Covering Area in a Disc by Finitely Many Triangles - Chen, Zihao; Ding, Keyan; Huang, Yanzhe; Jia, Xiaojun; Rosenblatt, Joseph; Su, Yuqing; Xue, Jeff (The PUMP Journal of Undergraduate Research, 2025)
We consider how to cover the most area inside of a circular disc by using finitely many triangles. Even in simple cases with the number of triangles being small, we do not know what is the maximum area that can be covered. However, as the number of triangles tends to infinity, we use some estimates and existing literature to derive the rate that the uncovered area goes to zero.