International Journal of Research and Scientific Innovation (IJRSI) | Volume V, Issue VI, June 2018 | ISSN 2321–2705

Construction of Magic Square of Any Order

Chaitra V¹, Madhura A²

 ¹Dept. of Mathematics, BMS College of Engineering, Bangalore, Karnataka, India
²Dept. of Telecommunication Engg., BMS College of Engineering, Bangalore, Karnataka, India

Abstract—A magic square is a square matrix of numbers with the property that the sums along rows, columns, and main diagonals are all equal to S which is called the “magic sum”. A magic square with n number of cells on a side is a magic square of order n. Such a square has n rows, n columns and n²cells

Keywords—Magic square, Lo Shu, odd magic square, singly even magic square, doubly even magic square.

I. Introduction

The study of magic squares dates back to prehistoric times. It has been a fascination to man for ages. Magic squares are used in statistical calculations, in factorial experiments of low order and to balance linear trend from main variable effects.

A magic square is a square matrix of numbers with the property that the sums along rows, columns, and main diagonals are all equal to S which is called the “magic sum”. A magic square with n number of cells on a side is a magic square of order n. Such a square has n rows, n columns and n2 cells. Generally entries are natural numbers 1, 2, ….. n2 and such a magic square is called classical or normal magic square.
Magic square is divided into three categories based on the order.

Order of magic square n is divided by 4. If the remainder is zero, then magic square is doubly even, if remainder is 2, then magic square is singly even and if remainder is 1 or 3 then, magic square is odd.

II. History of magic squares

The history of magic square revolves around three ancient cultures: Chinese, Indian and Islamic. The earliest documentation of magic square comes from sources in China and India.