A Magic Square is a series of numbers arranged in a square so that (at least) the values in each row, each column and both diagonals add up to the same total (T).

Although repeat values are sometimes permitted, the most elegant magic squares have different values in each cell.

Basic Magic Squares use the series of whole numbers from 1 to n, where n = the number of cells in the square.

Magic Squares of different sizes can be created, for example:

8 1 6 3 5 7 4 9 2 T = 15

1 15 14 4 12 6 7 9 8 10 11 5 13 3 2 16 T = 34

17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 T = 65

1 35 34 3 32 6 30 8 28 27 11 7 24 23 15 16 14 19 13 17 21 22 20 18 12 26 9 10 29 25 31 2 4 33 5 36 T = 111

While, minimally, every row, column, and both diagonals must add up to the same total (T), some magic squares permit the total to be achieved in many more ways.

Our Magic Square Generator produces 'most perfect' 4 x 4 magic squares where T (if an even number) can be found in 52 different ways!

The mathematics, symmetry and symbolism of magic squares have fascinated people for thousands of years. In many cultures they are believed to be imbued with ‘magical’ qualities, and are sometimes worn as amulets to bring fortune.

TEDx Talk on Magic Squares by Michael Daniels

## The Lo Shu Square

The Lo Shu square is an ancient 3x3 magic square which features in Chinese divination. Some people claim that it may date from around 2800 BCE.

All other basic 3x3 magic squares are rotations and/or reflections of the Lo Shu square.

4 9 2 3 5 7 8 1 6 The Lo Shu Square

## The Jaina Square

This famous square is believed to date from the 11th Century CE.

The Jaina Square (so named because it is also found in a 12th or 13th Century Jaina/Jain inscription at Khajuraho, Northern India) is an example of what has been termed a ‘diabolic’ or ‘most-perfect’ magic square because the total (T) can be produced in many (52) different ways.

7 12 1 14 2 13 8 11 16 3 10 5 9 6 15 4 The Jaina Square

## The Dürer Square

This 4x4 magic square is featured in Albrecht Dürer’s (1471-1528) famous engraving “Melencolia I” (1514).

Note the date 1514 in the bottom row.

16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 The Dürer Square

## The Agrippa Squares

Heinrich Cornelius Agrippa (1486-1535) was an occultist, astrologer and alchemist who attributed specific magic squares to the seven ‘planets’ known at the time.

## Saturn

4 9 2 3 5 7 8 1 6 T = 15

## Jupiter

4 14 15 1 9 7 6 12 5 11 10 8 16 2 3 13 T = 34

## Mars

11 24 7 20 3 4 12 25 8 16 17 5 13 21 9 10 18 1 14 22 23 6 19 2 15 T = 65

## Sun

6 32 3 34 35 1 7 11 27 28 8 30 19 14 16 15 23 24 18 20 22 21 17 13 25 29 10 9 26 12 36 5 33 4 2 31 T = 111

## Venus

22 47 16 41 10 35 4 5 23 48 17 42 11 29 30 6 24 49 18 36 12 13 31 7 25 43 19 37 38 14 32 1 26 44 20 21 39 8 33 2 27 45 46 15 40 9 34 3 28 T = 175

## Mercury

8 58 59 5 4 62 63 1 49 15 14 52 53 11 10 56 41 23 22 44 45 19 18 48 32 34 35 29 28 38 39 25 40 26 27 37 36 30 31 33 17 47 46 20 21 43 42 24 9 55 54 12 13 51 50 16 64 2 3 61 60 6 7 57 T = 260

## Moon

37 78 29 70 21 62 13 54 5 6 38 79 30 71 22 63 14 46 47 7 39 80 31 72 23 55 15 16 48 8 40 81 32 64 24 56 57 17 49 9 41 73 33 65 25 26 58 18 50 1 42 74 34 66 67 27 59 10 51 2 43 75 35 36 68 19 60 11 52 3 44 76 77 28 69 20 61 12 53 4 45 T = 369

## Create an incredible 4 x 4 magic square for any total (34-9999)

You can make a Magic Squares for your Birth Year, Lucky Number, Name Numerology, House Number, etc.

Total = Enter Magic Square Total in box above, then click Make Square

EVEN totals have 52 summation patterns

ODD totals have 36 summation patterns

## Create an incredible 4 x 4 magic square for any date

Note: These squares may contain repeated, zero, or negative values.

MMDD

DDMM

Click green buttons to show squares giving this total

## Books

- Andrews, W.S. (1960). Magic Squares and Cubes, Revised edition. Dover.
- Farrar, M.S. (2007). Magic Squares. BookSurge Publishing.
- Ollerenshaw, K. & Bree, D. (1998). Most Perfect Pandiagonal Magic Squares: Their Construction and Enumeration. The Institute of Mathematics and its Applications.
- Solberg, J.J. (2016). Magic Square Methods and Tricks. Sun Mountain Publications.

## Websites