{"id":3204,"date":"2025-03-07T10:15:06","date_gmt":"2025-03-07T09:15:06","guid":{"rendered":"https:\/\/blog.sagradafamilia.org\/?p=3204"},"modified":"2026-04-07T11:13:28","modified_gmt":"2026-04-07T09:13:28","slug":"the-magic-square-on-the-passion-facade","status":"publish","type":"post","link":"https:\/\/blog.sagradafamilia.org\/en\/el-quadrat-magic-de-la-facana-de-la-passio-totes-les-claus-per-entendrel\/","title":{"rendered":"The magic square on the Passion fa\u00e7ade: keys to understanding it\u00a0"},"content":{"rendered":"

While admiring the Passion fa\u00e7ade and all ofSubirachs\u2019 sculptural work<\/a>, more than once visitors are surprised to discover a series of numbers inside a square and wonder what they mean. <\/p>\n\n\n\n

Well, it is a magic square, but in this case, it is a very special one. In this article, we\u2019ll try to explain why. <\/p>\n\n\n\n

A magic square is a series of numbers on a square grid, placed so that any row, column or diagonal line always adds up to the same number<\/strong>.\u202fThis sum is known as the magic constant of the square<\/strong>. <\/p>\n\n\n\n

Magic squares start with 3\u00d73 grids, as there\u2019s no possible solution to a 2\u00d72 grid and a 1\u00d71 grid doesn\u2019t make sense. <\/p>\n\n\n\n

Normally, this means putting correlating whole numbers into the grid: for a 3\u00d73 grid, the numbers from 1 to 9; for a 4\u00d74 grid, the numbers from 1 to 16. Starting from these rules, the magic constant cannot be chosen and depends on the sum of the numbers used. For example, in a 3\u00d73 magic, square where the sum of 1+2+3+4+5+6+7+8+9=45, each row, column and diagonal line sums 45\/3 = 15; in a 4 x 4 magic square, where the sum of all the numbers from 1 to 16 is 136, the magic constant is 136\/4 = 34. So, for a 5\u00d75 square, the constant is 65; for a 6\u00d76, it\u2019s 111; and for a 7\u00d77, 175. <\/p>\n\n\n\n

However, the Sagrada Familia magic square is 4\u00d74 and doesn\u2019t meet these basic initial conditions<\/strong>. On the one hand, it doesn\u2019t have all the numbers from 1 to 16 (it is missing the 12 and 16) and some numbers are repeated. On the other hand \u2015and herein lies the symbolic key\u2015, the magic constant isn\u2019t 34 but 33. <\/p>\n\n\n\n

Subirachs took an existing magic square, from German painter Albrecht D\u00fcrer\u2019s engravingMelencolia I<\/em>, and adapted it, repeating the numbers 14 and 10 instead of 12 and 16, to make it add up to 33, the age Jesus is traditionally believed to have been executed<\/strong>. I diem \u00abtradicionalment suposada\u00bb perqu\u00e8, hist\u00f2ricament, aquesta dada mai no ha pogut ser validada al 100 %. No obstant aix\u00f2, el cert \u00e9s que el 33 \u00e9s tamb\u00e9 una xifra simb\u00f2lica, i en aquest sentit gens a l\u2019atzar, basada en la import\u00e0ncia del nombre 3, que, en el m\u00f3n cristi\u00e0, \u00e9s s\u00edmbol de la trinitat. <\/p>\n\n\n\n

\n
\n
\"Melencolia\u202fI,\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n\n\n\n
\n
\"Melencolia\u202fI,\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button>
Melencolia<\/em>I, Albrecht D\u00fcrer. France National Library. <\/figcaption><\/figure>\n<\/div>\n<\/div>\n\n\n\n

Nevertheless, D\u00fcrer\u2019s engraving was a very special starting point for Subirachs<\/strong>. A m\u00e9s de poder obtenir la constant m\u00e0gica sumant files, columnes o diagonals, aquesta tamb\u00e9 es pot obtenir a trav\u00e9s de moltes altres combinacions. Aix\u00ed mateix, com una mena de signatura o colof\u00f3 de l\u2019autor, les dues xifres centrals de fila inferior, el 15 i el 14, formen l\u2019any en qu\u00e8 s\u2019execut\u00e0 l\u2019obra: el 1514. <\/p>\n\n\n\n

The square at the Sagrada Fam\u00edlia also has some of these characteristics and, so, in addition to the rows, columns and diagonals, there are many other options that add up to the magic constant of 33<\/strong>.  <\/p>\n\n\n\n

For some examples, see the ones marked here in different colours, which are the most notable combinations of four numbers that add up to 33: <\/p>\n\n\n\n

\"\"\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n

Plus, in the magic square at the Sagrada Fam\u00edlia, there is also a sort of hidden subliminal signature<\/strong> : adding up the numbers that repeat and looking at their correspondence in the Roman alphabet, we get the initials INRI.<\/strong> <\/p>\n\n\n\n

\"The\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n
\"\"\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n

