Mylar balloon (geometry)

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In geometry, a mylar balloon is a surface of revolution. While a sphere is the surface that encloses a maximal volume for a given surface area, the mylar balloon instead maximizes volume for a given generatrix arc length. It resembles a slightly flattened sphere.

The shape is approximately realized by inflating a physical balloon made of two circular sheets of flexible, inelastic material; for example, a popular type of toy balloon made of aluminized plastic. Perhaps counterintuitively, the surface area of the inflated balloon is less than the surface area of the circular sheets. This is due to physical crimping of the surface, which increases near the rim.

"Mylar balloon" is the name for the figure given by W. Paulson, who first investigated the shape. The term was subsequently adopted by other writers. "Mylar" is a trademark of DuPont.