1. The problem statement, all variables and given/known data This isn't that hard but I cannot remember a nice Calculus way of doing it. I'm trying to find the ratio of height to diameter of a cylinder that produces the minimum material buckling (B_m)^2. The problem statement my professor provided states that the minimum is found at H/D=0.924, but my attempt at substitution has shown otherwise. 2. Relevant equations The formula for material buckling of a cylinder is (B_g)^2 = (2.405/r)^2 + (pi/h)^2 which I have simplified to (B_g)^2 = 4[(2.405/d)^2 + (3.1416/2h)^2] . 3. The attempt at a solution I ran a spreadsheet (attached) which varies the ratio H/D from 0.1 to 1.0. Material buckling decreased even beyond H/D=0.924. I fired up Maple but am not that competent with it so I got nowhere. If anyone has any ideas I would be much obliged. Thanks!