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

Author

Eric W. Weisstein, Sep 22 2007

Keywords

• nonn
• cons

Examples

			0.5960272467004827906810382599336845570977640354259015777499...
		

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

Programs

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 *)

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