Monday, April 18, 2011

Teaching math with a poem

Sarah Glaz is an algebraist (University of Connecticut) who uses poetry to teach mathematics. At her web page, scroll down to "Recent Articles" to see titles and links to three such papers.   One of the articles is "The Enigmatic Number e: A History in Verse and its Uses in the Mathematics Classroom" -- and it contains an annotated version of the poem whose opening stanzas are found below; it's found in the Digital Library of the Mathematical Association of America (MAA), Loci:  Convergence (April 2010). 

Here are several stanzas of Glaz's poem:

   The Enigmatic Number e      by Sarah Glaz

   It ambushed Napier at Gartness,
   like a swashbuckling pirate
   leaping from the base.
   He felt its power, but never realized its nature.
   e's first appearance in disguise—a tabular array
   of values of ln, was logged in an appendix
   to Napier's posthumous publication.
   Oughtred, inventor of the circular slide rule,
   still ignorant of e's true role,
   performed the calculations.

   A hundred thirteen years the hit and run goes on.
   There and not there—elusive e,
   escape artist and trickster,
   weaves in and out of minds and computations:
   Saint-Vincent caught a glimpse of it under rectangular hyperbolas;
   Huygens mistook its rising trace for logarithmic curve;
   Nicolaus Mercator described its log as natural
   without accounting for its base;
   Jacob Bernoulli, compounding interest continuously,
   came close, yet failed to recognize its face;
   and Leibniz grasped it hiding in the maze of calculus,
   natural basis for comprehending change—but
   misidentified as b.

   The name was first recorded in a letter
   Euler sent Goldbach in November 1731:
   "e denontat hic numerum, cujus logarithmus hyperbolicus est=1."
   Since a was taken, and Euler
   was partial to vowels,
   e rushed to make a claim—the next in line.

   We sometimes call e Euler's Number: he knew
   e in its infancy as 2.718281828459045235.

   On Wednesday, 6th of May, 2009,
   e revealed itself to Kondo and Pagliarulo,
   digit by digit, to 200,000,000,000 decimal places.
   It found a new digital game to play.

   In retrospect, following Euler's naming,
   e lifted its black mask and showed its limit:
   Bernoulli's compounded interest for an investment of one.

   Its reciprocal gave Bernoulli many trials,
   from gambling at the slot machines to deranged parties
   where nameless gentlemen check hats with butlers at the door,
   and when they leave, e's reciprocal hands each a stranger's hat.

   In gratitude to Euler, e showed a serious side,
   infinite sum representation:
   . . .  

"The Enigmatic Number e" continues at Loci:  Convergence.

Sarah Glaz also is an editor (joined by JoAnne Growney) of the poetry anthology, Strange Attractors:  Poems of Love and Mathematics (A K Peters, 2008).

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