Geometric reason for 3/4-power growth rate? It seems pretty well established that organisms grow
according to a 3/4-power law.
For example,
Niklas and Enquist, in their paper
"Invariant scaling relationships for interspecific plant biomass production rates and body size,"
PNAS 2001, 98(5):2922
-2927, say:

Annualized rates of growth $G$ scale as the 3/4-power of body mass $M$ 
  over 20 orders of magnitude of $M$ (i.e., $G \propto M^{\frac{3}{4}}$).

Does anyone know if there is some geometric reason to expect such
a growth-rate law?
$$\frac{d M}{d t} \sim M^{\frac{3}{4}}$$
Apparently attempts to derive this growth-rate law from
Kleiber's Law, which 
claims that metabolic rate scales
as $M^{\frac{3}{4}}$, are controversial.
So I was wondering if there might be some geometric viewpoint
that makes growth proportional to $M^{\frac{3}{4}}$ not unexpected.

h=height, M=mass, A=cross-sectional area of stem d=density of stem V=volume of plant
The total cross-sectional area of a plant remains roughly the same at the top as at the bottom. (Da Vinci's rule).
Plants collect light for photosynthesis along their cross-sectional area. 
The thickness of stem A needed to support a plant is proportional to $h^3$.
$A\propto h^3$
$M = Ahd$
$A \propto M^{3/4}$
growth rate $\propto$ area exposed to the sun for photosynthesis $\propto \frac{V}h \propto A$
