2020/02/07 by Chenguang Zhang, Zhang, Chenguang · 1 voice
Engineering · Computer Science · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2002.02622
The article explores a simple yet interesting geometric problem: how to fold a notebook page so it is the most visible when the notebook is closed (i.e., as a bookmark). We start with a square page, then proceed to the rectangular page. When an additional constraint is added to limit the vertical extent of the rectangular page, the problem shows the first-order phase transition: the optimal way of folding changes drastically when the aspect ratio of the page exceeds the critical value of about 1.20711.