N. V. Rasskazova, “Extremal values of the volume of <nobr>$3$</nobr>-dimensional parallelepipeds with a given intrinsic diameter”, Vladikavkaz. Mat. Zh., 2013, Volume 15, Number 4,Pages <nobr>44

Extremal values of the volume of $3$-dimensional parallelepipeds with a given intrinsic diameter

N. V. Rasskazova

Rubtsovsk Industrial Intitute, Branch of Altai State Technical University, Rubtsovsk, Russia

Abstract: It is proved that a parallelepiped with relation $a:b:c=1:1:\sqrt2$ for its edge lengths has maximal volume among all rectangular parallelepipeds with a given intrinsic diameter.

Key words: rectangular parallelepiped, geodesic (intrinsic) diameter, volume.

UDC: 514.17

Received: 18.10.2012