In the mathematical rope cutting problem, a rope with a length of n can be cut into several sections, so that the product of the lengths of these sections is the largest. The solution to this problem is to cut the rope into as many segments with a length of 3 as possible, and merge the remaining segment with a length of 1 or 2 with a length of 3. This conclusion is obtained through mathematical proof, and the specific proof can refer to the knowledge of "mathematical induction" and "mean inequality" in mathematics.

As for why the rope should be folded in half and fall from the middle point, this is because the folded rope can be divided into two pieces of rope with the same length, and then falling from the middle point can ensure that each piece of rope has the same length, so as to maximize the product of each piece of length. If you don't fold in half and fall from the middle point, the length of the two sections may be different, which may affect the correctness of the final result. Therefore, folding the rope in half and falling from the middle point is a common method to solve this problem.