Magic squares have a (literally) chequered history. They have fascinated men of science as well as laymen. They have been studied, explored and utilised by scientists and mathematicians as well as mystics and magicians. Magic squares are as old as Vedic civilisation itself. There is evidence of their practical application in the Vedic sciences of Jyotisha (Astrology) and Vastu (Architecture and Engineering science), for example, the Planetary numeric yantras described here.
Vedic literature classify the art of composing magic squares as among the 64 arts generally taught in the ancient school curriculum. In the purport to the Shrimad Bhagavatam 10th Canto, Chapter 45, verses 35-36, published by His Divine Grace AC Bhaktivedanta Swami Shrila Prabhupada and his disciples, this art called yantra-matrika is described as "composing magic squares, arranging of numbers adding up to the same total in all directions". Note the link between the Sanskrit terms yantra and matrika, and the latter's hint of being the root of the modern word "matrix".
The verse reference given above refers to the episode of the Divine Brothers Lord Krishna and Lord Balarama mastering the 64 arts within 64 days in the gurukula (ashram school) of Their guru Sandipani Muni. According to Vedic chronology, this event took place more than five thousand years ago.
Let's take a closer look at the math behind the magic square. A magic square resonates to a special number, the magic sum or constant. This constant is the sum of the numbers along any row, column or diagonal of the magic square.
In a magic square of NxN matrix, where the enclosed sequence of numbers ranges from 1..NxN, the magic constant is determined by the formula:
(N3 + N) / 2.
In a 3x3 magic square, as illustrated by the Sun yantra on our Planetary numeric yantras page, the magic constant is:
(33 + 3) / 2 = 15
Take for example the magic square in our logo on top, the Shri Rama yantra. The magic constant for this 4x4 matrix is:
(43 + 4) / 2 = 34
Guess how many different combinations (magic series) of four numbers add up to this magic sum? Click this magic number combinations in our logo link to get the answer, colour-coded.
