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.
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, 0<d<(25/100)}, d, AccuracyGoal->120, PrecisionGoal->100, WorkingPrecision->240]
CROSSREFS
KEYWORD
AUTHOR
Frank M Jackson, Jul 17 2011
STATUS
approved