OFFSET
1,1
COMMENTS
It is assumed that:
all cut edges must be straight-line segments or circular arcs,
the angle between any two cut edges sharing the same point is 120 degrees,
the sum of the curvatures of three cut edges meeting at a point is 0, and
cut edges meeting the unit circle must be perpendicular to the circle.
LINKS
EXAMPLE
3.945702967267185713842899552111799188874835401074741524...
MATHEMATICA
p[x_]:=Sin[x]/(Sin[Pi/3]+Sin[Pi/3-x]); q[x_]:=Sin[Pi/3-x]/(Sin[Pi/3]+Sin[Pi/3-x]); R[x_]:=q[x]/Tan[x/2]; S[x_]:=(Pi/3 - x -p[x]*Sin[Pi/3 -x] + R[x]^2*(x-Sin[x]))/2; d := FindRoot[S[x] - Pi/8, {x, 0.1, 0.5}, WorkingPrecision -> 150]; RealDigits[2*(p[x] + 2*x*R[x])/.d, 10, 100][[1]] (* G. C. Greubel, Jul 02 2019 *)
PROG
(PARI)
default(realprecision, 100);
p(t)=sin(t)/(sin(Pi/3)+sin(Pi/3-t));
q(t)=sin(Pi/3-t)/(sin(Pi/3)+sin(Pi/3-t));
R(t)=q(t)/tan(t/2);
S(t)=( Pi/3 - t - p(t)*sin(Pi/3-t) + R(t)^2*(t-sin(t)) )/2;
d = solve(t=0.1, 0.5, S(t)-Pi/8);
2*(p(d)+2*d*R(d))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Zhao Hui Du, Mar 30 2019
EXTENSIONS
Terms a(32) onward added by G. C. Greubel, Jul 02 2019
Edited by N. J. A. Sloane, Aug 16 2019
STATUS
approved