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- Mentor: Homin Lee
- Faculty coordinator: TBA
In this project, we will try to understand experiments in billiards on certain shape of tables. There are lots of interesting theorems that depends on the shape of the table. *
In this project, we will try to understand experiments in billiards on certain shape of tables. There are lots of interesting theorems that depends on the shape of the table. *
For instance, if you have square table, then the trajectory is either periodic or move “everywhere”. In other words, the square table is optimal. One can ask whether the same conclusion holds for triangular shape table.
For instance, if you have square table, then the trajectory is either periodic or move “everywhere”. In other words, the square table is optimal. One can ask whether the same conclusion holds for triangular shape table.
We will delve into various questions regarding a behavior of trajectory mainly on squaretiled tables. After that, we also study about billiards on other polygons. Ultimately, we may provide numerical evidences for the open questions, such as characterizing the slope of periodic trajectories in regular heptagon.
We will delve into various questions regarding a behavior of trajectory mainly on squaretiled tables. After that, we also study about billiards on other polygons. Ultimately, we may provide numerical evidences for the open questions, such as characterizing the slope of periodic trajectories in regular heptagon.
Surprisingly, it can be interpreted as in the language of “Riemann surface”. There is a deep and beautiful connection. If time permits, we will see some connections.
Surprisingly, it can be interpreted as in the language of “Riemann surface”. There is a deep and beautiful connection. If time permits, we will see some connections.
*Please read the article in Quanta magazine, “New Shapes Solve Infinite Pool-Table Problem”:
www.quantamagazine.org/new-shapes-solve-infinite-pool-table-problem-20170808/
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