Dürer's Matrix

The Renaissance engraving Melancholia I by the German artist and amateur mathematician Albrecht Dürer. This image is filled with mathematical symbolism, and if you look carefully, you will see a matrix in the upper right corner of the first picture while the second gives an enlarged view. This matrix is known as a magic square and was believed by many in Dürer's time to have genuinely magical properties. It does turn out to have some fascinating characteristics worth exploring.

[Notice that all rows, columns, diagonals add up to the magic number, 34, for a 4x4 matrix]

{The matrix in the image is: 16, 3, 2, 13; 9, 10, 11, 8; 5, 6, 7, 12; 4, 15, 14, 1}

Another fascinating feature of this matrix is that the elements in the second and third columns of the final row are 15 and 14, interestingly. The year in which Dürer came up with the matrix was 1514, too, incidently.