Because the cross-sectional area of any vessel is proportional to the square of its radius, another way of expressing this result is to say that the square of the radius of the parent tube has to be just twice the square of the radius of each of the daughters. So to ensure that there is no energy loss via reflections as one progresses down the network, the radii of successive vessels must scale in a regular self-similar fashion, decreasing by a constant factor of the square root of two (√2) with each successive branching.
