,1,8,5,9,5,7,9,4,
%U A232717 8,9,4,4,7,6,7,9,3,0,9,1,9,7,0,4,7,6,8,0,1,8,8,2,8,0,9,0,4,9,2,6
%N A232717 Decimal expansion of the ratio of the length of the boundary of any arbelos to the length of the boundary of its associated parbelos: Pi / (sqrt(2) + log(1 + sqrt(2))).
%C A232717 Same as decimal expansion of Pi/P, where P is the Universal parabolic constant (A103710). - _Jonathan Sondow_, Jan 19 2015
%H A232717 G. C. Greubel, <a href="/A232717/b232717.txt">Table of n, a(n) for n = 1..10000</a>
%H A232717 M. Hajja, <a href="https://zbmath.org/?q=an:1291.51018">Review Zbl 1291.51018</a>, zbMATH 2015.
%H A232717 M. Hajja, <a href="https://zbmath.org/?q=an:1291.51016">Review Zbl 1291.51016</a>, zbMATH 2015.
%H A232717 J. Sondow, <a href="http://arxiv.org/abs/1210.2279">The parbelos, a parabolic analog of the arbelos</a>, arXiv 2012, Amer. Math. Monthly, 120 (2013), 929-935.
%H A232717 E. Tsukerman, <a href="http://arxiv.org/abs/1210.5580">Solution of Sondow's problem: a synthetic proof of the tangency property of the parbelos</a>, arXiv 2012, Amer. Math. Monthly, 121 (2014), 438-443.
%F A232717 Equals A000796 / A103710.
%e A232717 1.36853556373191478886062626593258810842142480010621734905399...
%t A232717 RealDigits[Pi/(Sqrt[2] + Log[1 + Sqrt[2]]),10,100]
%o A232717 (PARI) Pi/(sqrt(2) + log(1 + sqrt(2))) \\ _G. C. Greubel_, Jul 27 2018
%o A232717 (Magma) R:= RealField(); Pi(R)/(Sqrt(2) + Log(1 + Sqrt(2))) // _G. C. Greubel_, Jul 27 2018
%Y A232717 Reciprocal of A232716. Ratio of areas is A232715.
%Y A232717 Cf. A000796, A103710.
%K A232717 cons,easy,nonn
%O A232717 1,2
%A A232717 _Jonathan Sondow_, Nov 28 2013