Dürer's Melencolia I Magic Square Has 86 Four-Number Combinations Summing to 34
Albrecht Dürer's 1514 engraving Melencolia I features a magic square in its upper right corner with 86 different four-number combinations summing to 34. The square includes the numbers 15 and 14 in the middle of the bottom row to indicate the year 1514. Each row, column, and diagonal adds to 34, and there are 13 ways to divide the square into four groups of four cells each summing to 34. The square is a gnomon magic square, where each 2×2 corner sums to 34, and any pair of numbers symmetrically placed about the center sums to 17. The engraving depicts a scientist surrounded by scientific equipment, contrasting the gloomy mood of Melencolia I with the jovial exercise of the magic square.
Key facts
- Albrecht Dürer created Melencolia I in 1514.
- The magic square is in the upper right corner of the engraving.
- Numbers 15 and 14 in the bottom row indicate the year 1514.
- Each row, column, and diagonal sums to 34.
- 86 different four-number combinations sum to 34.
- 13 ways to divide the square into four groups of four cells each summing to 34.
- Any pair of numbers symmetrically about the center sums to 17.
- The square is a gnomon magic square with 2×2 corners summing to 34.
Entities
Artists
- Albrecht Dürer