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

%I

%S 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,

%T 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,

%U 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

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

%C 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.

%C A cubic number with denominator 3. - _Charles R Greathouse IV_, Aug 26 2017

%H W. Lang, <a href="/A246644/a246644.pdf">Notes on Some Geometric and Algebraic Problems solved by Origami</a>

%F s = 0.442493334024442103328... See the comment above.

%o (PARI) polrootsreal(3*x^3-3*x^2+3*x-1)[1] \\ _Charles R Greathouse IV_, Aug 26 2017

%Y Cf. A002580.

%K nonn,cons

%O 1,1

%A _Wolfdieter Lang_, Sep 02 2014

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Last modified September 17 07:35 EDT 2021. Contains 347478 sequences. (Running on oeis4.)