Captain Astounding's NIGHTCLUB

x3 : What is it good for?
An example from our book The Power
What is it?
The club
The Staff
The Books
Maths Topics
x2
x3
x4
x5
The Trophy
Shop
Terms & conds
Nice links

All illustrations and text ©Dan Welchman Productions (our publisher). Not to be used or copied without written permission from the publisher.

The cube of a number, x3, is what you get when you multiply a number by itself and then by itself again. For example 43 equals 4 * 4 * 4 which equals 64. Rather like its sibling x2, it's easy to see where x2 gets its name from. If you want to work out the volume of a cube that's 3 metres wide then 3 cubed ( = 3 * 3 * 3 = 27) is the number of cubic metres you're looking for. So the word "cube" crops up straight away.

I'm not denying that x3 is very useful for working out volumes like this. It doesn't need to be a cubist kind of shape either. You might know the famous formula for the volume of a sphere: 4/3 pi * r3 (where r is the radius of the sphere). No matter what 3D shape you choose, if you scale it up evenly by a factor of 2 then it's volume will increase by a factor of 8 (because 23 = 8). But there are hundreds of other uses for x3 that have nothing to do with shapes and volumes.

For instance, here's our bass player, Doug, with his motorcycle. Now not a lot people know this, but the number of horsepower (or kilowatts, for you metric types) that you need to overcome the wind resistance against a bike goes up with the cube of your speed. So you would need 8 times as much power to go twice as fast. To triple your speed you would need a staggering 27 times as much power.

The wind pressure acting on you and the bike only goes up by x squared. when you multiply the speed by a cetain factor x. So doubling your speed makes gives you a four fold increase in wind drag. Thus is discussed on the x2 page. There, we were talking about wind rushing past a stationary object (the nightclub sign) rather than a moving object (the bike) rushing through stationary air. But the principle is the same. But if the bike starts going twice as fast then it also goes twice as far every second. So the engine has to push the bike four times as hard and two times as far. This takes 4 * 2 = 8 times as much energy every second, which also means that eight times as much petrol has to be burned every second. So in the general case, where you want to multiply your speed by some factor of your choice, x, then you have to push the bike x2 time harder and x times further so you'll need an engine that is x2 * x = x3 times as powerful!