# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Bubbles and Double Bubbles," by Joel Hass and Roger Schlafly. *The Scientist*, September/October 1996, pages 462-467.

This article discusses a variation of the "isoperimetric problem," an ancientconundrum mentioned in Roman mythology. It asks, Among all shapes of a givenperimeter, which encloses the greatest area? The 19th century mathematicianKarl Weierstrass proved that it is the circle. One can ask the analogousquestion in one dimension higher: Among all shapes of a given surface area,which encloses the greatest volume? The question can be recast this way: Givena certain volume, what is the most efficient way of enclosing it? That themost efficient shape is a sphere was proven in 1882 by the mathematicianHermann Schwarz. One of the expressions of this result in the natural world isthe fact that a soap bubble is spherical. What about when two equal-sized soapbubbles merge into a "double-bubble"? This is the creature studied by Hass andSchlafly. Relying on work of Brian White and Michael Hutchings, they haveshown that this double-bubble is the most efficient way of enclosing two equalvolumes. Their work is an ingenious mixture of mathematical theory andcomputer crunching. Accompanying the article are beautiful computer-generatedpictures of double-bubbles.

*-Allyn Jackson*