On symmetrical and pandiagonal magicsquares

Ng, Poh Teck (2022) On symmetrical and pandiagonal magicsquares. Master dissertation/thesis, UTAR.

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Abstract

Myprojectentitled "On Symmetrical andPandiagonalMagicSquares". Magic square is one of the branches of mathematics under the field of combinatorial and recreational. Magic square already existed for a very long time ago. It is starting from a scroll called Lo-Shu according to one of the versions of the magic square legend. A magic square of order n is an n×narray of natural numbers from 1,2,...,n2 that are arranged in the form of square, such that the sums of each row, column and diagonal are the same constant number. There are still many properties about the magic squares that are yet to be discovered. Besides, there are many interesting types of magic squares that attract the attention of mathematicians. In this project, we have studied on the symmetrical and pandiagonal magic squares. A symmetrical magic square is a magic square of order n where every pair of numbers that are symmetrically opposite with respect to the center sum to n2 + 1. A pandiagonal magic square is a magic square with the additional property that each broken diagonal sums to the magic constant. We also studied the methods of construction for magic square with different types and order. After that, we explore new methods of construction for these types of magic squares. Lastly, We will try to explore the possibility applying magic squares on cryptography.

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