A240969 - OEIS

%I #27 Jan 17 2020 05:25:15

%S 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,

%T 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,

%U 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

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

%C 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).

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, p. 493.

%H Jean-François Alcover, <a href="/A240969/a240969.gif">Figure 8.3 A caliper.</a>

%H Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 60.

%F See trig. formulas in Mathematica code.

%F Sec(phi), an algebraic number, is the positive root of 3x^6 + 36x^4 + 16x^2 - 64.

%e phi = 0.29004634452825946320905124629823276955932638591519522257237...

%e psi = 0.480931237564380337681715512959999015584157793267187574483...

%e beta = 0.43892536925946645674088526115852377421914938651438872683...

%t phi = ArcSin[1/6 + (4/3)*Sin[(1/3 )*ArcSin[17/64]]];

%t psi = ArcTan[(1/2)*Sec[phi]];

%t beta = (1/2)*(Pi/2 - phi - 2*psi + Tan[phi] + Tan[psi])^(-1);

%t RealDigits[beta, 10, 100] // First

%Y Cf. A227472.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Sep 04 2014