Authors:
Giuseppina Anatriello Dipartimento di Architettura, Università di Napoli, via Via Monteoliveto, 3, I-80134 Napoli, Italy

Search for other papers by Giuseppina Anatriello in
Current site
Google Scholar
PubMed
Close
and
Giovanni Vincenzi Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132, I-84084 Fisciano (SA), Italy

Search for other papers by Giovanni Vincenzi in
Current site
Google Scholar
PubMed
Close
Restricted access

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.

  • [1]

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

    • Search Google Scholar
    • Export Citation
  • [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, 255:98108, 2019.

    • Search Google Scholar
    • Export Citation
  • [3]

    P. Dulio and E. Laeng. Generalization of Heron’s and Brahmagupta’s equalities to any cyclic polygon. Aequationes Mathematicae, 95(5):941952, 2021.

    • Search Google Scholar
    • Export Citation
  • [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):913938, 2020.

    • Search Google Scholar
    • Export Citation
  • [5]

    M. Gaeta, and G. Vincenzi. Examples of pairs of ordered congruent-like 𝑛-gons with different areas. College Math. J., 54(2):99103, 2023.

    • Search Google Scholar
    • Export Citation
  • [6]

    C. E. Garza-Hume, M. C. Jorge, and A. Olvera. Quadrilaterals and Bretschneider’s Formula. The Mathematics Teacher, 111(4):310314, 2018.

    • Search Google Scholar
    • Export Citation
  • [7]

    M. Hajja and J. Sondow. Newton Quadrilaterals, the Associated Cubic Equations, and Their Rational Solutions. Amer. Math. Monthly, 121:1-16, 2019.

    • Search Google Scholar
    • Export Citation
  • [8]

    D. S. Macnab. Cyclic polygons and related questions. Math. Gaz., 65:2228, 1981.

  • [9]

    I. Newton. Universal Arithmetick, vol. 1, translated by J. Raphson, London, 1720; also available at http://hdl.handle.net/2027/mdp.39015035938995

    • Search Google Scholar
    • Export Citation
  • [10]

    I. Pak. The area of cyclic polygons: Recent progress on Robbins conjectures. Advances in Applied Mathematics, 34:690696, 2005.

  • [11]

    T. Peter. Maximizing the Area of a Quadrilateral. The College Math. Journal., 34:315316, 2003.

  • [12]

    I. Pinelis. Cyclic polygons with given edge lengths: Existence and uniqueness reading a newspaper. J. Geom., 82(1-2):156171, 2005.

  • [13]

    M. Radić. Some inequalities and properties concerning chordal polygons. Math. Inequal. Appl., 2:141150, 1999.

  • [14]

    D. P. Robbins. Areas of polygons inscribed in a circle. Discrete and Computat Geom., 12:223236, 1994.

  • [15]

    D. P. Robbins. Areas of polygons inscribed in a circle. Amer. Math. Monthly, 102(6):523530, 1995.

  • [16]

    I. E. Vance. Minimum Conditions for Congruence of Quadrilaterals. School Science and Mathematics, 82(5):403415, 1982.

  • [17]

    T. G. Will. Pentagons with Permutable Angles. College Math. J., 2023.

  • Collapse
  • Expand

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333
E-mail: smh.studia@renyi.mta.hu

Indexing and Abstracting Services:

  • CABELLS Journalytics
  • CompuMath Citation Index
  • Essential Science Indicators
  • Mathematical Reviews
  • Science Citation Index Expanded (SciSearch)
  • SCOPUS
  • Zentralblatt MATH

2023  
Web of Science  
Journal Impact Factor 0.4
Rank by Impact Factor Q4 (Mathematics)
Journal Citation Indicator 0.49
Scopus  
CiteScore 1.3
CiteScore rank Q2 (General Mathematics)
SNIP 0.705
Scimago  
SJR index 0.239
SJR Q rank Q3

Studia Scientiarum Mathematicarum Hungarica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article (only for OA publications)
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2025 Online subsscription: 796 EUR / 876 USD
Print + online subscription: 900 EUR / 988 USD
Subscription Information Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)