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The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases.
Many of his examples are based on the square–cube law, although he does not use that terminology. The bigger an animal gets, the more it would have to change its physical shape, but the weaker it would become.
Some of the economies of scale recognized in engineering have a physical basis, such as the square–cube law, by which the surface of a vessel increases by the square of the dimensions while the volume increases by the cube. This law has a direct effect on the capital cost of such things as buildings, factories, pipelines, ships and airplanes ...
The ratio between the volumes of similar figures is equal to the cube of the ratio of corresponding lengths of those figures (for example, when the edge of a cube or the radius of a sphere is multiplied by three, its volume is multiplied by 27 — i.e. by three cubed). Galileo's square–cube law concerns similar solids.
An example is found in frogs—aside from a brief period during the few weeks after metamorphosis, frogs grow isometrically. [12] Therefore, a frog whose legs are as long as its body will retain that relationship throughout its life, even if the frog itself increases in size tremendously. Isometric scaling is governed by the square–cube law ...
I noticed that in the wikipedia entry for this law (Square-cube law), no proof of the law is given. I would like a proof that the ratio of the areas and volumes of 2 similar figures is the square and cube of their scale factor respectively. Thanks. 175.156.52.140 00:06, 1 January 2015 (UTC) I think you can just prove that visually.
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Because of the necessary phase change, the expander cycle is thrust limited by the square–cube law. When a bell-shaped nozzle is scaled, the nozzle surface area with which to heat the fuel increases as the square of the radius, but the volume of fuel to be heated increases as the cube of the radius.