Vedic Magic Square
Vedic Math Magic Square
"Magic Squares" is a term given to squares which are filled with consecutive integers and the total of whose rows,columns and diagonals is always the same. When the numbers in any row, column or diagonal are added up they reveal the same total. Many people have found this squares fascinating and so they have been regarded as magic.
Magic Squares
This technique is not a part of formal Vedic Mathematics as discovered by Swamiji. However, the oriental schools of astrology. Feng Shui, numerology and other mystical sciences were of this technique. Feung Shui, numerology and other parts of the world often used magic squares for their aid. The Vedic seer undoubtedly used the principles of magic squares for various applications. We have included this technique in this book because in lower level competitive exams, questions on magic squares are often asked.
A sample magic square is given below. It is a three-by three grid and you will find that the total of all rows, columns and diagonals is '15'. Since there are '9' squares in the grid, we have used numbers from '1' to '9'.
| 4 | 3 | 8 |
| 9 | 5 | 1 |
| 2 | 7 | 6 |
We can verify the various totals
R1 : 4 + 3 + 8 = 15
R2 : 9 + 5 + 1 = 15
R3 : 2 + 7 + 6 = 15
C1 : 4 + 9 + 2 = 15
C2 : 3 + 5 + 7 = 15
C3 : 8 + 1 + 6 = 15
D1 : 4 + 5 + 6 = 15
D2 : 2 + 5 + 8 = 15
Let us have a look at another magic square. This is a five by five grid and the total of all sides will add up to '65'. Since there are '25' squares in the grid, we have used numbers from 1 to 25
| 11 | 10 | 4 | 23 | 17 |
| 18 | 12 | 6 | 5 | 24 |
| 25 | 19 | 13 | 7 | 1 |
| 2 | 21 | 20 | 14 | 8 |
| 9 | 3 | 22 | 16 | 15 |
The total of the rows, columns and diagonals add up to '65'. The obvious question is, how are these magic squares formed?
Rules to form Magic Square
1) Always put the number '1' in the center most square of the last column.
2) After inserting a number in a square move to the square in the south east direction and fill it with the number next number.
3) If the square in the south east direction cannot be filled then move to the square in the west and fill it with the next number.
4) When you have filled a number in the last square of the grid, fill the next number in the square to its west.
These are the four rules that we will be following. However they will not be followed exactly as mentioned above. We will apply them in a slightly different manner.
To make the magic square, we shall be making some imaginary squares to effectively follow the four rules mentioned above. But, we shall not explain what are these imaginary squares at this point of time. We shall deal with them straight away in the course.