cp's OEIS Frontend

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

%I A240969 #27 Jan 17 2020 05:25:15
%S A240969 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 A240969 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 A240969 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 A240969 Decimal expansion of the breadth of the "caliper", the broadest worm of unit length.
%C A240969 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 A240969 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, p. 493.
%H A240969 Jean-François Alcover, <a href="/A240969/a240969.gif">Figure 8.3 A caliper.</a>
%H A240969 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 60.
%F A240969 See trig. formulas in Mathematica code.
%F A240969 Sec(phi), an algebraic number, is the positive root of 3x^6 + 36x^4 + 16x^2 - 64.
%e A240969 phi = 0.29004634452825946320905124629823276955932638591519522257237...
%e A240969 psi = 0.480931237564380337681715512959999015584157793267187574483...
%e A240969 beta = 0.43892536925946645674088526115852377421914938651438872683...
%t A240969 phi = ArcSin[1/6 + (4/3)*Sin[(1/3 )*ArcSin[17/64]]];
%t A240969 psi = ArcTan[(1/2)*Sec[phi]];
%t A240969 beta = (1/2)*(Pi/2 - phi - 2*psi + Tan[phi] + Tan[psi])^(-1);
%t A240969 RealDigits[beta, 10, 100] // First
%Y A240969 Cf. A227472.
%K A240969 nonn,cons
%O A240969 0,1
%A A240969 _Jean-François Alcover_, Sep 04 2014