Dürer's Magic Square

[scale=.3]/troves/MathOzTeX/graphics/gifs/melencol.jpg DurersMagicSquare

Dürer's magic square is a magic square with magic constant 34 used in an engraving entitled Melencolia I by Albrecht Dürer (The British Museum, Burton 1989, Gellert et al. 1989). 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.


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 (Hunter and Madachy 1975, p. 24). It is thus a gnomon magic square. 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.

See also

Dürer's Solid, Gnomon Magic Square, Magic Square

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Boyer, C. D. and Merzbach, U. C. A History of Mathematics. New York: Wiley, pp. 296-297, 1991.Burton, D. M. Cover illustration of Elementary Number Theory, 4th ed. Boston, MA: Allyn and Bacon, 1989.Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). Appendix, Plate 19. VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989.Hunter, J. A. H. and Madachy, J. S. Mathematical Diversions. New York: Dover, 1975.Livio, M. The Golden Ratio: The Story of Phi, the World's Most Astonishing Number. New York: Broadway Books, pp. 140-141, 2002.Rivera, C. "Melencolia."

Referenced on Wolfram|Alpha

Dürer's Magic Square

Cite this as:

Weisstein, Eric W. "Dürer's Magic Square." From MathWorld--A Wolfram Web Resource.

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