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
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 04 2014
STATUS
approved