id: 06644800
dt: j
an: 2016f.01058
au: Ancora, Luciano
ti: Quadrature of the parabola with the square pyramidal number. (Quadratura
della parabola con il numero piramidale quadrato.)
so: Archimede 66, No. 3, 139-144 (2014).
py: 2014
pu: Le Monnier, Firenze
la: IT
cc: G70 K20
ut: parabolas; triangles; square pyramidal numbers
ci:
li:
ab: 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.
rv: