What is the biggest shadow that a cube of side length 1 can have, with the sun at its peak?

Note: "The biggest shadow of a figure with the sun at its peak" is understood to be the biggest possible area of the orthogonal projection of the figure on a plane.

Given the assumptions in the problem, I would think that the max projection would occur when the cube i balanced on a vertex, in such a way that each of the 3 sides that end at that vertex have the same angle to the flat surface that the cube is resting on.

Posted by Kenny M on 2024-01-06 08:04:47