Neka je
unija poligona u trodimenzionalnom prostoru. Znamo da je projekcija
na svaku od ravnina
,
i
kvadrat stranice duljine 1.
Odredite najmanju moguću površinu od .
NAPOMENA: Ovaj je zadatak bio dio MBL QQ 2023.
Let
be a union of polygons sitting inside three dimensional space. We know that the projection of
onto each of the three planes
,
and
is a square with side length 1.
What is the minimal possible area of ?
NOTE: This problem was a part of MBL QQ 2023.
[lang=hr]
Neka je $S$ unija poligona u trodimenzionalnom prostoru. Znamo da je projekcija $S$ na svaku od ravnina $x = 0$, $y = 0$ i $z = 0$ kvadrat stranice duljine 1.
Odredite najmanju moguću površinu od $S$.
\textit{NAPOMENA: Ovaj je zadatak bio dio \href{https://mathsbeyondlimits.eu/wp-content/uploads/2023/04/QQ-Social-Media-Version.pdf}{MBL QQ 2023}.}
[/lang]
[lang=en]
Let $S$ be a union of polygons sitting inside three dimensional space. We know that the projection of $S$ onto each of the three planes $x = 0$, $y = 0$ and $z = 0$ is a square with side length 1.
What is the minimal possible area of $S$?
\textit{NOTE: This problem was a part of \href{https://mathsbeyondlimits.eu/wp-content/uploads/2023/04/QQ-Social-Media-Version.pdf}{MBL QQ 2023}.}
[/lang]