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.
%I A258146 #29 Feb 16 2025 08:33:25 %S A258146 1,8,1,6,9,0,1,1,3,8,1,6,2,0,9,3,2,8,4,6,2,2,3,2,4,7,3,2,5,4,9,7,1,2, %T A258146 7,5,9,3,1,0,8,0,7,0,8,5,1,9,0,8,7,1,0,2,5,0,4,6,6,5,3,1,1,8,8,2,2,0, %U A258146 6,4,0,4,7,3,1,5,4,6,9,2,9,8,1,9,7,7,2,3,9,4,4,6,7,4,9,3,8,2,8,0,8 %N A258146 Decimal expansion of (1 - 2/Pi)/2: ratio of the area of a circular segment with central angle Pi/2 and the area of the corresponding circular half-disk. %C A258146 The formula for the ratio of the area of a circular segment with central angle alpha and the area of one half of the corresponding circular disk is (alpha - sin(alpha))/Pi. Here alpha = Pi/2. %C A258146 This is also the ratio of the area of a circular disk without a central inscribed rectangle (2*x, 2*y) together with the two opposite circular segments each with central angle beta and the area of the circular disk. This is the analog of the ratio of the volume of a sphere with missing central cylinder symmetric hole of length 2*y and the area of the sphere. See a comment on A019699. In two dimensions this problem is not remarkable, because the radius R of the circle does matter. The formula is here: area ratio ar = 1 - (beta + sin(beta)/Pi) where beta = arcsin(2*yhat*sqrt(1-yhat^2)), with yhat = y/R, and beta = Pi - alpha from above. %C A258146 The astonishing result from three dimensions, ar_3 = yhat^3, could suggest ar = yhat^2, which is wrong. Thanks to Sven Heinemeyer for inspiring me to look into this. %C A258146 Essentially the same digit sequence as A188340. - _R. J. Mathar_, Jun 12 2015 %H A258146 G. C. Greubel, <a href="/A258146/b258146.txt">Table of n, a(n) for n = 0..5000</a> %H A258146 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CircularSegment.html">Circular Segment.</a> %H A258146 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a> %F A258146 Area ratio ar = (1 - 2/Pi)/2 = 0.181690113816209... %F A258146 For Buffon's constant 2/Pi see A060294. %t A258146 RealDigits[(1-2/Pi)/2,10,120][[1]] (* _Harvey P. Dale_, Sep 23 2017 *) %o A258146 (PARI) 1/2 - 1/Pi \\ _Michel Marcus_, Oct 19 2017 %Y A258146 Cf. A019699, A060294, A258147, A258148. %K A258146 nonn,cons,easy %O A258146 0,2 %A A258146 _Wolfdieter Lang_, May 31 2015