We were discussing "Limericks" in my Calculus class. Specifically, "equation Limericks".

A Limerick is a poem with five lines.

The first, second, and fifth lines should have nine syllables each and rhyme with each other,
and the third and fourth should have six syllables each and rhyme with each other.

An obscure subtype of the limerick is the "equation Limerick", which states an equation.

Here are some examples given in class:

enter image description here

A dozen, a gross, plus a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared (and not a bit more).

enter image description here

The integral tee squared dee tee
From one to the cube root of three
Times the cosine
Of three pi over nine
Is the log of the cube root of e.

enter image description here

The log of e to the four
Times the square root of ten twenty-four
Adding six dozen please
Minus eight twenty-three's
Is sixteen, case is closed, shut the door.

I was able to come up with a couple of my own Limericks, but they are a bit simple compared to the ones above.

Surprisingly, there are not many resources online regarding equation Limericks. Can anyone come up with their own that they would like to share?

  • 2
    $\begingroup$ This is a fantastic post and the limericks are really clever. I pity the downvoter for his lack of humour (but, alas, I'm not surprised...) $\endgroup$ Nov 22, 2013 at 18:58
  • $\begingroup$ I attempted to fix two typos: 'lon' --> 'log' and 'en' --> 'ten', but the system wouldn't let me, saying that edits have to be at least 6 characters. $\endgroup$
    – user584285
    Nov 24, 2018 at 18:29
  • $\begingroup$ math.stackexchange.com/questions/1692395/mathematical-limerick $\endgroup$
    – user584285
    Nov 24, 2018 at 18:37

7 Answers 7


WARNING: What you see below is my first-ever attempt at poetry in English.

My take on the classics: $e^{\pi \cdot 2i} = 1$.

We start with the constant called $\pi$ / And then multiply by $2i$ / Apply exponential / (This step is essential) / And one's the result who-knows-why!

  • $\begingroup$ Wow, that's amazing! Great work Dan! However, it seems like your first, second, and fifth lines have 8 syllables instead of 9. Regardless, I still like your first-ever attempt at poetry. $\endgroup$
    – Matthew
    Nov 23, 2013 at 2:24
  • 3
    $\begingroup$ Close enough. After all, 9-8=1 is a famous result in diophantine equations. $\endgroup$ Nov 23, 2013 at 5:42
  • 1
    $\begingroup$ @Zelent they do have 8 syllables. In my defense, so does the first example in the original post )) $\endgroup$
    – Dan Shved
    Nov 23, 2013 at 6:19
  • $\begingroup$ Good point Dan. I looked into Limericks in more detail, and it seems like there are different interpretations for the structure. For example, one source I found said the first, second, and fifth lines had to have nine syllables. Another source stated they had to have seven to ten. I assume the writer of the first example based it off the second variation. $\endgroup$
    – Matthew
    Nov 23, 2013 at 15:08
  • $\begingroup$ Maybe the common thread is the number of stressed syllables per line being 3,3,2,2,3. At least this seems to fit most I've seen, without necessarily counting syllables. There once was a seaman named Cass, etc starts with 8 syllables but conforms to the 3 long syllables in the first line. (This is a somewhat "dirty" limerick, and it's in some collections.) $\endgroup$
    – coffeemath
    Nov 23, 2013 at 18:04

Take two thousand one ninety seven,

Find cuberoot and add to eleven.

Now divide this by eight,

And get almost by fate

The number of vowels in "heaven".

[equation $(\sqrt[3]{2197}+11)/8=3.$]

  • 1
    $\begingroup$ This ones great too. I particularly like the last line. $\endgroup$
    – Matthew
    Nov 23, 2013 at 15:11

Based on the first limerick (this one is not a limerick, just saying)

Take a baker's dozen,

Multiply it by a regular dozen,

Add one and divide by seven,

Multiply by eleven

You will get one-ninety-seven

And a dozen.

$(((13 * 12) + 1)/7) * 11 = 197 + 12$


e ^(π×2 i) = -e^( i π)

The product of pi and 2i
- though only a scholar knows why -
as the power of e
Just so happens to be
negative e to the i pi

$\int_{0}^{\pi/6} {sec}\ {y}\ dy = \ln \sqrt{3}\ (i)^{64}$

"The integral sec wye dee-wye
From zero to one sixth of pi,
is the log to base e
of the square root of three
times the sixty fourth power of i."

Five times the cube root of eight, times three now that is pretty great, plus eight and eleven, the square root is seven, plus eleven is ten and an eight.


You start out with seventy-four, take eleven away from a score. If then you divide and set eight aside, you'll have half of point infinite fours

74/(20-11)-8 = 0.444.../2


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