If you ever visit one of the biggest Gaudí’s (1852-1926) architectural achievement in the beautiful city of Barcelona, the world-wide known and still under construction Sagrada Família, and you are passionate about maths, you might want to take a closer look at the sculpture of Judas’ betrayal; right by its side you can find embedded on the Sagrada Família’s Facade of Passion a 4×4 matrix, known as the magic square.
Magic squares are square matrices with feature integer numbers, which add up to the same amount in columns, rows and diagonals. That amount is known as the magic constant and the one concealed in Sagrada Família is the number 33. Check it out:
Notice that there are more combinations which add up to 33. For example, sum the red numbers and the green ones in each square:
This magic square is also included as a decoration in one of the main doors of the Passion Façade. Can you find it?
And what does it stand for? While some people argue it might have something to do with the highest degree in the Masonic lodges – and consequently relates the architect to Freemasonry – the truth is that its author is Josep Maria Subirachs (1927-2014) (Catalan sculptor famous for this design) who chose the number 33 since it’s the age at which Jesus died on the Cross. Whether or not there might be other curious legends surrounding it, it’s remarkable how maths has found room in such a masterpiece. For those who never got along with numbers, here they have a whole new and much more artistic rather than scientific perspective that might light up their face whenever they come across a magic square. Thus everyone can fully enjoy the world of maths!
This post has been written by Carles Raich in the subject Història de les Matemàtiques (History of Mathematics, 2014-15).
Location: Sagrada Família in Barcelona (map)
Some mathematical objects also exhibited here like this Gunter’s square made in 1567. Gunter also invented his scale for computing adapting the new logarithms invented by Napier in 1614. Hence, it’s time to start our visit to all the Napier’s rods and slide rules of the exhibition. Let’s have a look to a couple of them, like these English Napier’s rods from 1720…
or this other ivory set made from the 17th century:
From Gunter scales the slide rules were invented and this spiral logarithmic scale by John Holland (1650) is a very good example of the great inventions of the men from the Renaissance:
After the slide rules and before the computers, ihis fragment of the ‘Difference Engine No. 1’ by Charles Babbage (1832-3) assembled by his son Henry Babbage (c.1880) must also be exhibited:
Finally, a very curious mathematical object: this magic cube made by A. H. Frost in 1877:
Each row, each column and each diagonal have the same sum!
One of the curious objects of the collection is this Tamil charm with a magic square that is not dated. The copper plate carries a magic square in Tamil characters where the letters are equivalent to numbers.
We can also find these Italian engraved discs from the 17th or 18th century:
Although the purposes of these brass discs is not fully known, the were probably magical. [The left one] is engraved with a solar calendar, the signs of the zodiac, and the names of the angels supposed to govern them. [The other disc] has a representation of the Aristotelian cosmos.
And this is the Monument to Mathematics:
This alabaster sculpture illustrates the regular polyhedra and it was presented to the Bodleian Library in 1620 by Sir Clement Edmonds, Fellow of All Souls:
It’s possible to visit a very interesting exhibition in Madrid about Albert Durer’s engravings in the Biblioteca Nacional of Madrid (from the 6 of February to 5 of May):
I was in the Spanish National Library last March and I had the opportunity to visit it. There are 122 engravings designed by this important German artist and we can admire his great Melancolia I between them. We see a lot of geometrical instruments surrounding the main character of the picture but we must pay attention to the truncated rhombohedron with a faint human skull on it and the 4×4 magic square:
We can read the number 1514 on the lower row of the square which is the date of the engraving. As you can see, the four numbers of each row, each column and each diagonal sum up to 34. Durer was 43 when he painted this picture and maybe his passion for the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34,…) was enough to reverse the two figures of the number of his age. So it was a very good opportunity to see this iconic picture in a real exhibition.