It's no big surprise that they call it "x squared" when you multiply a
number by itself. After all, when you want to know the area of
a square that's (say) 9 metres wide, then you'd probably work out
9 * 9 = 9^{2}
= 81 square metres as quick as a flash. It's easy to see because you can think of
the big square as nine rows of nine 1metre squares. It works for other shapes as well.
You may know the famous formula for the area of a circle:
pi * r^{2} (where
r is the radius of the circle). Just like the square, if you double the width of
a circle you get four times the area. Or if you make the circle (or
square) nine times as wide then you'll get 81 times
the area.
But there's more to x^{2} than just working out areas. That's me (right)
clinging on to the new sign on the roof of the nightclub. Now obviously, the faster the
wind blows, the harder it pushes on you. But when the wind speed doubles the pressure it
exerts on objects it flows past doesn't merely double; it actually quadruples.
In fact, the wind pressure goes up with the square of wind speed.
That's a very interesting thing to know if you're trying to work out how many nails
will be needed to stop your nightclub sign blowing away. It means, for example, that if
the wind gets 20% faster (that's a factor of 1.2) then the wind pressure will rise by
a factor of 1.2 * 1.2 = 1.44 (ie a 44% wind pressure increase).
And that's just one of many phenomena where you need an x squared to work out
the right answer. Another case is the amount of energy in a bullet from a gun.
This is important because it's a pretty good measure of how much damage the bullet
will do when it hits. The kinetic energy of the bullet depends on it's weight and also
on it's speed. If you triple the weight of your bullet then you'll
triple the amount of energy (if the speed is the same). But if you triple the
speed of the bullet then you'll have nine times as much
energy.
