Question #1e5d1

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MeneerNask
Feb 24, 2015

Apparently he did, because #12^3=1728#

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

Say you have a cube of #1xx1xx1# and you compare it to a cube of #nxxnxxn# then:

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

The volume of the greater cube will be #n*n*n=n^3#
Rule 2: if you multiply the length (and width and height) by #n#, then the volume will be multiplied by #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# times the amount of stone blocks.

BTW: Gulliver would need less food, as his skin surface would be only #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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