PreprintCC BY-SA 4.0arXiv
The Four Periodic Inscription Problem
Abstract
We prove that four periodic curves in ℂ inscribe a family of isosceles trapezoids for every angle θ∈(0,π), whose similarity types are determined by the signed areas between the quotients of the curves in the infinite cylinder. In the smooth case, the problem is identified with a Lagrangian intersection problem in ℝ× S1×ℂ, while the continuous case follows by a convergence argument.
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BibTeX
@misc{sadr2026four,
title = {{The Four Periodic Inscription Problem}},
author = {Ali Naseri Sadr},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24376},
eprint = {2610.24376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24376},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - The Four Periodic Inscription Problem
AU - Ali Naseri Sadr
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24376
UR - https://arxiv.org/abs/2610.24376
AB - We prove that four periodic curves in ℂ inscribe a family of isosceles trapezoids for every angle θ∈(0,π), whose similarity types are determined by the signed areas between the quotients of the curves in the infinite cylinder. In the smooth case, the problem is identified with a Lagrangian intersection problem in ℝ× S^1×ℂ, while the continuous case follows by a convergence argument.
ER -