A353049 Decimal expansion of 8*sqrt(2) / 3.

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

Offset

1,1

Comments

8*sqrt(2) / (3*a) is the maximum curvature of the Folium of Descartes x^3 + y^3 - 3*a*x*y = 0, occurring at the point M of coordinates (3a/2, 3a/2). The corresponding minimum radius of curvature is (3*sqrt(2))*a/16.

This point M is at the intersection of the first bisector with the loop, distinct from O (see curves).

Links

Table of n, a(n) for n=1..98.

Robert Ferréol, Cartesian folium, Mathcurve.

John A. Tierney, Problem 417, Crux Mathematicorum, Vol. 5, No. 10 (1979), pp. 308-310.

Eric Weisstein's World of Mathematics, Folium of Descartes.

Wikipedia, Folium of Descartes.

Index to sequences related to curves.

Formula

Equals 8*A131594.

Example

3.771236166328253463471169931225...

Maple

evalf(8*sqrt(2)/3, 100);

Mathematica

RealDigits[8*Sqrt[2]/3, 10, 100][[1]] (* Amiram Eldar, Apr 20 2022 *)

Prog

(PARI) 8*sqrt(2)/3 \\ Michel Marcus, Apr 20 2022

Crossrefs

Cf. A295709 (arc length of the loop of the Folium of Descartes).

Cf. A002193, A131594.

Sequence in context: A009467 A258982 A227336 * A288093 A131608 A131707

Adjacent sequences: A353046 A353047 A353048 * A353050 A353051 A353052

Keyword

nonn,cons

Author

Bernard Schott, Apr 20 2022

Status

approved