Florence

Florence (It. Firenze) is an historic and beautiful city which straddles the river Arno. A mass of red terra-cotta tiled roofs is punctuated by the façades of the many old palaces, churches and villas which are the glory of the city. The skyline is dominated by the immense dome of the cathedral (Duomo) and its bell tower, and the tower of the town hall (Palazzo Vecchio). This city of 500 000 people, a major centre of art and learning in Italy, was home to Leonardo da Vinci, Raphael and Michelangelo.

In the square in front of the town hall stands a copy of the huge statue of David by Michelangelo. The original was removed in 1873 to the Academy (Galleria dell ‘Accademia), just a few streets away, where it may be seen today along with other sculptures by Michelangelo, and many other Florentine works of art. David is arguably the most recognized single statue in the history of art.
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Michelangelo and David

Michelangelo (or Michelagniolo Buonarroti) (1475–1564) became an artist, against his father’s wishes, at the age of 13. Originally apprenticed as a painter, he rapidly achieved fame also as a sculptor, and later in life as a poet and architect. The range of his supreme talent is highlighted by his four greatest works: the Pietà in St Peter’s in Rome, the Last Judgement on the wall of the Sistine Chapel in the Vatican, the dome of St Peter’s Basilica in Rome, and the statue of David in Florence. David was carved from a single piece of white Carrara marble which had been rejected by other sculptors as being too shallow. The statue was originally commissioned to decorate the cathedral, but became the first since the time of ancient Rome to be presented separately on its own plinth. It represents the moment at which the youthful David is about to slay Goliath, and is filled with political and cultural symbolism. For the Florentines it represented the ideal of the self-sufficient republic ready to withstand any pressure from its neighbours. For Michelangelo, David was the embodiment of his personal ideal of male strength and beauty. It is more Greek than Hebrew in its representation, and while alluding to Lorenzo de’ Medici, the ruler of Florence, it bears some facial resemblance to the artist himself. This single work established Michelangelo as the greatest sculptor in Italy.































David and human proportion (I)

Michelangelo made countless drawings and measurements of the human body (living and dead, as well as Greek and Roman statues) in order to understand its shape, proportions and variations. Of course, human proportions vary with the individual, but in classical art, the body of the ideal figure is 8 head-lengths from head to toe. In real life the adult human body is 7 to 8 head-lengths. Dürer favoured 7.5 head-lengths in his pictures, Rembrandt used 7, while Giacometti at times used 12. The figure of David uses 7 head-lengths.

 Investigate Taking the head-length as the vertical distance from under the chin to the top of the head, measure the height of a number of people in h-l. What is the average height and how does it relate to the classical ideal?

For the classically-trained artist, these ‘rules of thumb’ indicate the relative proportions of the human body:
Age
Height
(in head-lengths)
1
4
8
12
16
adult
old age
4
5
6.5
7
7.5
8
7
 Investigate Check the above figures against body measurements found in paintings and sculptures. Survey people of different ages to check the figures with real-life data.

The choice of 7 head-lengths for David emphasized his youth, but was probably used to correct for distortion due to the observer’s position: David’s head is some 7 m above ground level. If rendered in ‘correct’ proportion, the head would appear too small.

























David and human proportion (II)

Taking the eight head-lengths body as a standard, there are other rules of thumb adopted by artists for depicting the human body (allowing for male-female differences). Some are given in the table below. Lengths are in head-lengths.

Lengths
Body benchmarks      
0.5
 • eye level to top of the head
• pelvic ridge to bottom of rib cage		 • knuckles to finger-tips
0.75
 • length of hand: wrist to finger tips
• length of collar-bone       		 • vertical height of shoulderblade
• length of breastbone
1
 • bottom of shoulderblade to back of neck (top of protruding vertebra)
• distance between male nipples
• distance between pelvic ridges      		 • length of foot
• height from navel to nipple-line
• distance from navel to pubic bone
1.5
 • distance across chest (male)
 • distance across male hips
2
 • leg from knee to ankle
• lower arm from elbow to fingertip
• width of female torso including arms at mid-chest height		 • leg from top of hip bone to knee
• leg from top of hip bone to knee
• width of male shoulders betwen shoulder joints
3
 • navel to top of the head
• length of outstretched arm from armpit to fingertip		 • navel to knee cap

 
4
 • pubic bone to top of the head
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Leonardo and human proportion

A variation of the above view of human proportion may be found in the work of Leonardo da Vinci, and is embodied in the adjacent diagram. It suggests that the navel divides the height of the body in a golden section (:1 1.618:1, compared with 8:5 above), and is the centre of a circle enclosing the outstretched arms and legs. As well, the erect body is contained within a square bounded by the bottom of the feet, the top of the head and the fingertips of the outstretched arms held to the sides at shoulder height. The pubic bone divides the height exactly in half. Note that the figure uses the convention of eight head-lengths. This view was current in Ancient Greece and conveyed to Leonardo via the works of Vitruvius, who also influenced Michelangelo. In recent times this view was revitalized by Le Corbusier.

