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 A307238 This is claimed to be the minimal cut length required to cut a unit circle into 4 pieces of equal area after making certain assumptions about the cuts (compare A307234). 3
 3, 9, 4, 5, 7, 0, 2, 9, 6, 7, 2, 6, 7, 1, 8, 5, 7, 1, 3, 8, 4, 2, 8, 9, 9, 5, 5, 2, 1, 1, 1, 7, 9, 9, 1, 8, 8, 8, 7, 4, 8, 3, 5, 4, 0, 1, 0, 7, 4, 7, 4, 1, 5, 2, 4, 2, 6, 8, 1, 6, 9, 6, 7, 1, 3, 1, 8, 7, 4, 3, 2, 9, 8, 3, 8, 1, 6, 2, 0, 0, 8, 4, 8, 7, 8, 5, 1, 4, 7, 7, 3, 8, 6, 0, 2, 1 (list; constant; graph; refs; listen; history; text; internal format)
 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 Zhao Hui Du, Picture showing the minimum cut length 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 Cf. A307234, A207235, A307237. Sequence in context: A321120 A243711 A247553 * A161773 A212992 A021721 Adjacent sequences: A307235 A307236 A307237 * A307239 A307240 A307241 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

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Last modified February 3 12:24 EST 2023. Contains 360035 sequences. (Running on oeis4.)