An algorithm shapes a poem

Mathematics sometimes appears in poetry via patterns that follow the Fibonacci numbers. The pattern of Pascal's triangle also has been used.  In her intriguing collection, Do the Math  (Tupelo Press, 2008),  poet Emily Galvin (now also a California attorney) uses these and more.  Just as Euclid's Algorithm involves an interaction between two numbers, the following poem by Galvin applies the algorithm in a conversation between two voices.

Euclid's Algorithm    by Emily Galvin

These ten scenes happen on the blank stage.

A and B could be any two people, so long as

they've been together for longer than either

can remember.