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*.

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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…..

Fascinating!

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.

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

http://mathandmultimedia.com/2011/05/21/math-teachers-at-play-38/

You and your readers may want to check it out.

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.

Latin Square of the Moon can generate a Magic Square. If we replace the numbers in the first column of “moon” with their respective root numbers we commence filling a root Square. Read more about it on my blog: http://www.glennwestmore.com.au/category/latin-squares/.

Thank you for this interesting article. I was wondering : Are all of the 880 essentially different fourth-order magic squares related to Jupiter? In 1533 Heinrich Cornelius Agrippa used a slightly different fourth-order magic square to represent Jupiter in his book “De Occulta Philosophia libri tres” (Three books of occult philosophy, book II, chapter xxii) translated by “J.F.” (John French?) and printed by Moule, London, in 1651. For the digital edition of Agrippa’s book by Peterson JF see http://www.

esotericarchives.com/agrippa/agrippa2.htm#contents.

Did Agrippa deliberately choose a particular fourth-order square, or did he just mean that any fourth-order magic square could represent Jupiter? If you have more information I would like to know.

More research on Dürer’s “Melencolia I” square can be found here: https://carresmagiques.blogspot.fr/2014/12/melancholy-in-magic-squares-tribute-to.html

and also in an earlier article in French here:

https://carresmagiques.blogspot.fr/2010/08/les-carres-magiques-et-les-spheres-3.html

thank you wonderful article.

I just double checked the the Jupiter square from the digital Agrippa. and the Jupiter square referenced here in this article are identical to each other! It is wonderful having the hebrew equivalent for the square.

i would like to know why if Durer’s magic square has the year at the bottom and hi initials square with 4 and 1 in them respectively why did he not just swap collumns

{original Durer}

16 3 2 13

5 10 11 8

9 6 7 12

4 15 14 1

modified durer with switched columns initials of Albrecht Durer in correct honorable sequence. the switch does not make the Square no more or no less magic than the square in Melencolia I

13 3 2 16

8 10 11 5

12 6 7 9

1 15 14 4

Here are few more interesting links on the magic square summing up to 34

https://books.google.co.in/books?id=cLqiEJVT3u8C&pg=PA861&redir_esc=y#v=onepage&q&f=false

https://books.google.co.in/books?id=nAADBAAAQBAJ&pg=PA48&redir_esc=y#v=onepage&q&f=false