

A193180


The decimal expansion of the value of d that maximizes the expression (1+1/(1d)+1/(12d))*(1+1/(1d)+1/(12d))*(11/(1d)+1/(12d))*(1+1/(1d)1/(12d)) for d in the interval [inf, 1/2] where 1/(1d) and 1/(12d) 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
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OFFSET

0,1


COMMENTS

If the sides of a triangle form a harmonic progression in the ratio 1 : 1/(1d) : 1/(12d) 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



EXAMPLE

0.2158561226...


MATHEMATICA

NMaximize[{Sqrt[(1+1/(1d)+1/(12d))(1+1/(1d)+1/(12d))(11/(1d)+1/(12d))(1+1/(1d)1/(12d))]/4, 0<d<(25/100)}, d, AccuracyGoal>120, PrecisionGoal>100, WorkingPrecision>240]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



