Monthly Archives: March, 2013

The Museo del Prado

Sight (1617)
Jan Brueghel “the Elder” and Peter Paul Rubens
Source: Museo del Prado

The Museo del Prado deserves a long time to enjoy all the masterpieces which can be found in it. There are a lot of very important paintings and we can also find some mathematical ones which aren’t the most important pieces of the museum but also deserve a moment in the time of a mathematical tourist. This is the case of Ruben’s Sight. According to the web of the Museum:

This set of paintings on the five senses was one of the most successful collaborations of Peter Paul Rubens and Jan Brueghel “the elder.”

Rubens placed his figures in the magnificent courtly scenes created by Brueghel as settings for these allegories of the senses, resulting in a series of enormous quality and esthetic appeal. The subject was widely employed in Flemish painting.

Sight was considered the most important of the senses since the time of Aristotle. Here, Cupid shows Venus a painting on a Christian therme, The Healing of the Blind Man, which alludes to the recovery of sight through one of Christ’s miracles and thus touches on both physical and spiritual vision.

The presence of a canvas with Saint Cecilia, a copy of Raphael’s original, alongside some Roman busts, recalls the soul’s introspective vision, an image of chastity and virtue.

Jan Brueghel was a protégé of the Archdukes Alberto and Isabel Clara Eugenia, and in this work he includes their portraits and a view of their Palace at Mariemont.

This work is signed on a paper close to the goddess’s seat.

The painting has a lot of mathematical details which I want to show to you. For example, there are a portable sundial, some compasses and a quadrant on the table in the lower left corner:

Detail of the painting

Detail of the painting

There also are one compass more on the floor next to the table with a homothetic ruler and an astrolabe next to it:

Detail of the painting

Detail of the painting

There is an armilar sphere on the cupboard behind the table at the left of Venus:

Detail of the painting

Detail of the painting

Between Venus and Cupid we find two telescopes, a compass and some coins:

Detail of the painting

Detail of the painting

Finally, in a central position there is a globe and a compass on the floor:

Detail of the painting

Detail of the painting

The other pictures of the serie are also interesting but not in our mathematical sense. Walking from Velazquez to Goya, the visitor must admire this masterpiece.

Location: Museo del Prado (map)

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A sundial in Madrid

Photography by Carlos Dorce

Photography by Carlos Dorce

I have found this sundial walking along the Paseo de la Castellana from Cibeles Square to Colon Square. Its location is in fornt of number 15 of the Castellana and it’s in the midle of the trees.

Another globe in Madrid

Celestial globe (XVIIIth century)Photography by Carlos Dorce

Celestial globe (XVIIIth century)
Photography by Carlos Dorce

This celestial globe is in front of the mathematical box of Charles II in the Biblioteca Nacional of Madrid. It was part of the furniture of Manuel Godoy’s personal library. Manuel Godoy was the Spanish prime minister of Charles IV in the periods 1792-1797 and 1801-1808 and preseumed lover of Charles IV’s wife, Maria Luisa of Parma, so he could join a huge fortune and a lot of important possessions.

Portrait of Manuel Godoy (1790)
Francisco Bayeu
Source: Wikimedia Commons

It cannot be dated exactly because there isn’t any inscription or scientific evidence that allow to know more things about the globe.

Location: Biblioteca Nacional of Madrid (map)

The Royal Palace of Madrid

The Royal Palace of Madrid
Source: Wikimedia Commons

The Royal Palace of Madrid isn’t a mathematical place. Today I have visited it but I haven’t found mathematics in the interesting tour through its rooms. The palace was built by Philip V of Spain on the site of a former palace which was partially destroyed by the fire in 1734. The first Spanish king who lived in the palace was Charles III (Philip V’s third son) and Charles IV, Joseph Bonaparte, Ferdinand VII, Elisabeth II, Alfonso XII and Alfonso XIII also lived here.

