In 1638, Galileo Galilei described a simple law:

The ratio of two volumes is greater than the ratio of their surfaces.

To understand what Galileo was talking about, just imagine a cube. If you double the size of a cube, the surface area increases by the square of the length (2len^{2}) and volume increases by the cube of the length (2len^{3}). The surface area will be 4 times larger (2^{2} = 4) and the volume will be 8 times larger (2^{3} = 8). The ratio of volumes is greater than the ratio of surfaces.

The square-cube law says that as a shape grows in size, its volume grows faster than its surface area. This turns out to be a powerful idea for many scientific fields. For example, in mechanical engineering, it explains why a scale model engine won’t account for the heat loss of a full-scale engine, or why an airplane’s wings need to scale faster than the planes fuselage, or why building taller and taller skyscrapers is increasingly difficult.

Continue reading “Natural Science #12: Square-Cube Law”