The natural algorithm of the balanced squares and its applications

In this study, the natural algorithms of the balanced squares have been investigated, which is established by A. A. Abiyev [1]. Some important properties of the balanced squares have been revealed by graphs and number theories.If the numbers in their respective locations in these natural magic squares are considered as point-masses, then the mass center and geometric center of such a system will be the same. For that reason; the `magic squares? will be called as `balanced squares?. Also, using the biggest and the smallest numbers in the center of the squares, some chain identities and the number series have been investigated, that provides the equation of .Some application areas of the balanced squares are calculus, graphs theory, probability theory and astronomy. The study is under progress for possible applications of balanced squares and cubes; Cryptology, optimal problems, investigation of genetic code, planning of the city and architecture.Key Words: Balanced squares, natural algorithm, arithmetic sequence, graph, mass center, Fibonacci numbers, Lucas numbers.