loki, if you want a direct answer to your question, pi can be expressed as the ratio of the circumference of a circle to its diameter; this comes from rearranging the well-known formula
Code:
circumference = 2 * PI * radius;
therefore
Code:
PI = circumference / (2 * radius);
// or
PI = circumference / diameter;
However, if you wanted to compute pi using this ratio you'd be screwed because to accurately compute the circumference of a circle you need to know pi. You're much better off (from a programming point of view) using Imperito's solution of
Code:
const double pi = 4.0 * atan(1.0);
and just use that computed value of pi for all of your calculations.

If you need a mathematical definition for why this works, here goes (I'll try to keep in mind that you haven't had trig yet). If nothing else this will help you when you do get to trig:

Consider a right triangle (one angle is 90 degrees, the others are arbitrary but must add up to 90 degrees themselves). The tangent of an angle can be defined using this triangle; set one of the other angles equal to the angle that you are trying to calculate, the other to (90 - angle). The three sides of the triangle can be referred to as the adjacent, the opposite, and the hypotenuse:
Code:
         |\
         | \
         |  \  hypotenuse
opposite |   \
         |    \
         |_____\<-- angle of interest
        adjacent
As you can see, the hypotenuse is the longest side and is across the triangle from the right angle, while the opposite is across from the angle you are interested in, and the adjacent is the third side. The tangent function can be defined as the ratio of the lengths of the opposite and the adjacent. Now, a 360 degree angle can also be referred to as 2*pi radians (take my word for it if you aren't familiar with radians, they're another way to talk about angles and I don't have the time to get into it here.) You can't have a right triangle with a 360-degree angle in it, but you can have a right triangle with a 45-degree angle in it (45 = 360 / 8). Since the angles have to add up to 180, that means that the two non-right angles must both be 45 degrees, which means that the opposite and the adjacent angles must be equal, so the tangent of 45 degrees is the ratio of two equal quantities, which is 1.

Still with me? Good. Now, we have the expression tangent(45 degrees) = 1. Since 360 degrees = 2*pi, 45 degrees = pi / 4. We now have tangent(pi / 4) = 1. Here is where the atan function comes in; atan(x) returns "the angle for which the tangent is x". Since we are interested in the angle pi / 4, we take atan(1), and to get pi we multiply by 4. Thus, pi = 4 * atan(1).

A bit long-winded, but I think it will help you considerably when you start studying these things in school.