Resumen de Beer head with numbers.
The article discusses the application of mathematician John von Neumann's theories on two-dimensional surfaces to three-dimensional microscopic crystal grains. Von Neumann stated changes due to surface tension in any two dimensional region will depend on the region's number of sides. Materials scientist David J. Srolovitz has helped form an equation that uses mean width to determine volume change caused by tension in three dimensions. The equation may help physicists create stronger materials.
