Beer crate square shape versus rectangle shape I am being asked this question by a consultant to test my logic and I was wondering whether one of you had an interesting mathematical perspective on it:
Why are beer crates usually shaped in rectangles rather than squares? He is asking me whether it would make sense to launch a beer crate that holds 4x4 bottles rather than the usual 3x4 or 4x6. 
Appreciate any thoughts! 
Thanks
 A: Apart from the aesthetics, another factor that plays a role in the shape of the crate/box relates to a twist on the "square/rectangle" packing problem (usually about the maximum number of fixed-sized circles that can be packed (fit) into the square/rectangle) but here, we've got a 3d packing problem, where height is determine by the height of the upright bottles/cans, with the aim to maximize the number upright bottles/cans that can fit into a crate with given dimensions for width and length. 
(In this case, I suspect, to minimize the cost of materials needed to construct the crates (boxes), the crates are usually constructed with the aim being to minimize the surface area of the crate (minimize the material needed) in order to hold a given number of same-sized bottles).
See this interactive demonstration about optimal rectangle for packing circles.
And apart from these considerations, there is also a UX component: "user experience" aspect that takes into account the ease of handling/carrying/storing the crate/box.
A: I think this is related to human perception of "beauty" rather than mathematical optimization. We are inclined to love rectangles whose sides' ratio is roughly the golden ratio $\sim 1.6$.
A: From my point of view, this has more to do with stability: taking a beer crate or any box by its extreme points (so that the distance between points for supporting the item is important) make the whole more stable, especially if some cans are absent from the crate (so the gravity center is not at the geometrical center).
