A232715 - OEIS

A232715

Decimal expansion of the ratio of the area of a parbelos to the area of its associated arbelos: 4/(3*Pi).

%I #17 Oct 01 2022 00:13:59

%S 4,2,4,4,1,3,1,8,1,5,7,8,3,8,7,5,6,2,0,5,0,3,5,6,7,0,2,3,2,6,7,0,4,9,

%T 6,5,4,2,5,2,2,5,7,2,1,9,7,4,5,5,0,5,2,9,9,9,3,7,7,9,5,8,4,1,5,7,0,5,

%U 8,1,2,7,0,2,4,6,0,4,0,9,3,5,7,3,6

%N Decimal expansion of the ratio of the area of a parbelos to the area of its associated arbelos: 4/(3*Pi).

%C Also distance from the diameter of unit semicircle to its centroid. - _Franck Maminirina Ramaharo_, Oct 22 2018

%H 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 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.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 0.424413181578387562050356702326704965425225721974550529993779...

%t RealDigits[4/(3 Pi),10,100]

%o (PARI) 4/Pi/3 \\ _Charles R Greathouse IV_, Oct 01 2022

%Y Reciprocal of A177870. Ratio of lengths of boundaries is A232716.

%K nonn,cons,easy

%O 0,1

%A _Jonathan Sondow_, Nov 28 2013