OFFSET
0,1
COMMENTS
If the side lengths of a triangle form a harmonic progression in the ratio 1 : 1/(1+d) : 1/(1+2d) where d is the common difference between the denominators of the harmonic progression, then when d = 0.290772978969... it forms a unique right triangle. The angles (in degrees) are approximately 39.2195, 50.7805, 90.
FORMULA
d as given by the real positive root of 4*d^4 + 12*d^3 + 8*d^2 - 1 = 0.
EXAMPLE
0.29077297896941138371325966971645222964831895500614673035846014851282...
MATHEMATICA
N[Reduce[-1+8d^2+12d^3+4d^4==0, d], 100]
RealDigits[x/.FindRoot[4x^4+12x^3+8x^2-1==0, {x, .2}, WorkingPrecision-> 120]][[1]] (* Harvey P. Dale, Feb 15 2015 *)
PROG
(PARI) polrootsreal(4*x^4+12*x^3+8*x^2-1)[2] \\ Charles R Greathouse IV, Apr 15 2014
CROSSREFS
KEYWORD
AUTHOR
Frank M Jackson, Aug 02 2011
STATUS
approved