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"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 ancient conundrum mentioned in Roman mythology. It asks, Among all shapes of a given perimeter, which encloses the greatest area? The 19th century mathematician Karl Weierstrass proved that it is the circle. One can ask the analogous question in one dimension higher: Among all shapes of a given surface area, which encloses the greatest volume? The question can be recast this way: Given a certain volume, what is the most efficient way of enclosing it? That the most efficient shape is a sphere was proven in 1882 by the mathematician Hermann Schwarz. One of the expressions of this result in the natural world is the fact that a soap bubble is spherical. What about when two equal-sized soap bubbles merge into a "double-bubble"? This is the creature studied by Hass and Schlafly. Relying on work of Brian White and Michael Hutchings, they have shown that this double-bubble is the most efficient way of enclosing two equal volumes. Their work is an ingenious mixture of mathematical theory and computer crunching. Accompanying the article are beautiful computer-generated pictures of double-bubbles.
-Allyn Jackson
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