A133742 Decimal expansion of cap height at which the area of a circular segment equals 1/4 that of the entire circle.

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, 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, 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

Offset

0,1

References

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)

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Thibaut Dochy and Eszter Dudás, Thermal stratification for various design of LH2 tanks, Int'l Conf. More Elec. Aircraft (2024). See p. 4.

Eric Weisstein's World of Mathematics, Circular Segment

Eric Weisstein's World of Mathematics, Quarter Tank Problem

Example

0.5960272467004827906810382599336845570977640354259015777499...

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A010720 A094389 A057821 * A134879 A051158 A117605

Adjacent sequences: A133739 A133740 A133741 * A133743 A133744 A133745

Keyword

nonn,cons

Author

Eric W. Weisstein, Sep 22 2007

Status

approved