A379565 Decimal expansion of (2/3)*x where x is the real solution of the equation x^2 + 2*sqrt(1 - x^2) = 2*x*(x + arccos(x)).

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

Offset

0,1

Comments

This constant gives an upper bound to the distance between the circumcenter and the centroid of a convex body in the plane divided by the circumradius.

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.19, p. 536.

Links

Table of n, a(n) for n=0..99.

P. R. Scott, Centre of gravity and circumcentre of a convex body in the plane, The Quarterly Journal of Mathematics, Volume 40, Issue 1, March 1989, Pages 111-117.

Example

0.42787339712472801644403700644665265778060759466336...

Mathematica

First[RealDigits[(2/3)x/.NSolve[x^2 + 2Sqrt[1- x^2] == 2x(x+ArcCos[x]), x, Reals, WorkingPrecision->200], 10, 100]][[1]]

Crossrefs

Cf. A244054.

Sequence in context: A128226 A049817 A203575 * A120871 A019689 A332651

Adjacent sequences: A379562 A379563 A379564 * A379566 A379567 A379568

Keyword

nonn,cons

Author

Stefano Spezia, Dec 26 2024

Status

approved