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 462467. 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 equalsized soapbubbles merge into a "doublebubble"? This is the creature studied by Hass andSchlafly. Relying on work of Brian White and Michael Hutchings, they haveshown that this doublebubble 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 computergeneratedpictures of doublebubbles. Allyn Jackson
