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 A193211 The decimal expansion of the value of r that maximizes the Brahmagupta expression Sqrt((-1+r+r^2+r^3)(1-r+r^2+r^3)(1+r-r^2+r^3)(1+r+r^2-r^3))/4 1
 1, 6, 5, 3, 7, 4, 5, 5, 1, 5, 0, 7, 7, 7, 7, 1, 9, 2, 9, 7, 0, 7, 9, 0, 6, 2, 3, 8, 3, 6, 6, 4, 5, 9, 7, 1, 4, 5, 6, 6, 2, 2, 3, 0, 7, 0, 2, 5, 1, 8, 4, 1, 6, 9, 2, 7, 0, 1, 1, 0, 5, 2, 0, 2, 9, 4, 6, 5, 6, 8, 6, 4, 8, 0, 8, 8, 3, 1, 8, 2, 7, 2, 1, 5, 6, 9, 3, 1, 5, 1, 6, 5, 0, 1, 3, 9, 8, 5, 9, 5, 7, 8, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The area of a convex quadrilateral with fixed sides is maximal when it is organized as a convex cyclic quadrilateral. Furthermore in order that a quadrilateral can have sides in a geometric progression 1:r:r^2:r^3 its common ratio r is limited to the range 1/t120, PrecisionGoal->100, WorkingPrecision->240][[2]]][[1]] RealDigits[r/.FindRoot[1+r^2+18r^4+2r^6+5r^8-3r^10==0, {r, 2}, WorkingPrecision -> 120]][[1]] (* Harvey P. Dale, Jan 14 2019 *) CROSSREFS Sequence in context: A143304 A021157 A242494 * A195713 A306712 A109063 Adjacent sequences:  A193208 A193209 A193210 * A193212 A193213 A193214 KEYWORD nonn,cons AUTHOR Frank M Jackson, Sep 08 2011 EXTENSIONS First Mathematica program fixed by Harvey P. Dale, Sep 10 2011 Second Mathematica program added by Harvey P. Dale, Jan 14 2019 STATUS approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)