6 papers
Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover
Zhipeng Deng
Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest pro…
Universal Triangle Covering Curve and Polygonal Chain: Escaping Forest and Fitting Worm
Zhipeng Deng
In this paper, we present a general formulation to address the problems of covering curves and polygonal chains with triangle, and fitting these curves into triangle. These problem…
Proof and More Variations of Bellman's Lost-in-a-forest Problem
Zhipeng Deng
In this paper, based on our previous general formulation and computational solution to Bellman's Lost-in-a-forest Problem, we provide the proof of general solution and obtained mor…
Revisit escape path for infinite unit strip forest and unit broadworm
Zhipeng Deng
Building on our previous general computational solution to Bellman's Lost-in-a-Forest Problem, we present a new approach and analytical formulas for the previously well-known escap…
A General Solution to Bellman's Lost-in-a-forest Problem
Zhipeng Deng
We present a general solution and formulation framework to Bellman's lost-in-a-forest problem. The forest boundary is known and may take any shape. The starting point and the orien…
Solving Moving Sofa Problem Using Calculus of Variations
Zhipeng Deng
In 1966, Leo Moser introduced the "moving sofa problem," which seeks to determine the largest area of a shape that can be maneuvered through a 90-degree hallway of unit-width. This…