AMDD x AWM: Playing Billiards with Maryam Mirzakhani

This booth is sponsored by the Student Chapter of the Association for Women in Mathematics at the University of Arkansas.

If you shoot a pool ball, which pocket will it end up in? The answer to this question can be found by “unfolding the table”! What happens if we change the table shape? A table has optimal dynamics if any trajectory either repeats or cover the whole table. Standard rectangular tables are optimal… but so are other shapes! Which pool table shapes are optimal? This question was studied by the first woman Field’s Medalist Maryam Mirzakhani who with her coauthor Alex Wright discovered two completely new optimal tables in 2014. 

Videos:

• Donald Duck plays Billiards: https://www.youtube.com/watch?v=cdVRvYnqj6w
• About Maryam Mirzakhani: https://www.youtube.com/watch?v=QbHff-1-Icc

Additional Resources:

• Quanta article explaining Mirzakhani’s work on Billiards: http://: https://www.quantamagazine.org/new-shapes-solve-infinite-pool-table-problem-20170808/
• A billiards simulator: https://scratch.mit.edu/projects/152682559/
• A lesson plan on billiards: https://mathforlove.com/2023/02/the-award-winning-lesson-plan-the-billiard-ball-problem/

Technical Resources:

• A survey paper on Mirzakhani’s work on Billiards by Wright: https://www.ams.org/journals/bull/2020-57-03/S0273-0979-2020-01687-3/S0273-0979-2020-01687-3.pdf