A240969 Decimal expansion of the breadth of the "caliper", the broadest worm of unit length.

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

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

Table of n, a(n) for n=0..99.

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 A368551 A175047

Adjacent sequences: A240966 A240967 A240968 * A240970 A240971 A240972

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 04 2014

Status

approved