INSPIRATION OF A SHEET OF A4 PAPER¹⁾

In order to explain the phenomenon that "a sheet of printing paper cannot be erected, while a certain degree curved one can" in terms of mechanics, the geometric properties of the cross section under two different states are analyzed to form a formula for the principal centroidal moments of inertia, which is verified by numerical simulations. The stability of the sheet of paper or a curved one is reduced into the stability of a column under its own weight. It is found that the curvature of the arc has a great influence on the stability. When the arc is 2.52, the critical value of the evenly distributed axial load of the cylindrical A4 paper is about 3.7\times10^5 times of that of the planar one.