Doge’s Palace in Piazza San Marco is one of the most touristic attractions of Venice. The palace (XIVth c.) is very beaytiful and there is a hidden mathematical secret in one of the capitals of its columns. The capitals of the columns of the palace are dedicated to some biblical passages, quotidian Medieval scenes and… there is one capital dedicated to the Liberal Arts! So we can find here our famous three most representative figures of the Arithmetic, the Geometry and the Astronomy:
Pythagoras is counting money and next to his coins we can read the number 1399 and Euclid has a compass in one of his hands. The column is the first one next to the corner in front of the sea:
You must see this column in Venice!
Location: Piazza San Marco (map)
Next to the Basilica di San lorenzo there is a small building in the corner of two streets with two little polyhedra in the facade. It’s a little detail that nobody notice walking from the Basilica to Santa Maria Novella!
The University of Padua was founded in 1222 after a group of law students from Bologna arrived in the city. After Padua came under the rule of Venice in 1406, the University had a period of splendor to last for two centuries because the Venetian Senate granded Padua the monopoly of university education so nobody could graduate on the Venetian State from a university other than that of Padua.
In 1493, the University of Padua was placed in Palazzo Bo (“Ox”, in Italian). The current building with its courtyard was designed by Andrea Moroni in 1552. The name of the palace is because its proximity to a quarter traditionally occupied by the butchers. In 1405, Francesco I da Carrara who was lord of Padua, donated the former building to a butcher who had assured him of regular supplies of meat. The butcher placed an inn (Hospitium Bovis) in it and the emblem of an ox skull began to be famous in the city. Also dating in the XVIth century is the anatomical theater which remained in use until 1872:
The building is designed around a rectangular arcaded courtyard and the walls are full of important families and graduates coats of arms. In 1688 the Venetian Republic ordered that no new coats of arms should be affixes due to the great number of them which were in the walls.
When we arrived at Padua, the Palazzo Bo was closed but we were lucky because there was an act of homage and we could see the Sala dei Quaranta. This room takes its name from forty famous students of the University of Padua: the English physician William Harvey (1578-1657) and the Danish Thomas Bartholin (1616-1680) among them. These forty portraits were painted by Giacomo dal Forno in 1942. In front of them there is Galileo’s podium. According to the tradition, this podium was used by Galileo Galilei in his lessons in the University. It was located in the Aula Magna until the XIXth century when it was moved to the current location. Galileo Galieli taught at the University of Padua from 1592 to 1610, period in which he improved his telescope and made the first observations of the heaven together with the discovery of the four biggest moons of Jupiter:
The act of homage were placed in the Aula Magna which was the dining room of the old Hospitium Bovis. This Aula Magna was inaugurated on November 7, 1856 and Albert Einstein held a conference there in 1921.
In the XXth century, the wing for the Faculty of Jurisprudence was built and nowadays it’s possible to enjoy a sculpture dedicated to Galileo Galilei:
We can read in the pedestal:
Il Comune, il Rettore e il Senato Accademico dell’ Università di Padova posero nel quattrocentesimo anniversario della chiamata di Galileo Galilei alla Cattedra di Matematica.
Dono della Fidia Farmaceutici.
The reverse of the monument is dedicated to the Sidereus Nuncius.
Location: Palazzo Bo (map)
The Spanish Chapel is one of the most wonderful chapels which can be enjoyed in Santa maria Novella. My students didn’t want to visit it but the teacher could convince most of them to enter the church and they weren’t disappointed.
The fresco entitled The Triumph of St. Thomas Aquinas was painted by Andrea di Bonaiuto (1365-1367) and it was dedicated to…
the great Dominican Doctor of the Church who, illuminated by the spirit of Wisdom, as described in the book lying open in his hands, and supported by the Theological and Cardinal Virtues and the study of the biblical writers of both the Old and New Testaments, defeats heresy, personified by Nestor, Arius and Averroes, and dominates the sciences. These are represented by fourteen allegorical female figures, alluding in part to the Sacred Sciences (left) and in part to the Liberal Arts (right). Each of these is accompanied by a historical personage, famous for having distinguished himself in that articular discipline.
The Theological and Cardinal Virtues are the Charity (over St. Thomas), the Faith and the Hope (at her respectively left and right sides), the Prudence (below the Faith), the Temperance (at the left side of the Prudence), The Justice (below the Hope) and the Fortitude (at her right). On the left of St. Thomas, there are (from left to right) the Biblical authors Job, David, St. Paul, St. Mark and St. Matthew, and on his right (from left to right), St. John the Evangelist, St. Luke, Moses, Isaiah and Solomon. Below St. Thomas, we find Nestor, Arius and Averroes:
The fourteen allegorical women and the corresponding eminent men are (from left to right): the Civil Law with Justinian, the Canonical Law with Clement V, the Philosophy with Aristotle, the Holy Scriptures with St. Jerome, the Theology with St. John of Damascus, the Contemplation with St. Dionysius the Areopagite, the Preaching with St. Augustine, the Arithmetic with Pythagoras, the Geometry with Euclid, the Astronomy with Ptolemy, the Music with Tubalcain, the Dialectics with Pietro Ispano (?), the Rhetoric with Cicero and the Grammar with Priscian (?):
Finally, here you are my privileged students who enjoyed the wonderful Spanish Chapel:
I didn’t only walk through Galileo Galilei’s steps in Pisa two weeks ago. It wasn’t my first time in Pisa but I hadn’t never visited the cemetery of the Piazza dei Miracoli before. I admit that the Camposanto Monumentale is a very interesting place. I could’n imagine that I would enjoy this place so much.
