It was at this point that the simple exercise began to seem more like magic than math. I puzzled over the slices for some time before arranging them in an alternating pattern, one piece pointing up and the next piece pointing down. Finally, they wedged together perfectly, with the curved, scalloped edges forming the long sides of a rectangle. “Done!”
“Very good,” Dad said. “Now, what is the area of a rectangle?”
“Length times width,” I parroted impatiently. But what did the rectangle have to do with the area of the circle? Dad smiled and waited. And just as he expected, something clicked. This had originally been a circle, but it was now reshaped as a rectangle …
Suddenly, it all became clear: the width was r, the radius of the former circle. The length was half of the circumference, or πr. Pi times r times r was … “pi r squared!” I announced, mesmerized by my father’s “trick”–and my very first mathematical derivation.
Dad’s lessons–which were often embedded in discussions of music, finance, history, medicine, genetics, politics, and even sports–have had the power to transcend their subject matter. So it’s not surprising that when I encounter a particularly troubling decision, I still draw on his trusty mathematical advice. First, I list the givens, or what I know to be right and true. As is often the case in algebra, the act of writing down what I do know may be enough to uncover what uncertainties still remain. Next, I’m careful to label all the unknown variables: x, y, z. I draw parallels to connect past circumstances to situations I’m facing in the present. And I never forget to use Dad’s favorite power tool, dotted “auxiliary lines”–which, in life as in geometry, help me extrapolate beyond what’s in plain view, allowing a clearer picture of all the possibilities ahead.
Deborah Pan ‘03, who majored in chemistry and minored in writing, says her father dreamed of attending MIT while growing up in Kaohsiung, Taiwan. Deborah currently works as a medical editor and publications consultant for the pharmaceutical industry.
Hear more from MIT at EmTech MIT.