Investigation of center of mass by using magic squares and its possible engineering applications

Abstract

A magic square is an n × n matrix of the integers from 1 to n 2 such that the sum of every row, column, and diagonal is the same. There are several ways for generating certain types of magic squares, which results different magic squares of the same order. But until the work done by Abiyev [A.A. Abiyev, Sayılı sihirli karelerin doğal şifresi (in Turkish), Enderun Ofset Matbaacılık, ISBN: 975-95318-3-6, Ankara, 1996] there was not a known general methodology for generating magic squares of any order. Moreover, Abiyev's method is not restricted to a certain type of numbers (real, integer, etc.). By his method magic squares of any order can be obtained for any type of numbers including complex numbers. Abiyev's work is now its maturing stage and magic squares generated by his method shows some very interesting symmetrical properties, which are not possible to obtain via other techniques. These properties may open some research directions for several scientific disciplines like genetic engineering, operational research, intelligent computation, physics, etc. Such an attempt is made in this paper to show how center of mass can be analysed by using Abiyev's magic squares.