The word proportional is a rather common one. It is used a lot in the context of human height and shape. For example, perhaps you’ve heard a friend say something along the lines of, “She is proportional.” What they might have meant is that the ratio of her leg length to her torso length is what it ought to be. Similarly, her head and feet may look to be the right size for her body, and so on.

With “ought to be” and “right size”, an ideal set of proportions is implied. Leonardo Da Vinci also presents this same implication with his Vitruvian Man. No overall dimensions are specified, but rather only relative dimensions. For instance, the body is eight heads tall. In other words, the height of the head is proportional to the height of the body. Note that the term proportional can be replaced with the symbol ∝ in equations.

To explore proportionality of the human body further, a box can be a useful analogy. Assume length (L) and width (W) are both proportional to height (H). If the height of the box is doubled while maintaining this proportionality, then both length and width must also double as in the figure below.

W ∝ H and L ∝ H.

This is an over simplification of how people scale. Yet this approximation, in conjunction with the square-cube law, is helpful when explaining why the properties of the body change with height.