cp's OEIS Frontend

A256367 Decimal expansion of sec(phi), a constant related to the "broadworm" (or "caliper") problem.

%I A256367 #18 May 27 2025 11:11:05
%S A256367 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,
%T A256367 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,
%U A256367 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
%N A256367 Decimal expansion of sec(phi), a constant related to the "broadworm" (or "caliper") problem.
%C A256367 A cubic number of denominator 3 and minimal polynomial 3x^6 + 36x^4 + 16x^2 - 64. - _Charles R Greathouse IV_, May 13 2019
%D A256367 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, pp. 493-494.
%H A256367 J.-F. Alcover, <a href="/A240969/a240969.gif">Figure 8.3 A caliper.</a> [after Steven Finch]
%H A256367 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 63.
%H A256367 Steven R. Finch and John E. Wetzel, <a href="https://web.archive.org/web/20240530044019/https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Finch645-654.pdf">Lost in a Forest</a>
%H A256367 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>
%F A256367 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.
%e A256367 1.0435901095949847538118417712870227333548896969340378971...
%t A256367 RealDigits[Root[3*x^6 + 36*x^4 + 16*x^2 - 64, x, 2], 10, 103] // First
%o A256367 (PARI) polrootsreal(3*x^6 + 36*x^4 + 16*x^2 - 64)[2] \\ _Charles R Greathouse IV_, May 13 2019
%Y A256367 Cf. A240969, A244046.
%K A256367 nonn,cons,easy
%O A256367 1,3
%A A256367 _Jean-François Alcover_, Mar 26 2015