Remember that the four vertices of the quadrilateral are ABCD, the diagonal intersection is O, the stool is placed on the ground, at least three feet touch the ground, O is the rotation axis, and the initial position of AC is the polar axis. When AC turns to θ, remember that the sum of the distances from A and C to the ground is F (θ), and the sum of the distances from BD to the ground is g(θ). Because there are three feet in contact with the ground at any position, there is always F (θ) *. Obviously, F(θ) is continuous. For the initial position, let F (0) = 0 and G (0) ≥ 0, then F(0)=-g(0). When the stool turns from point D to point A, we can know from symmetry that g(θ)=f(0)=0, so f(θ)≥0.

So F(θ)*F(0)=-g(0)*f(θ)≤0. According to the intermediate value theorem of continuous function, at least one point on [0, θ] makes F(x)=0, that is, f(x)=g(x)=0, so a rectangular stool can always be placed stably.