Jupiter's magic square

Albrecht Dürer’s engraving Melencolia I contains an interesting magic square toward the top right corner.

Here’s a close-up of the magic square:

The square has the following properties:

  • Every row, column, and diagonal sums to 34.
  • The four squares in the center sum to 34.
  • The four squares in the corners sum to 34.
  • Each quadrant sums to 34.
  • The year the engraving was made, 1514, appears in the bottom row.

I’d seen all this years ago, but this week I learned something else about this square.

Magic squares of different sizes were traditionally associated with planets in the solar system. … the 4 × 4 square in Melancolia is Jupiter’s … One suggestion for Dürer’s use of the square is that it reflected the mystical belief that Jupiter’s joyfulness could counteract the sense of melancholy that pervades the engraving.

From The Number Mysteries.

Regarding “Jupiter’s joyfulness,” here’s the etymology of jovial from Online Etymology Dictionary.

1580s, from Fr., from It. joviale, lit. “pertaining to Jupiter,” from L. Jovialis “of Jupiter,” from Jovius (used as gen. of Juppiter) “Jupiter,” Roman god of the sky. The meaning “good-humored, merry,” is from astrological belief that those born under the sign of the planet Jupiter are of such dispositions. In classical L., the compound Juppiter replaced Old L. Jovis as the god’s name. Related: Jovially.

Related posts:

Albrecht Dürer’s art and math
A knight’s tour magic square
A king’s tour magic square

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5 comments on “Jupiter's magic square
  1. Sara says:

    This is fascinating, I was not happy with my Latin Square design until I used a 4×4, I just wasn’t feeling that 3×3…..

  2. Amras says:


  3. Tracy Harms says:

    Your second and third items can be collapsed to a single rule:

    Tessellating as a torus by squares of four, orienting from the center, each square sums to 34.

    This adds two such sums, to boot.

  4. Hi John. Math Teachers at Play 38 is already up (with this article included) at


    You and your readers may want to check it out.

  5. George Jelliss says:

    The magic square usually associated with Jupiter is the one having half the numbers in natural order and half in the reverse of natural order, as given by Durer’s contemporary Agrippa. Durer’s magic square is a modification of the Jupiter with some pairs transposed.

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