Mathematics of Securing a Box With a Single Rubber Band

In this article, we study the configuration of a rubber band wrapped around a (sweet) box. The rubber band is a loop trying to attain minimum length. We, therefore, study such curves, also known as closed geodesics, on a cuboid which is the typical shape of such a box. The arguments should be accessible even to a high school student, while the conclusions have elements of surprise and hence interest.