How Do You Build the Perfect Sandcastle?
Date published: Aug. 6, 2020
According to a team of University of Dallas juniors — Marie-Therese Aglialoro, William
Kostuch and Cameron Nottingham — there’s an optimal water-to-sand ratio, roughly 6%,
along with a borrowed methodology that’s endured the test of time dating back to the
relics of the Old Kingdom. The students’ research, titled “The Best Sandcastles Are
Egyptian: Pyramids Reign Supreme,” was awarded a Meritorious designation in the International
Mathematical Contest in Modeling (MCM) — a first in university history.
The only U.S. team to receive such designation or higher, the UD castle-building mathletes
placed in the top 8% of 13,749 teams participating in this year’s MCM.
The MCM challenges teams across the globe to clarify, analyze and propose a solution
to their choice of one of three open-ended, real-world problems. Teams develop and
apply mathematical models to solve their chosen problem by utilizing essentially any
available resource — websites, books and articles, computers, and databases.
Each team is given four days to solve their problem, after which they publish a 20-page
research paper that communicates their approach and findings. Teams are awarded one
of five designations: Successful Participant, Honorable Mention, Meritorious, Finalist
Agialoro, Kostuch and Nottingham chose to construct a mathematical model that would
identify the best three-dimensional geometric shape to use as the castle’s foundation.
Each shape underwent the same durability modeling test along the seashore — taking
into account a battering endurance of waves, tides and rainfall.
After determining the optimal sand-to-water mixture for the castle’s foundation, the
team tested their myriad of shapes, including cubes, cylinders, pyramids and cones,
with their mathematical mode. The team then authored a two-page nontechnical summary
suitable for publication in a fictitious vacation magazine.
In their paper, Aglialoro, Kostuch and Nottingham identified the best water-to-sand
ratio by adapting their known results on granular cohesion. The computer model tested
the sandcastle’s strength, providing analysis of collapse due to stress, erosion and
As faculty adviser of nine UD teams to compete in the MCM these past six years, Assistant
Professor of Mathematics John Osoinach, Ph.D., plans to impart the same sort of creative solution thinking to future UD
students. “UD students are very well suited for this contest, as it’s as much about
clear writing as it is about mathematical modeling,” said Osoinach. “It’s an exceptionally
well-written paper that uses mathematics in both practical and creative ways.” Praising
the team’s ingenuity, he added, “Their sandcastle paper will be used as a guide for
future UD teams.”