Geometrical construction of the Vitruvian Man by Leonardo da
Vinci
The Vitruvian Man is a world-renowned drawing created by
Leonardo da Vinci around the year 1487 It is accompanied by notes
based on the work of Vitruvius. The drawing, which is in pen and
ink on paper, depicts a nude 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'Accademia in
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 architect
Vitruvius 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. Other
artists had attempted to depict the concept, with less success.
The drawing is traditionally named in honour of the architect.
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."
It is also believed by some that Leonardo symbolized the material
existence by the square and spiritual existence by the circle. [
Source: Wikipedia.org ]
It is assumed that proportions of the circle and square reflect
Golden Division.
Here we present analysis that shows that this assumption is
incorrect.
Fig. 1 Comparison of true Golden Rectangle
with Vitruvian Man drawing
Fig. 2 Circle and square based on Golden Section
If a circle has radius = 1 unit, square side is equal to:
1.656 for Vitruvian Man
1.618 for Golden section construction
1.571 for the condition: circumference of the circle = perimeter
of the square
1.772 for the condition: area of the circle = area of the square
Squaring the circle is a problem proposed by ancient geometers. It
is the challenge of constructing a square with the same area as a
given circle by using only a finite number of steps with compass
and straightedge.
Fig. 2b Squaring the circle.
Image on the right: Squaring the circle: the areas of this square
and this circle are equal.
Image on the left: Circumference of the circle equals the
perimeter of the square.
Fig. 2b Left shows a circle with Radius = 1 and a
square with side = 1.571.
The Circumference of the Circle = 6.28... [ 2 x Pi = 6.28 ]
The square with side 1.571 has perimeter equal 6.28 [ 4 x 1.571 =
6.28 ].
Fig. 2b Right shows a circle with Radius = 1 and a
square with side = 1.772.
The Area of the circle is 3.14 [ as determined by pi multiplied by
the radius squared ].
The area of the square is also 3.14... [1.772 x 1.772 ].
Vitruvian Man - methods of geometrical construction
of the circle and the square
The simplest composition is based on a square, which is
duplicated and rotated 45º to form an octagram. The distance
between the base line of the first square and the apex of the
rotated one simply represents the diameter of the circle.
Fig. 3 The simplest way to describe
the
geometrical construction of the Vitruvian Man.
* * *
Another method of geometrical construction of
the Vitruvian Man:
Step 1: Draw a square and circle (radius R1) as
shown on the Fig. 4
Fig. 4 Click to enlarge
Step 2: Move circle so point A overlaps with
point B (see Fig. 5):
Fig. 5 Click to enlarge
Step 3: Locate center of the final circle (point
O) by Dividing distance AB in a half.
Draw new circle with radius R2=OA (see Fig.6)
Fig. 6 Click to enlarge
The result matches perfectly Leonardo's drawing:
Fig. 7 Superimposed image of Fig.6 and
Leonardo's drawing.
Return to the main article:
Fibonacci Numbers in Nature & the Golden
Ratio
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