The Wonder of Magic Squares

Learn about Magic Squares and their construction

What is a Magic Square?


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 Magic of Magic Squares


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 magic, myth and math of magic squares | Michael Daniels | TEDx Douglas
Python Guess The Number Game




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.


Lo Shu 3x3 magic square
The Lo Shu Square
Count the number of dots in each position
 4   9   2 
 3   5   7 
 8   1   6 
The Lo Shu Square




The Jaina Square


Magic square at the Parshvanatha temple, Khajuraho
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





Albrecht DÜRer - Melencolia I - Google Art Project
Melencolia I


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.


Albrecht Dürer - Melencolia I (detail)
Melencolia I (detail)

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





Heinrich Cornelius Agrippa von Nettesheim
Agrippa

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




Magic Square Generators




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
 



Learn How to Construct Magic Squares


If you want to impress your friends, these ebooks will teach you how to quickly make a 4 x 4 Magic Square for any total.


Further Resources


Books




Websites