Some students love math while others ask, “What is the point of math?” and resent every minute spent on it. This is the first of a series of columns that will explore the usefulness of math–straight from the mouths of students. In today’s column, Maya Gotthard, a competitive swimmer in northern California and an incoming freshman at Woodside High School, shares how understanding the algebra and physics of swimming make her a faster swimmer.

“Most people know that swimming fast takes a lot of practice and energy. During the summer, I swim five mornings a week and will increase to six times a week in the fall. Swimmers spend many hours in the pool building endurance and improving technique, both of which reduce drag. Drag is the force that pushes against and slows a swimmer, and is a major challenge for all swimmers. Unfortunately, swimming faster increases drag, so the swimmer’s goal is to create as little drag as possible.


Maya Gotthard

“The most basic thing a swimmer can do to reduce drag is to wear a cap because it streamlines their shape in the water. Being streamlined reduces surface area, and hair has a lot of surface area. The fast, technical suits the Olympians wear can save a couple seconds in a 100m race, but these suits are expensive and don’t last very long. Not many club swimmers make this investment in gear. Swimmers who compete at high levels will shave all their body hair to remove its drag.

“An example of streamlining is the tight body position a swimmer takes to dive off the starting block and enter the water. The swimmer has less surface area since the legs are pressed together and the arms are pressed straight to the ears with the palms are on top of each other. Most swimmers streamline off the pool wall at the end of each flip turn.

“Competitive swimmers constantly work on their technique. One way to go faster is to increase tempo, which means increasing the number of strokes per lap.

Once tempo is increased, however, drag is increased too. A swimmer may try various techniques to make her stroke more efficient and create less drag.

“How does this relate to math? Here’s the algebraic equation for drag:

Drag = 1/2 * Density * Viscosity * Surface Area * Velocity2

“Density and viscosity are determined by the water, not the swimmer. Velocity is squared, which means that drag increases dramatically as the swimmer goes faster. The equation also shows that as surface area gets smaller, so does the swimmer’s drag. This mathematical explanation shows what a swimmer needs to do to swim faster: reduce surface area and make each stroke efficient. Figuring out this algebraic equation helped me understand how to improve my swimming.”

Ferah Aziz is a college coach with launchphase2. Visit or call 720-340-8111 to learn more about coaching for college bound students, and success coaching for college students. P. Carol Jones is the author of “Toward College Success: Is Your Teenager Ready, Willing, and Able.” Visit to read excerpts and to follow her blog.

Photo Credit: “Swimming” by Jim Bahn. Licensed under CC Attribution 2.0