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Home Azerbaijan Technologies Balanced Abiyev’s Squares

Balanced Abiyev’s Squares


It is known that in a magic square of nth order elements of the number set {1, 2, ….., n2} in n×n square so that the sum of the numbers on any row, column or diagonals equals a constant. The magic square called a balanced square by Abiyev differs from its analogues according to the special arrangement of numbers and symbols. There are two invariants of a relative symmetrical displacement of their elements which is not included into the squares developed till nowadays. These invariants enable the balanced squares to be applied in wide fields of science and technology. A balanced square by Abiyev is the most perfect magic square well-known in mathematics according to its unique characteristics. It opens new directions in scientific- research and applied problems such as cryptology, nanotechnology, town planning, architecture, art, medicine (genetics), process optimization, etc.

Innovative Aspect and Main Advantages

A special symmetrical programming of matrices eases the calculation in the applied fields of technology.

Areas of Application

The balanced square may be applied in cryptology, encoding and decoding of texts and information, developing unique signatures and so on.

Fig. 1 The balanced square of 12th order.

Stage of Development

Covered by patent of Azerbaijan №679 05/c-527-04. The book “The Natural Code of Numbered Magic Squares” was published on September 17, 2004.

Contact Details

Institute of Radiation Problems
Contact person: Dr. Matanat Mehrabova
Address: 9 F.Aghayev St. AZ1143 Baku, Azerbaijan
Tel: (+994 12) 438 3224, (+994 50) 731 8177
Fax: (+994 12) 432 5187
E-mail: This e-mail address is being protected from spambots. You need JavaScript enabled to view it

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