Pin-ended column buckling load is 2.73% lower than Euler's

A verification calculation was aimed at further proving that the least critical load gives the Euler buckling load for a pin-ended column to be : Pcr=(PI)2*EI/L2. Selecting a parabolic function for this purpose, that meets the boundary conditions and is almost exactly similar to the symmetrical function sin(x). It was expected to obtain a critical load that is larger than the load given by the sine function. The parabolic function produced  LOWER CRITICAL LOAD by about 2.73%.