Minimal Surface of Revolution

Author

Eric W. Weisstein
April 14, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Surfaces/MinimalSurfaceofRevolution.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MinimalSurfaceofRevolution.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Properties

Point of Minimum

Reduce[1==a Cosh[(1/(2a))],a,Reals]

FullSimplify[%]

Subtract@@FullSimplify[-2+2 Cosh[(1/(2 #1))] #1&[x]==0]

FindRoot[-1+x Cosh[(1/(2 x))]==0,{x,.2}]

Surface Area

Reduce[u(Sqrt[(u^2)-1])+ArcCosh[u]-(u^2)==0,u,Reals]

FullSimplify[%]

uu=Last[%]

FullSimplify[((ArcCosh[uu])/uu)]

N[%]

Reduce[u Tanh[u+ArcSinh[(1/(Sqrt[3]))]]==1,u,Reals]

FullSimplify[%]