# A building full of squares

This building is full of crystal squares and it’s located in the Rådhuspladsen of Copenhagen, next to Tivoli gardens.

**Location**: Rådhuspladsen (map)

# The wonderful vault of a Royal Library

The King Philip II of Spain decided in 1550’s that he wanted to have a great library near his court in Madrid and he chose the new Monastery of San Lorenzo de El Escorial to place it in spite of other bigger villages. He didn’t want that the new library was a regular room inside a monastery so it had to be a very important place. Therefore, the library was placed on the second floor of the monastery just above his royal chambers but never above the basilica. Between 1565 and 1576, the king bought almost 5.000 books and manuscripts and the library became one of the most important libraries in all Europe.

The mathematician and architect Juan de Herrera (1530-1597) designed a large room (54 m. long x 9 m. wide x 10 m. high) with big windows in both sides under a great barrel vault. This vault had to be decorated by an important painter and Philip II decided that Peregrino Tibaldi (1527–1596) had to be the right artist to do the work. Philip II was advised by Juan de Herrera and other humanists and he decided that the main subject of the paintings of the vault had to be the Liberal Arts. Furthermore, the seven arts would be together with the Philosophy and the Theology on both ends of the room. The Philosophy represented the compendium of the Human knowledge and she is accompanied by Aristotle, Plato, Seneca and Socrates:

The Theology is on the side next to the convent and she represented the Divine knowledge. Therefore the vault represented the way from the Human Philosophy to the Divine knowledge through the seven Liberal Arts: the Arithmetic, the Geometry, the Astronomy (Astrology), the Music, the Rhetoric, the Grammar and the Dialectic. We can see a mathematical detail on the fresco below the Philosophy: it represents the School of Athens and there is a discussion between the Academics leaded by Socrates and the Stoics leaded by Zeno of Elea.

The scholars aren’t listening to the speakers because each of them is “playing” with something different. We can see at the lower left corner a man measuring something with a compass and two books, a sphere and an armilar sphere, a dodecahedron and a compass in the middle of the picture:

Going from the Philosophy to the Theology, we arrive at the Arithmetic after admiring the Grammar, the Rhetoric and the Dialectic. The Arithmetic is a woman turned to a table with simple mathematical operations rounded by muscled young men with tablets with arithmetical operations ans counting with their fingers:

There is also a representation of the Queen of Saba talking with King Solomon According to the Book of the Kings (I,10,1), the Queen of Saba went to meet Solomon to ask some enigmas to him so we can see a ruler, a balance and a tablet with some numbers written on it. In the red tablecloth we can read “Everything has number, weight and measure” in Hebrew:

The other panel next to the Arithmetic represents the school of the Gymnosophists who lived near the Nile and thought their philosophical theories from the numerical computations. In the middle of the picture we can see one of the gymnosophist with a compass looking at a triangle with the word “Anima” and the arithmetic progression 1, 2, 3 and 4 and the geometric 1, 3, 9 and 27 written on it. The other gymnosophists are computing with numbers written on the sand:

Finally, at both sides of the Arithmetic on the roof we find four people related with this subject: Archytas of Tarentum (c.428–c.347 BC) and Boethius (c.480-c.525) in one side and the Platonic Xenocrates (c.396/5 – 314/3 BC) and Jordan in the other. They are writing numbers in their tablets.

There is the Music after the Arithmetic and we find the Geometry after it:

She has a compass in one of her hands and the young men around her have different geometrical instruments. The two scenes which are on the corresponding walls next to her are dedicated to some Egyptian monks drawing geometrical figures on the sand…

and Archimedes’ death:

Notice that Archimedes is drawing the demonstration of the Theorem of Pythagoras made by Euclid!

Finally, the four chosen figures are the Astronomer Aristarchus of Samos (IIIrd c. BC) and the Persian astrologer Abd del Aziz also known as Alcabitius (Xth century) in one side and Archimedes (c.287-212 BC) and Regiomontanus (1436-1476) in the other. Aristarchus is measuring angles and has a dodecahedron at his feet, Alcabitius has a carpenter’s square, Archimedes has a compass and a sphere to measure the Earth and Regiomontanus is pointing at a dodecahedron.

The last Liberal Art is the Astrology. She is backed on a terrestrial globe and her eyes are looking at the sky. She has a compass in one of her hands and the little boys around her have an armilar sphere and some astronomical books:

In one of the two panels on the walls we can see Dionysius the Areopagite observing a solar eclipse the day of Jesuschrist’s death in Athens (Luke, 23,45) We can notice a quadrant and an astrolabe in the hands of the amazed men!

The other fresco represents King Ezekiel resting in bed and looking how time is delayed 15 years by God because of the repentance of his sins:

The four famous men are Euclid, Ptolemy, Alfonso X and Johannes of Sacrobosco. Euclid is represented here meaning the relationship between Astrology and Geometry. He has drawn three geometrical schemes. One is a triangle and a square inscribed in a circle and another square. Another scheme seems to be two overlaid squares partially hidden by Euclid’s name. In the middle of both pictures there is a man measuring the stars. Johannes of Sacrobosco has a quadrant in his right hand.

King Alfonso X of Castile (XIIIth. c) is the author of the *Libros del Saber de Astronomía* (“Books of the Astronomical knowledge”) and on the tablet which he has in his hands we notice a compass and the Ursa Maior (the compass is anachronistic!). His left hand has an open book with a horoscope

So you can see that this wonderful vault is an open mathematical book designed by Tibaldi and Juan de Herrera. I’ve been twice in the library and now I am waiting for the next time that I could enjoy this artistic part of the monastery of San Lorenzo de El Escorial.

**Location**: San Lorenzo de El Escorial (map)

# Josef Alber’s squares

**Location**: Guggenheim (map)

Josef Albers was a German-born American abstract artist whose study of color made possible to create some beautiful geometrical compositions as the *Homage to the Square: Apparition* (1959) kept in the Guggenheim Museum of New York. He enrolled at the Bauhaus school of art in Weimar and where was appointed as a teacher in 1925. He remained in the school until the school closed in 1933 and then he emigrated to the USA. In 1950 he joined the University of Yale and began his famous *Homage to the Square* series. Here you have two paintings more:

**Location**: The Metropolitan Museum of Art (map)

# The Counter-Compositions

I’ve been reading about Theo van Doesburg and his art is definitely mathematical! Enjoy some of his paintings:

** Counter-Composition V** (1924) in Stedelijk Museum of Amsterdam (map)

** Counter-Composition VI** (1925) in the Tate Modern of London (map)

** Counter-Composition VII-The three graces** (1917) in the Mildred Lane Kemper Art Museum of St. Louis (map)

** Counter-Composition X** (1924) in Kröller-Müller Museum of Otterlo (map)

** Counter-Composition XIII** (1925-1926) in Peggy Guggenheim Collection of Venice (map)

** Counter-Composition XIV** (1925) in the Fundacion Villanueva of Venezuela

** Counter-Composition XV** (1925) in the Muzeum Sztuki of Lodz (map)

I think that this post won’t be the last about Van Doesburg!

# Arithmetic Composition

I have accidentally discovered the Dutch painter Theo van Doesburg (1883-1931). Van Doesburg founded the *De Stijl* (the Neo-Plasticism artistic movement) in 1917 together with Piet Mondrian, Bart van der Leck and Vilmos Huszar. The reason of my lucky discovery has been this *Arithmetic composition* although I’m not sure that the picture would represent a geometric progression in sptite of an arithmetic one.

I’m going to search more “Geometrical” pictures painted by Van Doesburg

See you later!

Location: Kunstmuseum Winterthur (map)