(caveat lector : there may already be a node about this (I did look!))

An important concept to keep in mind when considering the size and shape of things - animals, plants, silicon chips etc. The easiest way to show the relationship between area and volume is to calculate it for several different cube shapes:

length of side  area          volume          SAVR
      1        6*(1^2) = 6  (1^3) = 1          6:1
      2        6*(2^2) = 24 (2^3) = 8          3:1
      3        6*(3^2) = 54 (3^3) = 27         2:1
      4        6*(4^2) = 96 (4^3) = 64       1.5:1
So, the SAVR (is it usually called SAR?) decreases quite quickly as the length of the cube's side increases. This principle is behind calculations of dinosaurs metabolic rates (poikilotherms etc) and why natural objects are often fractal. Consider, for example, a leaf that has just caught your eye which happens to be square and 1mm on a side. You live in MathsWorld, perhaps. Anyway, say the cells are 1µm cubes and the leaf is three cells thick. Under a microscope, you split it carefully so that the inside is revealed (mwhuhahah!) to see that it has veins in a cross shape
                ___________________________
               |            | |            |
               |____| |_____| |____| |_____|
               |____   _____   ____   _____|
               |    | |     | |    | |     |
               |____________| |____________|
                                           |
                ____________   ____________|
               |            | |            |
               |____| |_____| |____| |_____|
               |____   _____   ____   _____|
               |    | |     | |    | |     |
               |____________|_|____________|

(this so won't come out right) The branches divide and divide until every cell in the middle layer is equally supplied with fluid. The ratio of cells to space is roughly 2:1, and if at least one of the surfaces of each cell is exposed to the sap the SAVR is one. Essentially, the leaf is a one dimensional object (a line) rolled up into a two dimensional one (plane). Obviously, the cubic cell itself is 3D - but their arrangement compromises between 2D (light capture -> surface) and 1D (gas exchange ->).Hmm, bit off topic perhaps.

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