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Answer 1 · 2015-02-24T09:32:23

Apparently he did, because $12^{3} = 1728$ $12^3=1728$

The scaling law of volume , which is the correct name:

Say you have a cube of $1 \times 1 \times 1$ $1xx1xx1$ and you compare it to a cube of $n \times n \times n$ $nxxnxxn$ then:

The outer surface goes from $6 \cdot 1 \cdot 1$ $6*1*1$ to $6 \cdot n \cdot n = 6 n^{2}$ $6*n*n=6n^2$
Rule 1 : if you multiply the length (and width and height) by $n$ $n$ , then the surface will be multiplied by $n^{2}$ $n^2$

The volume of the greater cube will be $n \cdot n \cdot n = n^{3}$ $n*n*n=n^3$
Rule 2: if you multiply the length (and width and height) by $n$ $n$ , then the volume will be multiplied by $n^{3}$ $n^3$

It is not so strange that Swift should know that, because this was also known by the Egytians. If you make a pyramid twice as high, you will need $2^{3} = 8$ $2^3=8$ times the amount of stone blocks.

BTW: Gulliver would need less food, as his skin surface would be only $12^{2} = 144$ $12^2=144$ as large, so in proportion he would lose less heat.

There are a lot of problems involved in upscaling or downscaling from the 'normal' size. These all have to do with the discrepancy between area-scaling and volume-scaling.

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