Moving rectangular sofas in planar and spatial corridors
Metric Geometry
2026-04-02 v1
Abstract
We consider eight natural planar corridors, including the standard -shaped one, and characterize the rectangles that can move around their corners. As a bi-product we describe completely the corresponding rectangles with maximum area, as well as the rectangular parallelepipeds with maximum volume that can move around the corners of the spatial analogues of the considered eight planar corridors.
Cite
@article{arxiv.2604.01174,
title = {Moving rectangular sofas in planar and spatial corridors},
author = {Oleg Mushkarov and Nikolai Nikolov},
journal= {arXiv preprint arXiv:2604.01174},
year = {2026}
}