Milan

Lying on the Lombard Plain between the River Po and the Alps, Milan (or Milano) is the major cultural, industrial, commercial and financial centre of northern Italy, and a city second only to Rome in size and importance in Italy. Its long and often turbulent history has provided it with a mixture of old and new buildings, from castles, palaces and churches to ultra-modern office blocks and shopping precincts. Outstanding destinations for the visitor include the magnificent Italian Gothic cathedral and La Scala Theatre, the famous Opera House, although soccer buffs will insist that any match with AC Milan playing is a must.

One of Milan’s ‘hidden’ treasures is Leonardo da Vinci’s masterpiece The Last Supper, which may be found on the wall of the refectory (dining hall) of the former Dominican monastery of Santa Maria della Grazie.   



























Leonardo and The Last Supper

Leonardo (1452-1519) was the greatest and most complex genius of the Renaissance, if not of all time. At once a mathematician, scientist, technologist, engineer, inventor, cartographer, anatomist, architect, poet, philosopher, sculptor, graphic artist and painter, he was not primarily a painter, yet the few paintings which he produced (including the Mona Lisa ) show that he was a supreme artist.

The Last Supper was painted on the wall at one end of the refectory using a form of linear perspective which created the illusion of the room of The Last Supper being continuous with the refectory. Unfortunately the surface quality of the wall (due to the underlying bricks) and the dampness of the hall caused the painting to deteriorate rapidly, so that today, despite a valiant final attempt at restoration between 1985 and 1999, only a hint of its former glory is evident. However, its masterful composition and mathematical precision can still be appreciated.

Further reading ...

Bouleau, C. (1980), The Painter’s Secret Geometry, Hacker Art Books.
Wallace, R. (1971), The World of Leonardo 1452-1519, Time-Life International.
http://www.artchive.com/artchive/      































The hidden structure of The Last Supper

The painting, The Last Supper, in real life is 4.6 m 8.8 m. The following links show some of the hidden structure. Relate the lines to the painting’s features

Renaissance artists commonly used diagonals and other interior lines or armature of a rectangle to divide rectangular space proportionally for compositional purposes without resort to a drawing compass. Thus, the main diagonals of a rectangle allow division into halves, both vertically and horizontally. Similarly, the diagonals of the halves allow division into quarters.     


























Rabatment

Another device used by Renaissance artists to construct pictures was rabatment, by which the shorter sides of the picture rectangle are rotated onto the longer. This produces vertical divisions of the picture, and creates overlapping squares, the overlap of which depends on the shape of the rectangle.

 Investigate  In the second example (lower right), the small central square has vertices which lie on the sides of the overlapping squares. Prove that the encompassing rectangle is a golden rectangle.

Here is an example of the use of rabatment by the artist Giotto in his painting Trial by Fire or St Francis before the Sultan painted around 1325. Note how the rabatment is used to define the sides of the throne.     

























Musical ratios and phi

   Introduction     The idea      Example     






























Example of the Golden Ratio

Here is a 3 4 retangle with ‘ divisions’, together with the relevant armature. The marks a side division of 1 : ; the ' a division of : 1. As usual, the horizontal and vertical lines and the armature lines were used to assist in the composition of the painting.

Division by was used by Dürer in his series of etchings The Apocalypse. This one is entitled The Opening of the Sixth Seal.

Check this.

    
























A final painting

This is a reproduction of Piero della Francesca’s The Flagellation. You can view some of the perspective lines. Which of the above methods do you think Piero used in composing the picture: rabatment? armature? musical ratios?