 Investigate  Find out whether 8:5 or = 1.618 ... is closer to the real-life proportion for the height of the body relative to the height of the navel. What about the other relationships allegedly apparent in the human body?

 





















Vitruvius and human proportion

Probably the earliest canon of human proportion in the Western world (the Ancient Egyptians had one much earlier) was that of Roman architect Marcus Vitruvius Pollo (31 B.C. – 14 A.D.). He wrote in his De architectura libri decem,

‘A magnificent temple cannot be constructed properly, unless it is built in an orderly manner with regard to symmetry and proportion of its parts, as is the case with a well-built man. For the human body is designed by nature, put together and created so that the head from the chin to the hairline measures one tenth of the entire body. Likewise the flat or extended hand from the wrist to the tip of the middle finger is equal to the distance from the chin to the part of the hair, i.e. one eighth part. Likewise from the bottom of the neck and the high point of the chest to the hairline, one sixth; and to the top of the head, one quarter. But to the level of the mouth, one third; from the tip of the chin to the nose, from the tip of the nose to the midpoint of the eyebrows, and thence to the root of the hair, each one third. The length of the foot is one sixth of the body length, the forearm one quarter, the chest one quarter. In this manner all other limbs have their proportional measurements, which were observed by ancient painters and sculptors.’

 Investigate  Check out the Vitruvian system of proportion by drawing some figures in accord with the system, or checking it against real-life data.

 



























Dürer and human proportion

Albrecht Dürer (1471 – 1528), German painter, engraver and mathematician, made a detailed study of the human form, and was thoroughly familiar with the work of Vitruvius, Leonardo and other Italian Renaissance artists. He explored many methods for constructing the human form according to their shape and proportion. He used circles, triangles, ratios and proportions, and polyhedra (a method known as stereometry), and was a pioneer in investigating the shape and proportion of the human body under the influence of ‘perspective projection’. Among these studies, he investigated the human head and its facial characteristics, distorting its shape using grid transformations.

 Investigate   Sketch a head in profile (say, from a magazine) within a 10 10 square grid. Now redraw the picture within grids in which the grid lines are spaced at other than equal intervals, or in which the grid lines are curved. What effect does this have on the shape or ‘look’ of the head?

 
























Human proportion: average vs ideal (Quételet) 
(for those with some statistics)

Based on thousands of measurements of the human body taken from the Renaissance artists and from his own collection, Adolphe Quételet (1796 – 1874), a Belgian astronomer, mathematician and statistician, defined the ‘average man’ whose measurements were the average of all measurements. For Quételet, the average was an ideal value: other measurements of the same trait were distributed about this according to the normal probability curve. The Average represented the Ideal of the species, and deviations from the Average were considered to be ‘errors of measurement’.

According to the normal distribution curve, if we measure (say) the height of 100 people in cms, then the heights will be distributed approximately as follows:

34 heights lie between the mean and +1 standard deviation (d.v.) from the mean,
14 heights lie between +1 and +2 d.v. from the mean,
2 heights lie beyond +2 d.v. from the mean,
and similarly for heights which lie below the mean. The heights are thus symmetrical about the mean.

 Investigate  Measure the heights of 100 people and plot them on a frequency histogram. Calculate the mean and standard deviation and mark these on the histogram. Count the number of heights within each standard deviation interval. Do your data follow the normal curve?
























Human proportion: average vs ideal (Galton)

Following Quételet, Sir Francis Galton (1822 – 1911), English scientist, explorer and anthropometrist, showed that if any set of measurements within a population (e.g. the heights of all people) is normally distributed, then so are sets of similar measurements of any subgroup of that population, and vice versa. He showed too there is a correlation between the measurements of different parts of the body.

For example, for white U.S. males aged 18 to 30 years, the relationship between the height of a person and the length of the upper arm bone (humerus) is

y = 3.08x + 70.45, where y = height in cms and x = length of humerus in cms.

For white U.S. females aged 18 to 30 years, the relationship is y = 3.36x + 57.97.

The expected or standard error for males is ± 4.05 cms, for females, ± 4.45 cms.

Such relationships are important in forensic pathology and anthropology as a means of predicting the likely height and other characteristics of a body from bone measurements. More widely, such data are critical in ergonomics: the size and shape of the ‘average person’ are important in designing human environments and equipment.It is interesting to ponder whether a person of the proportions of Michelangelo’s David would be comfortable in today’s world!