A flat, two-dimensional map of the spherical Earth must introduce some sort of distortion; though Carl Friedrich Gauss proved it nearly two centuries ago, cartographers have confronted the matter for some two millennia. The converse—covering a curved substrate with a 2D sheet—is also of technological and practical relevance, be it in depositing thin films, measuring materials properties, covering knuckles with bandages, or wrapping a snow globe to give as a gift. (See Physics Today, May 2012, page 15.) That problem is an active area of research, and Jérémy Hure (ESPCI ParisTech) and colleagues have recently approached it using a planar, elastic sheet on an adhesive, rigid sphere.
The image, 80 mm across, shows how a thin, 15-µm-thick sheet of polypropylene deforms on a sphere of radius 60 mm (the extent of the sphere is visible in the image’s corners). Yellow dye outlines the regions where the sheet...
