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 A133741 Decimal expansion of offset at which two unit disks overlap by half each's area. 1
 8, 0, 7, 9, 4, 5, 5, 0, 6, 5, 9, 9, 0, 3, 4, 4, 1, 8, 6, 3, 7, 9, 2, 3, 4, 8, 0, 1, 3, 2, 6, 3, 0, 8, 8, 5, 8, 0, 4, 4, 7, 1, 9, 2, 9, 1, 4, 8, 1, 9, 6, 8, 4, 4, 5, 0, 0, 1, 9, 5, 2, 0, 3, 4, 6, 7, 7, 4, 1, 0, 9, 9, 9, 4, 2, 5, 9, 0, 7, 0, 7, 0, 0, 2, 4, 8, 6, 7, 8, 0, 3, 3, 0, 4, 4, 5, 4, 5, 7, 4, 1, 8, 9, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Circle-Circle Intersection FORMULA Equals sqrt(1+A003957) - sqrt(1-A003957) = sqrt(2-2*sqrt(1-A003957^2)) = 2*A086751. - Gleb Koloskov, Feb 26 2021 EXAMPLE 0.8079455065990344186379234801326308858044719291481968445... MATHEMATICA d0 = d /. FindRoot[ 2*ArcCos[d/2] - d/2*Sqrt[4 - d^2] == Pi/2, {d, 1}, WorkingPrecision -> 110]; RealDigits[d0][[1]][[1 ;; 105]] (* Jean-François Alcover, Oct 26 2012, after Eric W. Weisstein *) PROG (PARI) default(realprecision, 100); solve(x=0, 1, 2*acos(x/2) - (x/2)*sqrt(4-x^2) - Pi/2) \\ G. C. Greubel, Nov 16 2018 (PARI) d=solve(x=0, 1, cos(x)-x); sqrt(2-2*sqrt(1-d^2)) \\ Gleb Koloskov, Feb 27 2021 CROSSREFS Cf. A003957. Equals twice A086751. Sequence in context: A183001 A262522 A174849 * A066606 A048729 A003131 Adjacent sequences:  A133738 A133739 A133740 * A133742 A133743 A133744 KEYWORD nonn,cons AUTHOR Eric W. Weisstein, Sep 22 2007 STATUS approved

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Last modified May 12 13:46 EDT 2021. Contains 343823 sequences. (Running on oeis4.)