Let's face it, we all hate decimals. Especially when it comes to irrational numbers. Who really wants to write something out for infinity when just writing "e" will do the job.

So I was thinking, can we take a decimal approximation and use it to find an irrational number that is near it? Now when I say near, what I mean is that hopefully, we will stumble upon the exact solution, if it is in fact irrational.

Let a, b, c, d, f, g, h, i, j, k, l, m, n, o be integers. A general equation for irrationals I have come up with is:

Which of course doesn't cover all irrationals, but it should cover a heck of a lot of them. If anyone can either:

1. Simplify this so that it includes less variables

2. Find an irrational this does not cover

I've already made code to handle this, although it takes a heck of a long time to run. And that's only for very small values. It was able to find pi and sqrt(pi) already, although those were easy tests. Right now, I'm having it run on

just for kicks, to see if it comes up with anything. For those of you who don't know, we only have an approximation for that summation.

Here is my code: