Paper Bag Surface
An expanded paper bag, cushion, or pillow has a distinctive shape. Given the dimensions of a flat rectangular bag with dimensions a, b, bounds for the maximum volume of closed sack obtained by inflating the bag are approximately given by
![画像: V=a^3[b/(pia)-0.142(1-10^(-b/a))]](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/PaperBagSurface/NumberedEquation1.svg){kind=link}
(Robin 2004).
See also
Chair Surface, Cushion SurfaceExplore with Wolfram|Alpha
WolframAlpha
References
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. Monthly 101, 953-958, 1994.Robin, A. C. "Paper Bag Problem." Math. Today 40, 104-107, June 2004.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, p. 103, 2004. https://www.mathematicaguidebooks.org/.Referenced on Wolfram|Alpha
Paper Bag SurfaceCite this as:
Weisstein, Eric W. "Paper Bag Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PaperBagSurface.html