An expanded paper bag, cushion, or pillow has a distinctive shape. Given the dimensions of a flat rectangular bag with dimensions , , bounds for the maximum volume of closed sack obtained by
inflating the bag are approximately given by
Baginski, F.; Chen, Q.; and Waldman, I. "Modeling the Design Shape of a Large Scientific Balloon." Appl. Math. Model.25,
953-956, 2001.Mladenov, I. M. "On the Geometry of the Mylar
Balloon." C. R. Acad. Bulg. Sci.54, 39-44, 2001.Paulsen,
W. H. "What Is the Shape of a Mylar Balloon?" Amer. Math. Monthly101,
953-958, 1994.Robin, A. C. Math. Today. pp. 104-107,
June 2004.Trott, M. The
Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 103,
2004. http://www.mathematicaguidebooks.org/.