Sunday, November 27, 2011

Mathematics an Art-Vitruvian Man(leonardo Da vinci)

The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci circa 1487. It is accompanied by notes based on the work of the famed architect, Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man. It is stored in the Gallerie dell'Accademiain Venice, Italy, and, like most works on paper, is displayed only occasionally.
The drawing is based on the correlations of ideal human proportions with geometry described  by the ancient Roman architectVitruvius in Book III of his treatise De Architectura. Vitruvius described the human figure as being the principal source of proportion among the Classical orders of architecture. Leonardo's drawing is traditionally named in honor of the architect.

Subject and title
This image exemplifies the blend of art and science during the Renaissance and provides the perfect example of Leonardo's keen interest in proportion. In addition, this picture represents a cornerstone of Leonardo's attempts to relate man to nature.Encyclopaedia Britannica online states, "Leonardo envisaged the great picture chart of the human body he had produced through his anatomical drawings and Vitruvian Man as a cosmografia del minor mondo (cosmography of the microcosm). He believed the workings of the human body to be an analogy for the workings of the universe."
According to Leonardo's preview in the accompanying text, written in mirror writing, it was made as a study of the proportions of the (male) human body as described in Vitruvius. The text is in two parts, above[a] and below[b] the image.
The first paragraph of the upper part reports Vitruvius: "Vetruvio, architect, puts in his work on architecture that the measurements of man are in nature distributed in this manner, that is:
  • a palm is four fingers
  • a foot is four palms
  • a cubit is six palms
  • four cubits make a man
  • a pace is four cubits
  • a man is 24 palms
and these measurements are in his buildings". The second paragraph reads: "if you open your legs enough that your head is lowered by one-fourteenth of your height and raise your hands enough that your extended fingers touch the line of the top of your head, know that the centre of the extended limbs will be the navel, and the space between the legs will be an equilateral triangle".
The lower section of text gives these proportions:
  • the length of the outspread arms is equal to the height of a man
  • from the hairline to the bottom of the chin is one-tenth of the height of a man
  • from below the chin to the top of the head is one-eighth of the height of a man
  • from above the chest to the top of the head is one-sixth of the height of a man
  • from above the chest to the hairline is one-seventh of the height of a man
  • the maximum width of the shoulders is a quarter of the height of a man
  • from the breasts to the top of the head is a quarter of the height of a man
  • the distance from the elbow to the tip of the hand is a quarter of the height of a man
  • the distance from the elbow to the armpit is one-eighth of the height of a man
  • the length of the hand is one-tenth of the height of a man
  • the root of the penis is at half the height of a man
  • the foot is one-seventh of the height of a man
  • from below the foot to below the knee is a quarter of the height of a man
  • from below the knee to the root of the penis is a quarter of the height of a man
  • the distances from the below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one-third of the face
Leonardo is clearly illustrating Vitruvius' De architectura 3.1.2-3 which reads:

