Square-cube Law

The square-cube law (or cube-square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the area as the shape's size increases or decreases. It was first described in 1638 by Galileo Galilei in his Two New Sciences.

Loosely speaking this principle states that, as a shape grows in size, its volume grows faster than its area. When applied to the real world this principle has many implications which are important in fields ranging from mechanical engineering to biomechanics. It helps explain phenomena including why large mammals like elephants have a harder time cooling themselves than small ones like mice, and why there are fundamental limits to the size one can build a sand castle.