# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Fractal Geometry Gets the Measure of of Life's Scales," by Nigel Williams. *Science*, 4 April 1997, page 34.

In examining the relation between body size and physiology, biologists found that the number 1/4 arises in a rather mysterious way. For example, life span varies in proportion to the 1/4 power of the mass of the organism; similar relations have been found with metabolic rate, age at first reproduction, and duration of embryonic development. What is confounding is the 1/4 power; the 1/3 power would make more sense if the geometry of body size were the main factor. This article describes the work of two ecologists and a physicist who used fractal geometry and hydrodynamics to develop a model for the networks of transport systems in organisms (for example, blood vessels and capillaries). The space-filling properties of certain fractals provided an excellent model for these networks. According to the article, "the model predicted values for the scaling of structural and functional variables that were in close agreement with measured values," including the 1/4-power scaling. The researchers are now looking at ways to further test their model.

*--- Allyn Jackson*