Mathematics & Poetry
Written by Alexis Haley
Prove root two is irrational number.
Assume root two is not irrational.
Root two is p o’er q, both integer.
Note, no common factor in fractional.
Let’s square both sides; multiply by q-squared.
Then see p-squared is an even number.
r an integer, p is 2r paired.
Substitute 2r for p, don’t encumb’r.
This means 2 r-squared is q-squared, but wait!
Then q-squared is now an even number.
q must be an even number. It’s fate!
We see p and q both even numbers.
p, q share a common factor nicely.
We reached a contradiction, finally!
“Hillsdale is all about the liberal arts education. How do the natural sciences relate to the humanities? And where do the arts and the social sciences fit into the mix? How do you relate mathematics to literature?”
Well, Dr. Gaebler might have found the answer. In his Math 403: Real Analysis course this semester, he offered an extra credit opportunity. Write a poem – a haiku, a limerick, or a sonnet – that encompasses some aspect of what we have learned so far this semester.
Thus, I present to you “Sonnet √2,” a proof of the irrationality of the square root of two, written in true Shakespearean style. We start by assuming that the square root of two is a rational number. That is, a number that can be written as a fraction. The proof then contradicts its assumptions, showing that the square root of two must indeed be an irrational number.
I’ll admit, my rhymes aren’t perfect. And for that reason, I’m sure the English department is grateful that I chose to major in math. That being said, it takes a special kind of school, and a special kind of professor, to encourage opportunities like this. At Hillsdale, we study the field we love, and we gain a deeper appreciation for the others through the process.
Alexis Haley is a senior majoring in mathematics. She is a member of two math and science honor societies, and she volunteers with Big Brothers Big Sisters and Domestic Harmony. When she graduates, she plans to join the United States Navy.