The mechanics of a thin elastic sheet can be explored variationally, by minimizing the sum of "membrane" and "bending" energy. For some loading conditions, the minimizer develops increasingly fine-scale wrinkles as the sheet thickness tends to 0. While the optimal wrinkle pattern is probably available only numerically, the qualitative features of the pattern can be explored by examining how the minimum energy scales with the sheet thickness. I will introduce this viewpoint by discussing past work on simpler but related problems. Then I'll discuss recent work with Hoai-Minh Nguyen, concerning the cascade of wrinkles observed by J. Huang et al at the edge of a floating elastic film (Phys Rev Lett 105, 2010, 038302).