Grouping terms in a Karnaugh map

Question

Why do the grouping of minterms in a k-map (Karnaugh Map) need to be rectangular? I have seen that if they're not rectangular then they don't reduce to a single term. I also think I get why the groups of 1's (I'm more comfortable with the Sum-of-Products) need to be a power of 2. But why does the group being rectangular make it work? Any help would be appreciated.

Answer 1

The expression does not necessarily need to simplify to a single term. Hence, it does not always need to be rectangular, it can also be a square.

Example:

This reduces to the SOP form:

$A_1A_0B_0$ (green) + $B_1B_0A_0$ (pink) + $A_1B_1$ (square)