A133742 - OEIS

%I #20 Sep 29 2024 09:19:51

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

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

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

%N Decimal expansion of cap height at which the area of a circular segment equals 1/4 that of the entire circle.

%D Mutiu F. Erinosho, ET Akinlabi, S Pityana, Effect of scanning speed and powder flow rate on the evolving properties of laser metal deposited Ti-6Al-4V/Cu composites, International Journal of Surface Science and Engineering, Volume 10, Issue 3, 2016; DOI: 10.1504/IJSURFSE.2016.076993 (Mentions this number)

%H G. C. Greubel, <a href="/A133742/b133742.txt">Table of n, a(n) for n = 0..10000</a>

%H Thibaut Dochy and Eszter Dudás, <a href="https://www.researchgate.net/profile/Eszter-Dudas-3/publication/384285218_Thermal_stratification_for_various_design_of_LH2_tanks/">Thermal stratification for various design of LH2 tanks</a>, Int'l Conf. More Elec. Aircraft (2024). See p. 4.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CircularSegment.html">Circular Segment</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Quarter-TankProblem.html">Quarter Tank Problem</a>

%e 0.5960272467004827906810382599336845570977640354259015777499...

%t RealDigits[x/.FindRoot[Pi/4 == ArcCos[1 - x] - (1 - x)*Sqrt[x*(2 - x)], {x, 0, 1}, WorkingPrecision -> 200], 10, 100][[1]] (* _G. C. Greubel_, Nov 16 2018 *)

%t RealDigits[Root[{Pi/4 - ArcCos[1 - #] + (1 - #) Sqrt[(2 - #) #] &, 0.5960272}], 10, 100][[1]] (* _Eric W. Weisstein_, Apr 26 2024 *)

%o (PARI) default(realprecision, 100); solve(x=0,1, acos(1-x) - (1-x)*sqrt(x*(2-x)) - Pi/4) \\ _G. C. Greubel_, Nov 16 2018

%K nonn,cons

%O 0,1

%A _Eric W. Weisstein_, Sep 22 2007