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 A193180 The decimal expansion of the value of d that maximizes the expression (1+1/(1-d)+1/(1-2d))*(-1+1/(1-d)+1/(1-2d))*(1-1/(1-d)+1/(1-2d))*(1+1/(1-d)-1/(1-2d)) for d in the interval [-inf, 1/2] where 1/(1-d) and 1/(1-2d) are always positive. 1
 2, 1, 5, 8, 5, 6, 1, 2, 2, 6, 1, 1, 5, 1, 8, 2, 0, 1, 1, 8, 1, 4, 9, 7, 1, 0, 5, 7, 1, 6, 2, 7, 8, 3, 0, 3, 2, 9, 7, 7, 4, 0, 9, 9, 4, 8, 6, 4, 4, 6, 5, 1, 7, 2, 4, 4, 4, 0, 3, 0, 9, 4, 4, 9, 5, 8, 7, 1, 6, 9, 0, 4, 3, 0, 1, 6, 5, 7, 3, 5, 8, 7, 8, 5, 3, 0, 5, 5, 7, 5, 3, 8, 7, 2, 4, 9, 5, 9, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If the sides of a triangle form a harmonic progression in the ratio 1 : 1/(1-d) : 1/(1-2d) then when d = 0.2158561226... it uniquely maximizes the area of the triangle. This triangle has approximate internal angles of 33.956, 45.423 and 100.621 degrees. LINKS Table of n, a(n) for n=0..99. EXAMPLE 0.2158561226... MATHEMATICA NMaximize[{Sqrt[(1+1/(1-d)+1/(1-2d))(-1+1/(1-d)+1/(1-2d))(1-1/(1-d)+1/(1-2d))(1+1/(1-d)-1/(1-2d))]/4, 0120, PrecisionGoal->100, WorkingPrecision->240] CROSSREFS Sequence in context: A109233 A257574 A316293 * A201743 A167816 A316292 Adjacent sequences: A193177 A193178 A193179 * A193181 A193182 A193183 KEYWORD nonn,cons,easy AUTHOR Frank M Jackson, Jul 17 2011 STATUS approved

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Last modified May 29 07:13 EDT 2023. Contains 363029 sequences. (Running on oeis4.)