Cube Square Law 

by Dominic Helm


The other night my son, Tom Jr., woke me up in the middle of the night because he was scared of something he saw on television.  Apparently, flipping through the channels, he had stopped on a 1950's B-movie Attack of the Giant Ants!  That night he had nightmares of enormous insects trying to eat him.  I of course laughed and told him that it was impossible for insects to grow into huge sizes.  He asked me why, to which I replied, because of the cube square law. 

The cube square law is, of course, a mathematical principle of proportion.  It says essentially that if an object were to increase proportionally in size, the volume of an object would be proportional to the cube of the multiplier, while the surface area would be proportional to the square of the multiplier.


For example, if you have a perfect cube measuring one unit length on each side.  The volume would be 1 cubic units and an area of 6 square units.  Now, let's say that the cube grew proportionally until the length of the cube had doubled.  The volume for the new cube has multiplied by 8, to 8 cubic units, and the area has multiplied by 4 to 24 square units, even though the length of each side of the cube has only doubled.


This is important because if you were to increase the length of an insect so much that it would be a giant threat to humans, the volume would increase at a much greater rate, thus increasing the weight.  Eventually, the insect would reach a point where its weight was too great for the strength in its legs to handle and it would collapse.  No national guard would need to be called in, as there would be no state of emergency.  Jack Black would then appear and say, "Twas the square-cube law that killed the beast."

I tried to explain this exactly like I did above to Tom Jr., who complained that he just didn't understand.  Two-year-olds can be so dumb sometimes.