A246644 Decimal expansion of the real root of s^3 - s^2 + s - 1/3 = 0.

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

Offset: 1

Author

Wolfdieter Lang, Sep 02 2014

Keywords

• nonn
• cons

Comments

In the origami solution of doubling the cube (see the W. Lang link, p. 14, and a Sep 02 2014 comment on A002580) (1-s)/s = 2^{1/3}, or s^3 - s^2 + s - 1/3 = 0 appears, which has the real solution s = (2^(2/3) - 2^(1/3) +1)/3. In the link s is the length of the line segment(B,C') shown in Figure 16 on p. 14.

A cubic number with denominator 3. - Charles R Greathouse IV, Aug 26 2017

Links

• W. Lang, Notes on Some Geometric and Algebraic Problems solved by Origami
• Index entries for algebraic numbers, degree 3

Crossrefs

Cf. A002580.

Programs

Mathematica

First[RealDigits[(2^(2/3) - 2^(1/3) + 1)/3, 10, 100]] (* Paolo Xausa, Jun 25 2024 *)

PARI

polrootsreal(3*x^3-3*x^2+3*x-1)[1] \\ Charles R Greathouse IV, Aug 26 2017

Formula

s = 0.442493334024442103328... See the comment above.