Unlocking the Secrets of Shape Optimization (Spring 2025)


Given a string of length L what is the largest area it can enclose? This problem, known as the isoperimetric problem, has an intuitively simple answer—a circle—which was known since ancient Greece, but it is hard to prove. This shape optimization problem lies at the heart of the calculus of variations and reveals profound connections between geometry, calculus, and the natural world.


We will explore the classical problem above, applications, and any variations you would like. For example, imagine trying to enclose regions with holes, obstacles, or other unexpected challenges—what shapes will emerge? You will be challenged to deepen your understanding of geometry, calculus, and mathematical reasoning. With this project, you will not only grasp the significance of the isoperimetric problem but also acquire their problem-solving skills and mathematical creativity.

For more information contact Thialita M. Nascimento (thnasc@iastate.edu)

People:

Pre-requisites: