A256367 Decimal expansion of sec(phi), a constant related to the "broadworm" (or "caliper") problem.
1, 0, 4, 3, 5, 9, 0, 1, 0, 9, 5, 9, 4, 9, 8, 4, 7, 5, 3, 8, 1, 1, 8, 4, 1, 7, 7, 1, 2, 8, 7, 0, 2, 2, 7, 3, 3, 3, 5, 4, 8, 8, 9, 6, 9, 6, 9, 3, 4, 0, 3, 7, 8, 9, 7, 1, 0, 6, 5, 8, 9, 3, 0, 6, 7, 0, 3, 3, 5, 5, 3, 4, 3, 4, 8, 9, 7, 2, 3, 7, 0, 4, 6, 9, 9, 3, 1, 7, 0, 5, 3, 3, 9, 9, 6, 4, 1, 8, 2, 8, 5, 6, 2
Offset: 1
Examples
1.0435901095949847538118417712870227333548896969340378971...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, pp. 493-494.
Links
- J.-F. Alcover, Figure 8.3 A caliper. [after Steven Finch]
- Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 63.
- Steven R. Finch and John E. Wetzel, Lost in a Forest
- Index entries for algebraic numbers, degree 3
Programs
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Mathematica
RealDigits[Root[3*x^6 + 36*x^4 + 16*x^2 - 64, x, 2], 10, 103] // First
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PARI
polrootsreal(3*x^6 + 36*x^4 + 16*x^2 - 64)[2] \\ Charles R Greathouse IV, May 13 2019
Formula
Sec(phi) = 1/sqrt(1 - (1/6 + (4/3)*sin((1/3)*arcsin(17/64)))^2), which is the positive root of 3*x^6 + 36*x^4 + 16*x^2 - 64.
Comments