The initials INRI meansIesus Nazarenus Rex Iudaeorum<\/em>(Jesus of Nazareth King of the Jews). This is the sign that Pontius Pilate wrote on the Jesus\u2019 cross and here, his signature. <\/p>\n\n\n\n

Subirach chose these four numbers because there is one from each row, column, diagonal and quadrant, and also because the sum of these repeated numbers is 48, or four times twelve. All within the symbolic framework of what the numbers represent. <\/p>\n\n\n\n

MAGIC SQUARES, A FASCINATION WITH NO KNOWN USE<\/strong> <\/p>\n\n\n\n

Els quadrats m\u00e0gics \u202frecorded as far back as the third millennium BC in ancient China<\/strong>. Segons una llegenda, calia ordenar les ofrenes per calmar la ira dels d\u00e9us segons un quadrat de 3 x 3. Tamb\u00e9 es coneixen combinacions d\u2019aquesta mena en la cultura \u00edndia, l\u2019eg\u00edpcia, l\u2019\u00e0rab i la grega. Segons les diferents tradicions, s\u2019han atribu\u00eft propietats astrol\u00f2giques i divines a aquests tipus de quadrats, que sovint van ser representats en talismans, i s\u2019han relacionat amb el sol, la lluna i els planetes del nostre sistema solar. A Occident van ser introdu\u00efts a partir del s. XIV pels \u00e0rabs i el monjo grec Mochopoulus i, a partir d\u2019aleshores, van atreure l\u2019atenci\u00f3 de grans matem\u00e0tics com ara Fermat, Pascal, Leibnitz o Euler, que hi van dedicar diverses obres malgrat que no se\u2019n conegui cap utilitat pr\u00e0ctica concreta. <\/p>\n\n\n\n

The basic 3\u00d73 square is quite simple to create, even for those who aren\u2019t expert mathematicians. By finding groups of three numbers that add up to 15, we see that only the number 5 can go in the centre, which must participate in four different combinations that add up to the magic constant (row, column and two diagonals). Continuing in the same manner, we find the numbers that have to go in the corners and on the sides. This will give us the one possible solution, although by turning it different ways we come up with eight possible variants. <\/p>\n\n\n\n

\"The\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n

The 4\u00d74 square, however, is much more complicated, with 110 possible solutions that, turned different ways, give us 880 variants. D\u00fcrer\u2019s is one of these. They all have 34 as the magic constant, but we can see that some solutions are more magical than others in terms of the number of possible combinations that add up to 34. <\/p>\n\n\n\n

En el cas del quadrat de la Sagrada Fam\u00edlia, \u202fhas a total of 310 combinations that add up to 33<\/strong>. Here are the seventeen possible combinations of three numbers: <\/p>\n\n\n\n

\"The\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n

With four numbers, there are 88 possible combinations that add up to 33; with five, there are 131; and with six, 66. With seven numbers, there are eight different combinations: <\/p>\n\n\n\n

\"The\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n

As 1+2+3+4+5+6+7+8=36, more than 33, there\u2019s no possible group of eight numbers or more that can add up to the magic constant of 33. <\/p>\n\n\n\n

MAGIC SQUARES TODAY<\/strong> <\/p>\n\n\n\n

Dan Brown\u2019s best-selling novel The Lost Symbol,<\/em>\u202fbest-seller<\/em>which takes place in Catalonia, Barcelona and at the Sagrada Fam\u00edlia, also uses D\u00fcrer\u2019s magic square as a key to the puzzle to be solved. The author uses an anagram of Isaac Newton with the same seven letters as his name in Latin, Isaacus Neuutonus, reorganised to spell out the message \u201cJeova Sanctus Unus\u201d. If we put these letters in the same order as the seven numbers in D\u00fcrer\u2019s famous magic square, they are encrypted as:<\/p>\n\n\n\n

\"\"\n\t\t\t\n\t\t\t\t\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n\n\n\n

As you can see, centuries and centuries go by but magic squares are here to stay. And at the Sagrada Fam\u00edlia we have a very special one that will go down in history. <\/p>","protected":false},"excerpt":{"rendered":"

Mentre s\u2019esguarda la fa\u00e7ana de la Passi\u00f3 i tot el\u202fconjunt escult\u00f2ric de Subirachs, m\u00e9s d\u2019una vegada, el visitant se sorpr\u00e8n en descobrir uns nombres encreuats dins d\u2019un quadrat i es pregunta: \u00abQu\u00e8 signifiquen aquests nombres?\u00bb.  En realitat, es tracta d\u2019un quadrat m\u00e0gic, per\u00f2 en aquest cas n\u2019\u00e9s un de for\u00e7a especial. En aquest article tractarem […]<\/p>\n","protected":false},"author":10,"featured_media":5664,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22],"tags":[115,139,57],"class_list":["post-3204","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-simbologia","tag-facana-passio","tag-sagrada-familia","tag-simbologia"],"_links":{"self":[{"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/posts\/3204","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/comments?post=3204"}],"version-history":[{"count":0,"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/posts\/3204\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/media\/5664"}],"wp:attachment":[{"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/media?parent=3204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/categories?post=3204"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sagradafamilia.org\/en\/wp-json\/wp\/v2\/tags?post=3204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}