I must recognize that I couldn’t leave the Royal Palace without getting a picture to write this post and finally I’ve got two “astronomical” details that justify these sentences. The first one is located on the facade of the palace and it’s an explicit reference to the horoscope:

Detail of the facade of the Royal PalacePhotography by Carlos Dorce

Detail of the facade of the Royal Palace
Photography by Carlos Dorce

Detail of the facade of the Royal PalacePhotography by Carlos Dorce

Detail of the facade of the Royal Palace
Photography by Carlos Dorce

The other interesting object is a clock which can be found in the small Porcelain Room next to the room where the king Charles III died in 1788: there is a wonderful clock representing Atlas holding the World:

Photography by Carlos Dorce

Photography by Carlos Dorce

And that’s all! Tomorrow I’m comig back to Barcelona but I’m sure that I’m going to talk about Madrid for some days.

Location: Royal Palace of Madrid (map)

The mathematical box of Charles II of Spain

Mathematical box of Charles II of SpainBiblioteca Nacional (Madrid)Photography by Carlos Dorce

Mathematical box of Charles II of Spain
Biblioteca Nacional (Madrid)
Photography by Carlos Dorce

Charles II (1661-1700) reigned Spain from 1665 to Novermber 1, 1700. He was the last Habsburg king of Spain because he hadn’t got sons although he got married twice! He was a person with a lot of physical and emotional disabilities and one of the worst rulers of the country. His death in 1700 led to the War of the Spanish Succession between the most important European countries.

Portrait of king Charles II of Spain (c.1685)
Juan Carreño de Miranda
Source: Wikimedia Commons

When Philip IV of Spain died, his son Charles II was only 4 years old. Philip IV had married Elisabeth of France (1602-1644) and they only had a son: the prince Balthasar Charles. He had to be the new king of Spain but he died of smallpox in 1646. Then, Philip IV decided to get married again and he chose Mariana of Austria (1634-1696). They had some children but only Charles II and his sister Margarita Teresa survived.

Portrait of Philip IV of Spain (1656)
Diego Velázquez
Source: Wikimedia Commons

In 1665, the young Charles II became the new king of Spain and his mother Mariana of Austria became regent of her son until 1675 when Charles II was declared of legal age. On this occasion, Juan Francisco de la Cerda, Duke of Medinaceli, gave the king this box. The box contains a series of interchangeable pieces with which it is possible to construc fourteen instruments useful for topographic measurements, designing drawings of fortifications or tuning musical instruments. There also is a book that explains the installation and functioning of all these instruments:

Photography by Carlos Dorce

Photography by Carlos Dorce

The set was built by the Spanish mathematician José de Zaragoza (1627-1679). The box is very interesting and it can be enjoyed in the Spanish National Library (Biblioteca Nacional) of Madrid and we can see the complete box, the book, a mathematical ruler and an equilateral triangle over all the set:

Photography by Carlos Dorce

Photography by Carlos Dorce

It’s a shame that a king who wasn’t too smart could have a jowel like this in his hands!

Location: Biblioteca Nacional of Madrid (map)

The paintings of San Lorenzo de El Escorial

Source: Wikimedia Commons

Source: Wikimedia Commons

Today has also been a very rainy day but the weather haven’t been able to wet our decision of visiting the Royal Site of San Lorenzo de El Escorial (about 50 km northwest of Madrid).

The Spanish king Philip II who reigned from 1554 to 1598 decided to build this wonderful bulding to commemorate his victory at the Battle of St. Quentin in Picardy against the French king Henry II in 1557. The complex includes a monastery, a royal palace, a museum, and a school and it’s one of the most interesting royal palaces which can be visited in Spain.

Portrait of Philip II (c. 1564)
Sofonisba Anguissola (1530-1625)
Source: Wikimedia Commons

One of the most interesting mathematical places inside the monastery is the library to which I want to dedicate a post written carefully:

The library of San Lorenzo de El Escorial
Source: http://www.patrimonionacional.es (San Lorenzo de El Escorial)

It’s forbidden to take photos but I have bought a book with some pictures about the library and its ceiling which is full of mathematical allegories. For now, I’ll just mention two “mathematical” paintings which I’ve noticed.

