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240 plants vs animals

# 240 plants vs animals - Surface to volume ratio Plants...

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Surface to volume ratio Plants versus animals T. F. H. Allen - U. Wisconsin

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8 Squared and cubed functions 1 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 Double the linear dimensions of a structure with all else equal and the surface area goes up as a squared function (times two gives 4 =2 2 ) while volume goes up as a cubed function (2 times give 8=2 3 ). Intrinsic sticky-togetherness gives a head start, but the volume being cubed will always overtake the surface area, which is only squared. The mass (cubic quantity) will overcome the integrity of the surface holding the volume in against gravity
Forces for stability or destruction Size Intrinsic cohesion Intrinsic cohesion is constant Surface area isa squared function Volume is a cubed function No matter what size intrinsic cohesion (sticky togetherness) stays the same. It gives stability a head start over destruction Surface area grows by a squared function by spreading out weight to relieve pressure. Volume and weight go up with a cubed function. Any cubed function overtakes any squared function even if the squared function has a head start. When this cubed function overtakes the surface area plus cohesion constant, gravity pulls the animal’s inside out through its bottom.

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Plant cells need only small molecules and light and so can live inside a
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240 plants vs animals - Surface to volume ratio Plants...

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