Retired Arkansas law professor (and former math teacher) Robert Laurence has fun with this pair of transcendentals using limerick stanzas. Get out your pencil and graph paper -- and enjoy puzzling through his rhymes.
A Transcendental Proof in Six Stanzas
by Robert Laurence © 2018
They are transcendent you see:
eπ and πe.
The prize you’ll win when,
With pencil or pen,
“I’m sure against Gauss it’s a sin,
But I don’t know where to begin.”
No need to squirm,
Take the ln of each term.
And I’ll show you the way you can win.
e ‧ ln π is the key.
Is it smaller than π? Well, let’s see.
f is e ‧ ln x,
And g is just x.
From there it’s simple. Trust me.
“Simple? Is that what you meant?”
Yes, the curves are at one point tan-gent.
The point is (e,e),
So now do you see,
That f below g is all bent?
“All bent?” you ask with a frown.
“You must think I’m some sort of clown.”
Forgive me my crime.
I was trying to rhyme.
And the curve is concave down.
Forget my original plea.
These rhymes have been all about me.
What’s done is what’s done;
I’ve spoiled all the fun:
The smaller is πe.