Wild Guess

Tune: original

A song about the <a href=”http://en.wikipedia.org/wiki/Euler-Mascheroni_constant#Properties”>properties of the Euler-Mascheroni constant</a>

If you sum one over k,

And you just won’t stop at all

It will not stop on its way,

Though it rises at a crawl

If you subtract a log, base e

At each step along your path

It converges you will see

Take time to do the math!

Gamma is the limit’s name

It’s easy to approximate

But you cannot hope to claim

We know something of its fate

Our math is still not quite enough

To know its properties, you see

But here’s a guideline that is rough

And I hope you will agree

[Chorus]

You should know the odds if you have to bet

And the odds are a zero to one

So I’m gonna say no, though I’m gonna sweat

For a shred of a proof I have none

Can we find two numbers whole

Their division to be this

If this is to be your goal

Your hope and prays I will dismiss

Rationality is rare

It is much too much to hope

And though I did not say its fair

I am going to say “nope”

[Chorus]

If it’s irrational, you see

Still polynomials abound

Whose co-efficients are in Z

Perhaps one of them can be found

Such that one among its roots

Is this Gamma that we seek

My guess it will bear little fruits

Though my arguments are weak

[Chorus]

Algebraic over pi

Or algebraic over e

Oh, tell me, why you try

Why you cannot let this be

It’s so easy just to guess

To just give up and say “no”

We are not assured success

Though the odds are good, you know

[Chorus]