Monday, March 29, 2010

"Mathematical" Limericks

A dozen, a gross, and 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.

Or, (12 + 144 + 20 + 3 x √4) / 7  +  5 x 11  =  9² + 0

The limerick above is attributed to Leigh Mercer. The poetic form called a limerick * might have been named for a city in Ireland. This verse-form was popularized by Edward Lear who is well known for his nonsense verse.

One of the Internet's great resources is the Omnificent English Dictionary In Limerick Form. The OEDILF has for its goal to write at least one limerick for each meaning of each word in the English language. Browsing the OEDILF led me to a "recursive" definition of "destined" by mephistopheles (Limerick #54311):

He awaits incarnation once more,
But his fated rebirth is a chore,
     Since he's destined to make
     The exact same mistake,
Coming back as himself. What a bore!

and a definition of "concentricity" by waterrocks (Limerick #40718):

This design shows two circles, one snared
In the bounds of the other. They're paired
     With enchanting simplicity
     And suave concentricity:
Two circles, one centre that's shared.

Philip Heafford (in The Math Entertainer (Emerson Books, 9th edition, 1976)) used limericks to pose mathematical puzzles. Here are two samples from his collection:

Said a certain your lady called Gwen
Of her tally of smitten young men,
     "One less and three more
     All divided by four
Together give one more than ten."

     How many boyfriends had Gwen?

Some freshmen from Trinity Hall
Played hockey with a wonderful ball;
     They found two times its weight,
     Plus weight squared minus eight,
Gave "nothing" in ounces at all.

     What was the weight of the ball?

*For review, here is the DEFINITION of limerick: A LIMERICK is a light humorous, nonsensical, or bawdy verse of five lines usually with the rhyme scheme aabba. Rhyming lines 1, 2, and 5 contain three anapests (that is, sequences of three syllables with an accent on the third syllable); lines three and four contain two such sequences. (Often the accent pattern varies a bit from the definition; for example, a line may being with only one non-accented syllable.) To find additional examples, a Google-search for "mathematical limericks" yields a plenitude of sources. For example, Randall Munroe of maintains a limerick database. Enjoy!


  1. Thanks for calling our attention to the Limerick Dictionary.

    I found this one in the dictionary:

    Limerick #13399 binomial
    By Bob Dvorak
    Revised: 12 Nov 2005



    Our prof summoned all her persuasion
    In algebra class, that occasion:
    "To an x you apply
    Plus or minus a y,
    To create a binomial equation."

    David Perrings

  2. Google's omnipotent search engine can "solve" this limerick automatically by entering the following slightly modified verse (copy and paste into the Google search bar):

    (a dozen, and a gross, and a score plus three times the square root of four) divided by seven plus five times eleven

    This is an example of machine intelligence in computer handling a non-numerical as well as a numerical task.