OFFSET
0,1
COMMENTS
The maximum area is x*/(2*(x^2 + 2)) = 0.154908..., where x is given in the Formula section.
LINKS
Amiram Eldar, Illustration.
Murray S. Klamkin, Problem E 1199, The American Mathematical Monthly, Vol. 63, No. 1 (1956), p. 39; Maximum Area Between a Hanging Chain and Its Chord, Solution to Problem E 1199 by C. M. Sandwick, Sr., ibid., Vol. 63, No. 7 (1956), pp. 495-496.
Wikipedia, Catenary.
FORMULA
Equals arcsinh(x)/x where x = 2.391374... is the positive root of the equation arcsinh(x)/x = 2*sqrt(x^2+1)/(x^2+2).
EXAMPLE
0.67162853059005963017701121889676242415980602507067...
MATHEMATICA
xmax = x /. FindRoot[ArcSinh[x]/x == 2*Sqrt[x^2 + 1]/(x^2 + 2), {x, 2}, WorkingPrecision -> 120]; RealDigits[ArcSinh[xmax]/xmax][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 03 2022
STATUS
approved