**ERIC Number:**EJ914739

**Record Type:**Journal

**Publication Date:**2011

**Pages:**12

**Abstractor:**As Provided

**Reference Count:**4

**ISBN:**N/A

**ISSN:**ISSN-1051-1970

In Search of the Big Bubble

Simoson, Andrew; Wentzky, Bethany

PRIMUS, v21 n2 p163-174 2011

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" [arrow right] [infinity] 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. (Contains 8 figures.)

Descriptors: Calculus, Algebra, College Mathematics, Mathematical Concepts, Scientific Concepts, Geometric Concepts, Mathematical Models, Teaching Methods, Mathematics Instruction

Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Higher Education

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A