Amrtamahotsavagranthamala-44
1.1. Magic square: A Magic square of order n is an arrangement of 2 different numbers (usually positive integers) in n rows and n columns such that the sum of the numbers along each row, each column, and along each main diagonal is same. This constant sum is called the magical-sum or magic-constant of the magic square. In a simple way, a magic-square of order n may be written in the form of a square array of its n ^ 2 numbers which may be called its elements. Usually the square array is depicted in a square consisting of n ^ 2 sub-squares or cells each of which contains an element. If the numbers of magic square are the consecutive integers form 1 to n ^ 2 the magic square is called a traditional magic-square or conventional magic Square or pure magic-square of order n. In addition to the constancy of the sum along every row, column, and main diagonal, if the sum of elements along each broken diagonal is equal to the same magic constant, then the array is called a diabolic or pan-diagonal magic-square.
1.2. . Origin and early History: Little is known as regards the origin of magic squares and other figures. Hindu tradition assigns them to God Śiva. Nārāyaņa (1356) says that the subject of progression, of which magic squares from a part, was taught by Śiva to Manibhadra, the magician. The earliest example of magic-square in India is that by the seer Garga. The seer is credited with the knowledge of several magic-squares (Ankayantra-1 and 2). Authors of Hindu scriptures (after stating the method of construction of squares) describe that wearing the magicsquare (Ankayantra-1) pacifies the troubles arising out of diseases as told by great seer Garga etc. Wearing of another magic-square (Ankayantra-2), an amulet of Mars, destroys the evil effects produced due to bad positioning of Mars, as told by Garga. Garga the author of Garga-samhita (a book on astrology) was different from Vrddha Garga. Garga is said to have been born in the beginning of Kaliyuga (3102 BC). Nīlakantha Somayājī, in his commentary on Āryabhațīya, written about 1502 AD (and published in the Trivandrum Sanskrit Series Nos. 101, 112, and 185,) adduces the evidence of Parāśara in this respect. 4x4 magic squares are considered to possess magical properties and are supposed to bring luck when worn as amulets. They are found on gates of buildings, on the walls where shopkeepers transact their business and on the covers of calendars used by astrologers even to this day. A 4x4 square occurs in a Jaina inscription of the 11th century, found in the ancient town of Khajuraho.
Dr. Venugopal D. Heroor, Chartered Engineer, Kalaburagi, is a serious and passionate researcher in the field of Bharatiya Ganita. He has brought out thirty (30) books related to BHARATIYA GANITA, They are definite contribution in the study of the history of Bharatiya mathematics. His works are excellent in quality, wideness as well as depth. He is quite good in compiling the material and presenting the results without injuring the original are marvelous and highly appreciable. Being an engineer, all his lines are measured, mostly correct and furnished with evidence from sources.
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