The first one is one of the copies of the known Marinus van Reymerswaele’s The moneychanger and his wife (1538):

The moneychanger and his wife (1538)
Marinus van Reymerswaele (c.1490–c.1546)
Source: Wikimedia Commons

The other is Federico Zuccardo’s Adoration of the Magi (1588):

The Adoration of the Magi (1588)
Federico Zuccardo

The reason why I can say that this painting is mathematical is the inscription below the throne of the Virgin:

Federicivs Zuccardvs

A.D. M D 88

We can see the date 1588 written in Roman and Arabic figures. Furthermore, the Roman figures are the former ⊂I⊃ I⊃ in spite of our M and D. Although the Museum of the Architecture and the Painting is not the most interesting part of the Royal Site, these two paintings deserve a detailed visit.

Location: San Lorenzo de El Escorial (map)

The mosaics of Segovia

The Roman Aqueduct of Segovia
Source: Wikimedia Commons

Segovia is one of the most beautiful Spanish cities. The staple of the city is the Aqueduct (Ist century AD) located in the Plaza del Azoguejo but all the old city is a monument which must be visited if you come to Spain. Another emblematic building of the city is the Alcazar (XIInd century) which was the Royal palace of the Kings of Castile in Medieval times:

Alcazar of SegoviaPhotography by Carlos Dorce

Alcazar of Segovia
Photography by Carlos Dorce

Segovia is also a very mathemtical place. There is not any particular museum or palace but a walk around the old city displays the reason why I am writing this post: it is full of mosaics on the facades of the buildings:

Photography by Carlos Dorce

Photography by Carlos Dorce

There are a lot of buildings with this kind of decoration and we can find some examples of the 17 symmetry groups in which we can clasify all the mosaics represented on the plane. For example:

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Cascales Palace
Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

Photography by Carlos Dorce

If you want to take pictures of mosaics you must go to Segovia and enjoy its mathematical facades. I think that I must come back to Segovia to o a mathematical study about all these wonderful mosaics.

Location: Segovia (map)

El Rastro of Madrid

El Rastro of MadridPotography by Carlos Dorce

El Rastro of Madrid
Photography by Carlos Dorce

El Rastro is a very typical market that you can enjoyin Madrid each Sunday morning. Its origin is in the XVth and XVIth centuries when junkmen, old clothes dealers and butchers and leather tanners around a new slaughterhouse began to meet and trade between the current La Latina and the Puerta de Toledo. Nowadays, a lot of street shops fill up Ribera de Curtidores Street and all the streets next to it.

You must be very careful because there are a lot of people walking and buying things that probably they are not going to use anytime but the flavour of the old Madrid is the essence of wasting your time in a Sunday morning. Indeed, my visit to Madrid has began walking by this special place and I have been able to find some mathematical objects waiting for some exclusive buyer:

DSC03581

Old calculator Facit C1-13 (1960s) in a shop near Puerta de Toledo
Photography by Carlos Dorce

Old calculator Hamann-Manus (1920s) in General Vara de Rey SquarePhotography by Carlos Dorce

Old calculator Hamann-Manus (1920s) in General Vara de Rey Square
Photography by Carlos Dorce

I have tried to haggle their price but I still have not money to buy them!

Location: El Rastro (map)

The centre of Spain

Km. 0
Photography by Carlos Dorce

We have arrived at Madrid this afternoon! We are going to spend some days in the capital of Spain and our first tour for the city has begun in the Puerta del Sol. In this central square there is this point known as “Km. 0” which is the origin of all the Spanish radial roads and motorways. We could say that it-s the origin of the Spanish coordinates!

Location: Puerta del Sol (map)

Josef Alber’s squares

Homage to the Square: Apparition (1959)
Josef Albers (1888-1976)
Guggenheim Museum of New York

LocationGuggenheim (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:

Homage to the Square: With Rays (1959) Metropolitan Museum of Art of New York

Homage to the Square: Soft Spoken (1969)
Metropolitan Museum of Art of New York

Location: The Metropolitan Museum of Art (map)