Melancholia Magic Square
|The most famous 4 x 4 magic square is the so-called Melancholia
magic square. In 1514, Albrecht Dürer used the square in his engraving
which depicts the indecision of the intellectual. The two numbers, 15 and
14, in the centre of the bottom row date the engraving.
|Durer never explained the rich symbolism of this masterpiece,
but most authorities agree that it depicts the sullen mood of the thinker
unable to engage in action. (In the Renaissance, the melancholy temperament
was thought characteristic of creative genius.) Unused tools of science
and carpentry lie in disorder around the disheveled, brooding figure of
Melancholy. There is nothing in the balance scales, no one mounts the ladder,
the sleeping hound is half-starved, the winged cherub waits for dictation
while time is running out in the hourglass above. The wooden sphere and
curiously truncated stone tetrahedron suggest the mathematical base of
the building arts. The lunar rainbow arching over what appears to be a
comet may signify the hope that the somber mood will pass.
|The magic constant of the square is 34. In
other words, the sum of the numbers in each of the four rows, the four
columns, and the two main diagrams is 34. However, this square has an amazing
number of other "magic" properties - including many more ways of attaining
the constant sum of 34. Can you discover some on your own? Click
here for the solution.