I’m no math genius. I’d love to understand it all, and I appreciate the complexities, but I’m just the noob first-time player walking across a field in Call of Duty where I’m a target to all the more experienced players. In short: The study of compound interest eventually gives rise to the mathematical concept of e, also known as Euler’s number.

Like π, e is an irrational, transcendental number that has properties so compelling that it would qualify as the centerfold for the math geek’s version of Playboy.

The most important thing I know about e is that it’s often called Euler’s number, after Swiss mathematician Leonhard Euler. And the most important thing about that knowledge tidbit is knowing that “Euler” is pronounced “Oiler.”

e is a constant: 2.718282… It’s considered the sum of an infinite series, which means that you can keep making specific calculations long enough that the total eeks up to the value of e.

This concept plays into the notion of compound interest (covered in last week’s Lesson), because as you continue to compound and compound, you end up with the value 2.718282… Centuries ago, mathematicians discovered this effect and they haven’t shut up about it since.

The following code is a variation on the compound interest calculation presented last week. It’s a type of infinite series, where values keep getting larger but the result eventually settles on a specific number, e:

#include <stdio.h>
#include <math.h>

int main()
{
    long n;
    float p;

    for(n=1;n<100000;n+=1000)
    {
        p = pow( ( 1.0 + (1.0/n) ), n );
        printf("%f\n",p);
    }

    return(0);
}

The function on Line 11 of the code is similar to the compound interest function described in last week’s Lesson. The term variable t is missing (or assumed to be 1) and the rate is set to 1, so it’s not shown. Figure 1 illustrates how the math geeks write it (two ways).

Figure 1. Two different ways that the value of e is calculated.

The output is 100 lines long, and the first few lines jump the value pretty close to e:

2.000000
2.716925
2.717603
2.717829

As the value of variable n increases, the output gets closer:

2.718267
2.718268
2.718268
2.718268
2.718268

The C library function log() is the natural logarithm, which uses e as the base. The concept completely befuddles me, though I’ve used the log() function to realistically animate a bouncing ball. I’m sure the log() function has other uses that would delight the propeller heads.

Mathematically, if you take e^e you get 15.154262. The natural logarithm of that value is e, which the following code proves:

#include <stdio.h>
#include <math.h>

int main()
{
    printf("e = %f\n",log(15.154262));

    return(0);
}

The log() function requires the math.h header file, included at Line 2. Here’s the output:

e = 2.718282

And that’s as far as I dare tread over the deep waters of mathematics.