fbpx
Connect with us

DailyArtMagazine.com – Art History Stories

The Mystery Of Durer’s Magic Square

Painting of the Week

The Mystery Of Durer’s Magic Square

Albrecht Dürer’s in his famous engraving Melencolia I showed many weird things. Among them is a magic square, a best-known and most enigmatic, with magic constant 34. The engraving shows a disorganized jumble of scientific equipment lying unused while an intellectual sits absorbed in thought. Dürer’s 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.

Durer Magic Square Albrecht Dürer, Melencolia I, 1514, Staatsgalerie Stuttgart

Albrecht Dürer, Melencolia I, 1514, Staatsgalerie Stuttgart

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) and 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 the Dürer’s square that sum to it’s magic number, 34!

Durer Magic Square Albrecht_Dürer_-_Melencolia_I_(detail)

Albrecht Dürer, Melencolia I, detail, 1514, Staatsgalerie Stuttgart

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 thirteen 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 Dürer 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.

Dürer’s magic square has the additional property that the sums in any of the four quadrants, as well as the sum of the middle four numbers, are all 34. It is thus a gnomon magic square. A gnomon magic square is a 4×4 magic square in which the elements in each 2×2 corner have the same sum. Dürer’s magic square,is an example of a gnomon magic square since the sums in any of the four quadrants (as well as the sum of the middle four numbers) are all 34. In addition, any pair of numbers symmetrically placed about the center of the square sums to 17, a property making the square even more magical.

 

Art Historian, founder and CEO of DailyArtMagazine.com and DailyArt mobile app. But to be honest, her greatest accomplishment is being the owner of Pimpek the Cat.

Comments

More in Painting of the Week

  • Ancient Greece

    Painting of the Week: Leonidas at Thermopylae by Jacques-Louis David

    By

    Whether you are within an academic environment or at a coffee shop, when the term ‘Neoclassicism’ and its huge influence on the visual arts arise, you are likely to hear the name Jacques-Louis David many times. David was not only the painter who developed an epochal...

  • 20th century

    Painting of the Week: Valentin Serov, Princess Olga Orlova

    By

    Late Tsarist Russia evokes images of great social inequality in respect of health, wealth, and happiness. In addition, it evokes images of extreme luxury, smothered in expensive fabrics and furs and layered in diamonds and pearls. Valentin Serov captured this glittering world through his evocative portraits...

  • Artists' Stories

    The Story of Vincent van Gogh’s Bedroom and Its Three Versions

    By

    The Bedroom(s) are among the most famous paintings of Vincent van Gogh. Why the plural? There are three similar paintings of the same title. All three versions are described in his letters, easily discernible from one another by the pictures on the wall to the right. The first,...

  • 20th century

    The Mysterious Road From Edvard Munch’s The Scream

    By

    The Scream by Edvard Munch is one of the most famous paintings in the world. It’s pretty obvious why – its expression and the way the pain and the anxiety of the man are depicted is universal for all human beings. We have all – at...

  • dailyart

    Painting of the Week: Saint George and the Dragon

    By

    There is a skirmish between the hero and the villain. Fabrics whip about, horse hoofs trample, and a dying scream erupts as Saint George slaughters the Dragon. The Christian saint kills the horrible creature as an act of religious zeal and civilization overcoming anarchy. Since the...

To Top