A345736 - OEIS

%I #4 Jun 25 2021 23:17:30

%S 7,5,3,7,8,0,3,2,0,5,8,0,4,5,7,7,9,7,8,8,2,6,5,1,8,2,2,0,6,9,2,8,3,0,

%T 3,4,5,5,1,1,9,3,5,9,2,1,5,2,6,1,1,6,9,3,8,8,4,8,1,3,7,3,1,4,5,1,9,0,

%U 5,0,8,8,8,2,0,4,3,9,2,2,8,2,3,7,3,7,2

%N Decimal expansion of the surface area of the catenoid-shaped soap film between two parallel coaxial unit-radius circular rings whose distance between their centers is maximal (2*A033259).

%H Markus Deserno, <a href="https://www.cmu.edu/biolphys/deserno/pdf/diff_geom.pdf">Notes on Differential Geometry, with special emphasis on surfaces in R^3</a>, 2004. See p. 28.

%H Lev A. Slobozhanin, J. Iwan, D. Alexander and Viral D. Patel, <a href="https://doi.org/10.1063/1.1420736">The stability margin for stable weightless liquid bridges</a>, Physics of Fluids, Vol. 14, No. 1 (2002), pp. 209-224. See p. 222.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalSurfaceofRevolution.html">Minimal Surface of Revolution</a>.

%F Equals 2*Pi*A085984.

%e 7.53780320580457797882651822069283034551193592152611...

%t RealDigits[2 * Pi * x /. FindRoot[x == Coth[x], {x, 1}, WorkingPrecision -> 120], 10, 100][[1]]

%Y Cf. A033259, A085984, A253545.

%K nonn,cons

%O 1,1

%A _Amiram Eldar_, Jun 25 2021