3 papers
math.MG2026
Exact colinearity of centroids of iterated midpoint hexagons
Jack Edward Tisdell
We study the iteration that replaces a planar hexagon by the hexagon formed by joining the midpoints of consecutive edges. While this iteration quickly drives any polygon toward a…
math.MG2025
On the number of defects in optimal quantizers on closed surfaces: the hexagonal torus
Jack Edward Tisdell, Rustum Choksi, Xin Yang Lu
We present a strategy for proving an asymptotic upper bound on the number of defects (non-hexagonal Voronoi cells) in the generator optimal quantizer on a closed surface (i.e.,…
math.LO2025
Solving infinitary Rubik's cubes
Jack Edward Tisdell
We develop infinitary analogues of the Rubik's cube. We'll be pushed to consider the possibility of transfinitely many twists and the foremost question we shall…