Maximizing the Area of Polygons via Quasicyclic Polygons-Reference-Cited by-同舟云学术

Maximizing the Area of Polygons via Quasicyclic Polygons

Published:2024-04-15 Issue:1 Volume:61 Page:43-58
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:SScMath

Author:

Anatriello Giuseppina¹,Vincenzi Giovanni²

Affiliation:

1. Dipartimento di Architettura, Università di Napoli, via Via Monteoliveto, 3, I-80134 Napoli, Italy

2. Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, I-84084 Fisciano (SA), Italy

Abstract

Based on Peter’s work from 2003, quadrilaterals can be characterized in the following way: “among all quadrilaterals with given side lengths 𝑎, 𝑏, 𝑐 and 𝑑, those of the largest possible area are exactly the cyclic ones”. In this paper, we will give the corresponding characterization for every polygon, by means of quasicyclic polygons properties.

Publisher

Akademiai Kiado Zrt.

Link

https://akjournals.com/downloadpdf/journals/012/61/1/article-p43.xml

Reference19 articles.

1. [1]G. Anatriello, F. Laudano, and G. Vincenzi. An algebraic characterization of properly congruent-like quadrilaterals. J. Geom. 110:36 (2019).

2. [2]A. Ausserhofer, S. Dann, Z. Lángi, and G. Tóth. An algorithm to find maximum area polygons circumscribed about a convex polygon. Discrete Applied Mathematics, 255:98-108, 2019.

3. [3]P. Dulio and E. Laeng. Generalization of Heron's and Brahmagupta's equalities to any cyclic polygon. Aequationes Mathematicae, 95(5):941-952, 2021.

4. [4]D. Fraivert, A. Sigler, and M. Stupel. Necessary and sufficient properties for a cyclic quadrilateral. Int. J. Math. Edu. Sci. and Technol., 51(6):913-938, 2020.

5. [5]M. Gaeta, and G. Vincenzi. Examples of pairs of ordered congruent-like -gons with different areas. College Math. J., 54(2):99-103, 2023.