In search of the big bubble.

• Autores: Andrew J. Simoson, Bethany Wentzky
• Localización: Primus: problems, resources, and issues in mathematics undergraduate studies, ISSN 1051-1970, Vol. 21, Nº. 2, 2011 (Ejemplar dedicado a: A Tribute to Brian J. Winkel), págs. 163-174
• Idioma: inglés
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• Resumen

  • Freely rising air bubbles in water sometimes assume the shape of a spherical cap, a shape also known as the big bubble. Is it possible to find some objective function involving a combination of a bubble's attributes for which the big bubble is the optimal shape? Following the basic idea of the definite integral, we define a bubble's surface as the limit surface of a stack of n frusta (sections of cones) each of equal thickness. Should the objective function's variables correspond to the n base lengths of the frusta, then the critical points of the objective function might yield an optimally shaped bubble for which the limit as n ? 8 exists. One simple objective function which appears to model the big bubble is a linear combination of the bubble's upper and lower surface areas. Furthermore, with a computer algebra system, we can see in real time the shape of these critical bubbles as we vary the parameters of the objective function. Such a modeling project is suitable for a vector calculus or numerical methods class.