Prove It

After observing that

               1  =  1
and         1 + 3  =  4
and         1 + 3 + 5  =  9
and         1 + 3 + 5 + 7  =  16
and         1 + 3 + 5 + 7 + 9  =  25

it seems easy to conclude that, for any positive integer n, the sum of the first n odd integers is n².

Graffiti Calculus

     In my dreams I am an artist -- a cartoonist, perhaps, or a graffiti artist -- so skilled with lines and curves and so clever that my art gives pleasure AND delivers a punch.
     And so I am gratefully into the math-art connections provoked by a new book by Mary-Sherman Willis -- aptly titled Graffiti Calculus (CW Books, 2013).  I first met Willis in December, at Cafe Muse (where I will read next Monday, Feb 3 with Stephanie Strickland) and it was my pleasure also to hear her read again from that collection at the Joint Mathematics Meetings.  These poems by Willis give us, in sixty poetic chapters, the story of a mother seeking her son by following his graffiti tags through the city.  Here is a sample, sections 5 and 6: 

If p, then q.

     Today's posting (as also on April 13)  presents variations of the conditional statment -- a sentence of the form "If ___, then ___" in which mathematical theorems often are expressed. (For example, "If m is an odd integer, then m² is an odd integer.")   More generally, a conditional is a statement of the form "If p, then q" -- where p and q denote statements. Poet E. C. Jarvis plays with the language of logical statements and with the idiomatic phrase "Mind your p's and q's" in his poem, "A Simple Proposition." 

Perfect as soap bubbles

An alert to today's poem came from Greg Coxson, a University of Wisconsin-educated, Silver Spring-based, radar engineer who loves mathematics and poetry.  The poem is by Howard Nemerov  (1920-1991) and it builds to a presentation of its perfect mathematical image near its end.  

Goldbach's conjecture -- easily stated but unsolved

This blog's July 20 posting featured work from poets who have spouses or siblings who are mathematicians.  Today, introducing the work of  Michele Battiste (who considers Goldbach's conjecture), we again honor that theme.  Goldbach's conjecture asserts that every even integer greater than 2 can be expressed as a sum of two prime integers.   For example, 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 7 + 3 or 5 + 5, and so on.  The conjecture was first proposed in 1742 by German mathematican Christian Goldbach in a letter to Swiss mathematician Leonhard Euler -- and in 2010--though it has been verified for many, many, many even integers--it still remains unproved. 

Poetry-application of The Fundamental Theorem of Arithmetic

Destructive effects of human greed and neglect on the earth's natural environment are echoed hauntingly in the repetitions within "We Are the Final Ones" -- a dirge-like poem I've constructed using the Fundamental Theorem of Arithmetic.  (For those unfamiliar with the theorem, brief explanation is included in paragraphs that follow the poem):