Magic Polygons and Degenerated Magic Polygons: Characterization and Properties

Main Article Content

Danniel Dias Augusto
Josimar da Silva Rocha


In this work we define Magic Polygons P(n, k) and Degenerated Magic Polygons D(n, k) and we obtain their main properties, such as the magic sum and the value corresponding to the root vertex. The existence of magic polygons P(n, k) and degenerated magic polygons D(n, k) are discussed for certain values of n and k.

Combinatorics, magic polygons, degenerated magic polygons.

Article Details

How to Cite
Augusto, D. D., & Rocha, J. da S. (2019). Magic Polygons and Degenerated Magic Polygons: Characterization and Properties. Asian Research Journal of Mathematics, 14(4), 1-18.
Original Research Article


Andress WR. Basic properties of pandiagonal magic squares. Amer. Math. Monthly. 1960;67:143-152.

Cammann S. The evolution of magic squares in China. J. Am. Oriental Soc. 1960;80:116-124.

Rosser B,Walker RJ. The algebraic theory of diabolic magic squares. Duke Math. J. 1939;5:705-728.

Chu KL, Drury SW, Styan GPH, Trenkler G. Magic moorepenrose inverses and philatelic magic square with special emphasis on the DanielsZlobec magic square. Croatian Oper. 2011; 2:4-13.

Ganapathy G, Mani K. Add-on security model for public-key cryptosystem based on magic square implementation. in: Proc.

Loly PD. Franklin squares: A chapter in the scientific studies of magical squares, Complex Systems. 2007;17:143-161. World Congress on Engineering and Computer Science 1 WCECS; 2009.

Chan CYJ, Mainkar MG, Narayan SK, Webster TD. A construction of regular magic squares of odd order. Linear Algebra and its Applications. 2014;457:293-302

Kim Y, Yoo J. An algorithm for constructing magic squares. Discrete Applied Mathematics. 2008;156:2804-2809.

Mattingly RB. Even order regular magic squares are singular. Amer. Math. Monthly. 2000;107:777-782.

Nordgren RP. New constructions for special magic squares. Int. J. Pure Appl. Math. 2012;78.

Ollerenshaw K, Br´ee DS. Most-perfect pandiagonal magic squares: Their construction and enumeration. The Institute of Mathematics and its Applications, Southend-on-Sea, UK; 1998.

Planck C. Pandiagonal magic squares of orders 6 and 10 without minimal numbers. Monist. 1919;29:307-316.

Jakicic V, Bouchat R. Magic polygons and their properties; 2018. Available:arXiv:1801.02262v1

Pickover CA. The zen of magic squares, circles, and stars, second printing and first paperback printing. Princeton University Press, Princeton, NJ; 2003.

Andreescu T, Andrica D, Cucurezeanu I. Some classical diophantine equations. First Online, Birkh¨auser Boston; 2010.