Patterns in the Melancholia
Magic Square

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

The four corner squares and the four centre squares both add up to
34 
16 
3 
2 
13 
5 
10 
11 
8 
9 
6 
7 
12 
4 
15 
14 
1 

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

The four opposite squares both vertically and horizontally add up to
34. 
16 
3 
2 
13 
5 
10 
11 
8 
9 
6 
7 
12 
4 
15 
14 
1 

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

Both sets of symmetrically placed squares (3 5 12 14) and (2 8 9 15)
add up to 34. 
16 
3 
2 
13 
5 
10 
11 
8 
9 
6 
7 
12 
4 
15 
14 
1 

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

Each corner group of four squares (like 16 3 10 5) adds up to 34. 
16 
3 
2 
13 
5 
10 
11 
8 
9 
6 
7 
12 
4 
15 
14 
1 

The sum of the first two rows
equals the sum of the bottom two rows and the sum of the squares
of the numbers in the first two rows equals the sum of the squares
of the numbers in the bottom two rows. Likewise for the columns. 

The same is true for the numbers of the first and third rows (and the
sum of their squares) as respects the numbers of the second and fourth
rows. Likewise for the columns. 

The sum of one set of symmetrically placed numbers, their squares and
cubes equals the sum of the other set of symmetrically placed numbers,
their squares and cubes. 
