H. Vaughan gave a wonderful proof in 1977. The key is not to consider each point individually, but in pairs. Considering the midpoint and length of the connecting line of each pair of points on the curve, as long as two different point pairs have the same midpoint and equal distance, then the two point pairs form a rectangle. So first draw a picture, put the closed curve on the horizontal plane, and draw a point with a height of |AB| just above the midpoint of each pair of points A and B on the curve to get a three-dimensional picture. This is a surface whose boundary is a closed curve. Therefore, the fact that two point pairs form a rectangle is equivalent to the fact that two point pairs are mapped to the same point on the surface. In other words, as long as it can be proved that the surface is self-intersecting, it is proved that there are two point pairs on the closed curve to form a rectangle.