For the human body is so designed by nature that the face, from the chin to the top of the forehead and the lowest roots of the hair, is a tenth part of the whole height; the open hand from the wrist to the tip of the middle finger is just the same; the head from the chin to the crown is an eighth, and with the neck and shoulder from the top of the breast to the lowest roots of the hair is a sixth; from the middle of the breast to the summit of the crown is a fourth. If we take the height of the face itself, the distance from the bottom of the chin to the under side of the nostrils is one third of it; the nose from the under side of the nostrils to a line between the eyebrows is the same; from there to the lowest roots of the hair is also a third, comprising the forehead. The length of the foot is one sixth of the height of the body; of the forearm, one fourth; and the breadth of the breast is also one fourth. The other members, too, have their own symmetrical proportions, and it was by employing them that the famous painters and sculptors of antiquity attained to great and endless renown. Similarly, in the members of a temple there ought to be the greatest harmony in the symmetrical relations of the different parts to the general magnitude of the whole. Then again, in the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.
The multiple viewpoint that set in with Romanticism has convinced us that there is no such thing as a universal set of proportions for the human body. Vitruvius' statements may be interpreted as statements about average proportions. Vitruvius takes pains to give a precise mathematical definition of what he means by saying that the navel is the center of the body, but other definitions lead to different results; for example, the center of mass of the human body depends on the position of the limbs, and in a standing posture is typically about 10 cm lower than the navel, near the top of the hip bones. Anthropometrical studies have shown that while the Vitruvius correctly proposed that the proportions of the human body are consistent between individuals, care should be taken in accepting the exact proportions proposed by him - for example a study comparing caucasian male American college students (average height of 180.6 cm and average foot length of 28.2 cm) and Japanese exchange students (171.4 and 25.8 cm respectively) gives ratios of 6.40 and 6.66 rather than 6.0 as proposed by Vitruvius.
Leonardo's drawing combines a careful reading of the ancient text with his own observation of actual human bodies. In drawing the circle and square he correctly observes that the square cannot have the same center as the circle, the navel, but is somewhat lower in the anatomy. This adjustment is the innovative part of Leonardo's drawing and what distinguishes it from earlier illustrations. He also departs from Vitruvius by drawing the arms raised to a position in which the fingertips are level with the top of the head, rather than Vitruvius's much lower angle, in which the arms form lines passing through the navel.
The drawing itself is often used as an implied symbol of the essential symmetry of the human body, and by extension, of the universe as a whole.
It may be noticed by examining the drawing that the combination of arm and leg positions actually creates sixteen different poses. The pose with the arms straight out and the feet together is seen to be inscribed in the superimposed square. On the other hand, the "spread-eagle" pose is seen to be inscribed in the superimposed circle.
The drawing was purchased from Gaudenzio de' Pagave by Giuseppe Bossi, who described, discussed and illustrated it in his monograph on Leonardo's The Last SupperDel Cenacolo di Leonardo da Vinci libri quattro (1810). The following year he excerpted the section of his monograph concerned with the Vitruvian Man and published it as Delle opinioni di Leonardo da Vinci intorno alla simmetria de'Corpi Umani (1811), with a dedication to his friend Antonio Canova.
After Bossi's death in 1815 the Vitruvian Man was acquired, along with the bulk of his drawings, by the Accademia.

Medical Origins and Context
Recently researchers at Imperial College London have analysed the drawing to identify that the image demonstrates that the subject has a likely groin disorder (left sided inguinal hernia). This is a common condition typically treated by surgery in the modern-era, but may also reflect that Leonardo da Vinci may have based the Vitruvian Man on a cadaver who may have died from this condition.

Representations in modern times
The Vitruvian Man is now used as a contemporary symbol of medical professionals and medical establishments. Many medical companies have adopted this artwork as the symbol of their group, company or organization, particularly in the United States, Saudi Arabia, India, and Germany. It has also come to represent alternative medicine and the holopathic approach to wellness.
The Vitruvian Man remains one of the most referenced and reproduced artistic images in the world today. The proportions for the human body, as proposed by Vitruvius, have inspired many other artists in drawing their version of the Vitruvian Man:
  • Cesare Cesariano (1521) who edited the important 1521 edition of De Archtectura of Vitruvius (Leonardo da Vinci is supposed to have provided the illustrations for this edition).
  • Albrecht Dürer (1528) in his book Vier Bücher von menschlicher Proportion (four books on human proportions)
  • Pietro di Giacomo Cataneo (1554)
  • Heinrich Lautensack (1618)
  • William Blake (1795) “Glad Day” (now known as "Albion rose"). This representation is without the circle and square.
  • Susan Dorothea White's version Sex Change for Vitruvian Man (2005).
As well as its use by the medical profession, the Vitruvian Man has been used in a variety of fictional and non-fictional media, for various symbolic purposes. For example, the image appears on the national side of Italian 1 euro coins, chosen by the Economy Minister (and later President of the Italian Republic) Carlo Azeglio Ciampi for its high symbolic meaning of "man as a measure of all things".
A space-suited figure in the same superimposed poses of Vitruvian Man appears on a patch worn on the right shoulder of the American Extravehicular Mobility Unit (EMU) space suit used by NASA. This patch, called the EVA patch, is also awarded to spacewalkers for use on uniform jumpsuits as an indicator that the individual has completed a spacewalk.
Stylized Vitruvian Man figures have been adopted for the icons representing accessibility in the Mac OS and Gnome desktop computer interfaces.
Particularly when used in fiction, the image of the Vitruvian Man is commonly modified to suit the setting by featuring a character, a skeleton or a non-human (such as a robot in science fiction or an animal). The easily-recognisable image lends itself to being referenced.

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