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 A240969 Decimal expansion of the breadth of the "caliper", the broadest worm of unit length. 3
 4, 3, 8, 9, 2, 5, 3, 6, 9, 2, 5, 9, 4, 6, 6, 4, 5, 6, 7, 4, 0, 8, 8, 5, 2, 6, 1, 1, 5, 8, 5, 2, 3, 7, 7, 4, 2, 1, 9, 1, 4, 9, 3, 8, 6, 5, 1, 4, 3, 8, 8, 7, 2, 6, 8, 3, 0, 1, 0, 7, 5, 9, 7, 5, 2, 9, 2, 6, 0, 4, 4, 2, 0, 4, 9, 2, 6, 6, 8, 7, 2, 4, 6, 0, 3, 3, 0, 0, 4, 1, 3, 7, 5, 7, 9, 1, 4, 9, 2, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A caliper consists of 2 circular arcs with 4 tangent segments, specifically configured (see link to Figure 8.3 from the book by Steven Finch). REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, p. 493. LINKS Jean-François Alcover, Figure 8.3 A caliper. Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 60. FORMULA See trig. formulas in Mathematica code. Sec(phi), an algebraic number, is the positive root of 3x^6 + 36x^4 + 16x^2 - 64. EXAMPLE phi = 0.29004634452825946320905124629823276955932638591519522257237... psi = 0.480931237564380337681715512959999015584157793267187574483... beta = 0.43892536925946645674088526115852377421914938651438872683... MATHEMATICA phi = ArcSin[1/6 + (4/3)*Sin[(1/3 )*ArcSin[17/64]]]; psi = ArcTan[(1/2)*Sec[phi]]; beta = (1/2)*(Pi/2 - phi - 2*psi + Tan[phi] + Tan[psi])^(-1); RealDigits[beta, 10, 100] // First CROSSREFS Cf. A227472. Sequence in context: A004125 A137924 A171527 * A198576 A175047 A316688 Adjacent sequences:  A240966 A240967 A240968 * A240970 A240971 A240972 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Sep 04 2014 STATUS approved

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Last modified January 26 08:31 EST 2021. Contains 340435 sequences. (Running on oeis4.)