Bizarre

The Mystery of Dürer’s Magic Square

Zuzanna Stańska 14 September 2023 min Read

Many strange symbols appear in Albrecht Dürer’s famous engraving Melencolia I. Among them is a magic constant 34, a well-known and enigmatic example. The engraving shows a disorganized clutter of scientific equipment lying around while a scientist sits absorbed in thoughts. The magic square is located in the upper right-hand corner of the engraving. The numbers 15 and 14 appear in the middle of the bottom row, indicating the date of the engraving, 1514.

Dürer Magic Square: Albrecht Dürer, Melencolia I, 1514, National Gallery of Art, Washington, DC, USA.

The sum 34 can be found in the rows, columns, diagonals, each of the quadrants, the center four squares, the corner squares, the four outer numbers clockwise from the corners (3+8+14+9), and likewise, the four counter-clockwise, the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows (e.g. 5+9+8+12), as well as several kite-shaped quartets, e.g. 3+5+11+15. Actually, there are 86 different combinations of four numbers from Dürer’s square that add up to the sum of the magic number, 34!

Dürer Magic Square, Albrecht Dürer, Melencolia I, 1514, National Gallery of Art, Washington, DC, USA. Detail.

Each row, each column, and each diagonal adds up to 34; these are the traditional magic properties. But there is more magic to be found here. There are actually 13 different ways of dividing this square into four groups of four cells, with each group of four cells adding to 34. The menu in the applet can be used to select among these. The positions in the square can be seen as a finite vector space in which each set of four groups of four cells is a set of parallel affine planes.

The magic square has additional properties: the sum in any of the four quadrants, as well as the sum of the middle four numbers, are all 34.  Because of that, it is called a gnomon magic square: a 4×4 magic square in which the elements in each 2×2 corner have the same sum. In addition, any pair of numbers symmetrically placed about the center of the square sum to 17.

Probably this magic square represents a jovial exercise, where jovial means happiness or cheerfulness – the opposite of the gloomy and sad mood associated with Melencolia I. Up to this day, this contrast of virtue and fortune enchants viewers who are willing to solve Dürer’s riddle hidden in this masterpiece.

Bibliography

1.

Weisstein, Eric W. “Dürer’s Magic Square.” MathWorldA Wolfram Web Resource. Accessed Jan 31, 2022.

Get your daily dose of art

Click and follow us on Google News to stay updated all the time

Recommended

Bizarre

Chilling Beauty: Exploring Europe’s Bone Churches

From the ancient period through the 18th century, European Catholics and Orthodox Christians displayed and maintained bones of the deceased to honor...

Julia Bourbois 30 October 2023

Art for Halloween: Roberto Comandante del Caos Diz, Story Twist, 2022. Artist's profile. Bizarre

Scary Monsters and Super Creeps for a Frightening Halloween!

Throughout the history of mankind, art has always been a window to the soul. We have witnessed ethereal beauty, magical nature, bizarre sceneries,...

Errika Gerakiti 30 October 2023

Bizarre

Trompe L’oeil: How Artists Deceived Our Eyes Throughout the Ages

Without knowing, you have more than likely seen an example or two of trompe l’oeil in art. It is a term that encompasses many art forms in its...

Rachel Witte 13 April 2023

Edvard Munch, Love and pain, 1895, oil on canvas. The Munch Museum, Oslo, Norway. Bizarre

5 Vampire Paintings in Art

Vampires are one of the most known mythical creatures in history. The origins of their legend date back to ancient civilizations. Some ancient...

Errika Gerakiti 31 October 2022