Geometry of Trees

     Donna Masini, one of my poetry teachers at Hunter College, offered this rule of thumb for use of a particular word in a poem:  the word should serve the poem in (at least) two ways -- in meaning and sound, or sound and motion, or motion and image, or  . ..  .
     Richard Wilbur (1921 - ) is a former US Poet Laureate (1987-88), a prolific translator, and one of my favorite poets -- and perhaps this is because he seems to maximize his word-choices with multiple uses.  When I read Wilbur, I see and hear and feel -- and, after multiple readings, these sensory impressions coalesce into understanding.  Here is one of his sonnets, a poem of the geometry of absence:

     In Trackless Woods    by Richard Wilbur

      In trackless woods, it puzzled me to find
     Four great rock maples seemingly aligned,
     As if they had been set out in a row
     Before some house a century ago,
     To edge the property and lend some shade.
     I looked to see if ancient wheels had made
     Old ruts to which the trees ran parallel,
     But there were none, so far as I could tell—
     There'd been no roadway. Nor could I find the square
     Depression of a cellar anywhere,
     And so I tramped on further, to survey
     Amazing patterns in a hornbeam spray
     Or spirals in a pine cone, under trees
     Not subject to our stiff geometries.

"In Trackless Woods" is found in Richard Wilbur's Collected Poems, 1943-2004 (Houghton Mifflin Harcourt, 2004). 
Multiple meanings of terms is not obligatory in mathematics as Masini suggested it should be for poetry.  BUT it frequently happens:  mathematics, like poetry, forms connections and patterns.  Indeed, the student who likes and knows mathematics fluently switches from one meaning to another.  The symbol "2" denotes an integer or a rational number or a real number or a complex number.  A real number is a point on a line or an infinite decimal or  a convergent Cauchy sequence or a Dedekind cut.  A function is a rule or a formula or a set of ordered pairs or a graph or  ... . And so it goes.