The

*Vitruvian Man* (1492) is the famous sketch by

Leonardo da Vinci
showing the various geometrical proportions in the

human body. Da Vinci
drew this sketch based on a description by the Roman

architect Vitruvius (1st century B.C.) In

*De
Architectura*, Vitruvius describes many aspects of architecture,
including

mensuration. It is his suggestion that the proportions in
the human body can be related to geometrical figures,

*i.e.* the
human body has a universal,

mathematical perfection.

Da Vinci's sketch shows a human figure with two sets of arms and two
sets of legs. The horizontally and vertically stretched arms and legs
touch a square indicating the relationship between the arm span and
height of the man. At the center of the square are the man's
genitals. The diagonally stretched arms and legs touch a
circle, with the navel at its center. An interesting observation is
the consonance of the square and the circle (*cf.* Squaring the
Circle). In classical history, the square represents the physical
world (*e.g.*the four elements, the four wind directions),
while the circle represents the spiritual world (mother earth, with
the navel at its center.)

There are many different geometrical proportions in da
Vinci's sketch. However, the most important one is the Golden Ratio,
and especially the division around the navel: the ratio of the length
from the man's head to the navel and the length from the navel to his
feet is equal to the ratio of the length from the navel to his feet and
the total height of the figure. But the golden ratio is present in all
scales. For instance: the length of the upper arm divided by the
length of the lower arm and stretched hand is equal to the length of the
lower arm and stretched hand divided by the length of the entire arm.

*Text accompanying Leonardo da Vinci's sketch of Vitruvian
Man:*

Vitruvius, the architect, says in his work on architecture
that the measurements of the human body are distributed by Nature as
follows that is that 4 fingers make 1 palm, and 4 palms make
1 foot, 6 palms make 1 cubit; 4 cubits make a man's height. And 4
cubits make one pace and 24 palms make a man; and these measures he
used in his buildings. If you open your legs so much as to decrease your
height 1/14 and spread and raise your arms till your middle fingers
touch the level of the top of your head you must know that the center of
the outspread limbs will be in the navel and the space between
the legs will be an equilateral triangle.
The length of a man's outspread arms is equal to his height.

From the roots of the hair to the bottom of the chin is the tenth of a
man's height; from the bottom of the chin to the top of his head is one
eighth of his height; from the top of the breast to the top of his
head will be one sixth of a man. From the top of the breast to the roots
of the hair will be the seventh part of the whole man. From the
nipples to the top of the head will be the fourth part of a
man. The greatest width of the shoulders contains in itself the fourth
part of the man. From the elbow to the tip of the hand will be the
fifth part of a man; and from the elbow to the angle of the armpit
will be the eighth part of the man. The whole hand will be the tenth
part of the man; the beginning of the genitals marks the middle of the
man. The foot is the seventh part of the man. From the sole of the
foot to below the knee will be the fourth part of the man. From below
the knee to the beginning of the genitals will be the fourth part of the
man. The distance from the bottom of the chin to the nose and from the
roots of the hair to the eyebrows is, in each case the same,
and like the ear, a third of the face.