The Geometric principle - As the size of an animal (or any other object) changes, surface increases (or decreases) proportionally to the square of linear dimensions while the volume changes proportionally to the cube of linear dimensions.
I wish to know of any worked examples (in detail) of the Geometric principle. I request any of you to appraise me of workings of this along with practical applications.
Thank you,
Balasubramanya Sharma
Dear Balasubramanya Sharma ,
The answer is yes. The literature is rich in many applications and examples..
For geometric principle, I think you meant the following proportional principle:
Surface area of solid(1)/ Surface area of solid (2) = (length(1)/ length(2) )^2
And
Volume of Solid(1)/ Volume of solid(2) = (length(1)/ length(2) )^3
This works for increasing or decreasing in the total (size change of the original shape ) of an object.
There are many applications in many fields as
(1) Mass and heat transfer.
(2) Metabolic theory of ecology.
(3) Mechanical Engineering.
etc.
See
(*) ecuip.lib.uchicago.edu/diglib/fathom/21701757/indexnew.html
(**) https://en.wikipedia.org/wiki/Square–cube_law
Best wishes
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