Nevertheless, I visited the cemetery because I was interested in a particular marble statue: Fibonacci is exhibited there! Leonardo da Pisa, Fibonacci (c.1170-c.1230), is one of the most famous mathematical names. We know very little about his life apart from his own biography written in his Liber abaci (1202):
After my father ‘s appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and, in view of i ts future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the ar t very much appealed to me before all other s , and for it I realized that all i ts aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter , while on business, I pursued my study in depth and learned the give-and take of disputation. But all this even, and the algorism, as well as the art of Pythagoras I considered as almost a mistake in respect to the method of the Hindus. Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid’s geometric art , I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters. Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its preeminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it , as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things.
The statue is one of the corners of the cloister and the inscription on the pedestal says: “A Leonardo Fibonacci. Insigne Matematico Pisano del Secolo XII (To Leonardo Fibonacci, eminent XII century Pisan mathematician)”.
The statue was planned by the marquis Cosimo Ridolfi and the baron Bettino Ricasoli from Firenze who wanted to promote the Tuscan culture among the people. Ricasoli was the prime minister of the Tuscany which had benn annexed to teh Savoy Reign in 1859 and Ricasoli was the secretary for education. So in September 23, 1859, they promoted a decree to finance a statue of Fibinacci as “the initiator of the algebraic studies in Europe” in the city of Pisa. The sculptor Giovanni Paganucci was commisioned fot that job and the statue was finished four years later and placed in the Camposanto of Pisa. In 1926, the Fascist goverment decided to place some statues of the cloister in some squares of Pisa trying to show eminent Pisan figures to the people: Fibonacci was one of them. Fibonacci was placed in front of the Ponte di Mezzo in the centre of Pisa. When in 1944 the Alied Troops arrived at Pisa, they bombed all the city and almost all the centre was destroyed. However, our statue of Fibonacci kept its position standing in the middle of the damaged city:
Fibonaci was also little damaged and nowadays he hasn’t got fingers in his hands.
After the II World War, the Camposanto was restored and Fibonacci was kept in a warehouse until he was moved to Giardino Scotto (map). In 1990’s, Fibonacci was accurately restored and was placed in the Camposanto monumentale.
Location: Camposanto monumentale (map)
I’ve been reading about Theo van Doesburg and his art is definitely mathematical! Enjoy some of his paintings:
Counter-Composition XIV (1925) in the Fundacion Villanueva of Venezuela
I think that this post won’t be the last about Van Doesburg!
One of the most intersting frescos painted on the interior walls of Santa Maria Novella is the famous Holy Trinity by Masaccio (1401-1428). The fresco is too big (667 x 317 cm) and is located along the middle of the basilica’s left aisle. According to Wikipedia:
Although the configuration of this space has changed since the artwork was created, there are clear indications that the fresco was aligned very precisely in relationship with the sight-lines and perspective arrangement of the room at the time; particularly a former entrance-way facing the painting; in order to enhance the tromp l’oeil effect. There was also an altar, mounted as a shelf-ledge between the upper and lower sections of the fresco, further emphasizing the “reality” of the artiface.
This picture is very interesting for us due to the perspective which can be observed in it. Giorgio Vasari (1511-1574) wrote about it that:
a barrel vault represented in perspective, and divided into squares full of bosses, which diminish and are foreshortened so well that the wall seems to be hollowed out.
So Masaccio created a three-dimensional space behind the main stars of the picture. If we look carefully at the vault over God and Jesus we’ll be able to trace all the ortogonals in the ceiling and check that the vanishing point is located below the base of the cross. Masaccio designed this vaulted space in an empirical way althought the artistical illusion of depth isn’t so sophisticated.
Anyway, when you come inside Santa Maria Novella, Masaccio’s fresco welcomes you and its vanishing point aligned with your eyes makes you feel a very good ad mathematical feeling:
Location: Santa Maria Novella (map)
Santa Maria Novella was the first great basilica in Firenze. The church was designed by Fra Sisto Fiorentino and Fra Ristoro da Campi and the construction began in the mid-XIIIth century. In the XVth century, the rich textile merchant Giovanni di Paolo Rucellai (1403–1481) hired the great Leon Battista Alberti (February 14, 1404 – April 20, 1472) to design the upper part of the facade of the church (1456–1470). Alberti designed a long frieze decorated with squares in the middle of the black and white marble facade.
In the XVIth century, the mathematician and cosmographer Egnazio Danti (April 1536 – October 19, 1586) lived in the convent of Santa Maria and he was commisioned to design and construct three astronomical instruments to do observations of the Sun. He designed a quadrant (on the right of the facade) bearing six sundials in 1572 and an equinoctial armilla (on the left) in 1574.
The third instrument was a gnomonic hole which he didn’t complete.
Additional information: you can find a statue of Leon Battista Alberti in the Courtyard of the Ufizzi Gallery:
Location: Santa Maria Novella (map)
In the XIVth century, the Italian sculptor Nino Pisano collaborated in the panels for the Campanile (the bell tower) of Santa Maria del Fiore of Firenze. One of his panels has a lot of interest here due to the picture represented in it: it’s Euclid with a compass!
You can find this panel next to the exit door of the church and this isn`t the only mathematical picture that you can find in it! If you follow the frieze you’ll find Ptolemy looking at the night sky using a quadrant in the south side of Giotto’s bell tower:
Location: Giotto’s Campanile (map)