Quadrature of the parabola with the square pyramidal number. (Quadratura della parabola con il numero piramidale quadrato.) (Italian)

Archimede 66, No. 3, 139-144 (2014).

Summary: Drawing the parabolic segment with the Archimedes triangle, equivalent triangles are detected into the $n\times n$ trapezoids grid; so we can measure a figure circumscribed to the segment and the entire construction triangle. It is seen that these figures contains respectively: $P_n$ (the square pyramidal number) and $n^3$ triangles. For $n$ tending to infinity the ratio of these quantities tends to $1/3$, that proves the Archimedean theorem.