One geometry is not enough

Writer Katharine Merow is in the Publications Department of the Washington DC headquarters of the MAA (Mathematical Association of America) and she is one of the poets who participated in the "Reading of Poetry with Mathematics" at JMM in Baltimore last January.  Here is the engaging poem Merow read at that event -- a poem that considers the 19th century development of new and "non-euclidean" geometries from variants of Euclid's fifth postulate, the so-called parallel postulate:

       Geometric Proliferation    by Katharine Merow

       Saccheri guessed, and Gauss kept mum,
       But Bolyai spread the news:
       What version of the Fifth to take?
       The scholar's free to choose!
       The Russian plumbed the new world,  too,
       Awash in lines estranged:
       A universe devoid of squares,
       With angle sums deranged.
       With Euclid but of many one—
       No longer absolute—
       The pious feared lest God Himself
       Not stand beyond dispute.
       But Riemann—dauntless—forged ahead,
       With constructs as extreme:
       No parallels—it's true—but still...
       A yet coherent scheme!
       Were 'common sense' the 'gospel truth,'
       Were warnings ne'er ignored,
       What vistas would remain unseen,
       What wilds unexplored!

"Geometric Proliferation" was first published in the November, 2007 issue of Math Horizons and is available along with other writing on Merow's webpage.  Here is a link to several of her math-related stories.