Vitruvian Man

Leonardo da Vinci's 'Vitruvian Man' was originally intended as an illustration for a book about the works of Marcus Vitruvius Pollio. It has subsequently become an iconic image representative of the humanistic culture of the Renaissance, in more recent times we have even sent this image into outer space to represent our species!

As an illustration, the construction was intended to show how in Vitruvius's architectural scheme, the proportions of the human form are in geometrical harmony with nature and the universe. The square and the circle. But how was this geometrical construction drawn? It is true that starting with the proportions of the human body and following Vitruvius’s text, given in mirror writing on Leonardo’s drawing, a construction may be achieved. However, a more complex geometrical association lies behind the relationship of this square and circle besides its implied symbolism.

If one accepts that the construction is representative of a more significant geometrical principal, then as the drawing appears complete, with no constructional geometry in evidence, the implication is then that the method used to make the drawing must be commonly understood, at least that is, by the person that made the drawing.

The relevance of this construction to our studies of viola geometry may not be at first apparent, until the two constructional systems are compared. My own work has led me to employ a simple way of achieving certain desired proportion by using a square and a circle, this geometric device being much more sympathetic to the proportions apparent in the viola pattern than other popular systems, such as those based on the golden section etc. Once I started applying this system to my drawings everything on the design just kept falling into place!

This page explores the similarity in the constructions of this famous Renaissance drawing by Leonardo da Vinci and the core geometry of the workshop viola design. Also a simple construction, based on the viola geometry, shows how the square and circle of the Vitruvian Man may be drawn.

The proportional relationship between the square, its inscribed circle and the second larger circle is attained by an arc scribed from the point c, with a center C, to establish point K on the horizontal axis, thus establishing the radius of the larger secondary circle.

This construction establishes a principal of proportion that may be used throughout the viola drawing. The equilateral triangles are shown drawn for the secondary circle, which significantly also relate directly to the f hole layout.

This practical geometry may also be observed in Leonardo’s drawing the ‘Vitruvian Man’. Here the secondary circle is again established, in this instance with an internal equilateral triangle constructed. If a line is drawn from the base corner of this triangle to the opposite corner of the square, the point at which it intersects the vertical axis is the center for the final circle with a given radius from the navel to point K.

It is interesting also to note the position of the fingers where the respective circles cut the boundary of the square, the position of the upper hands in relation to the diagonals, but even more striking is the detail of the hair of Leonardo's drawing falling exactly within the upper part of the triangle.

A construction may be summarized as follows:

For a given square ABCD an internal circle is scribed with a center O.
A tangential arc is scribed off the circle at c using a center at the corner of the square C.
This cuts the horizontal axis at K.

An internal equilateral triangle EFG is now constructed in this secondary larger circle.
Take a line from triangle corner G to square corner B.

Where this line intersects the vertical axis a new center J is established.

Using a radius r from J to K the final circle may be drawn.

J is therefore the navel of the Vitruvian Man.

In any geometric systematic drawing, further geometrical associations may always be found within a particular drawing. Indeed, the author of such a drawing would most likely not have been aware of all the possible connotations, even if he was aware of the geometric and mathematical potential of the system. It is, however, often useful to highlight those that may have relevance to the subject in hand.

This drawing shows the square circle triangle construction that I use as the central construction for the viola patterns, overlaid onto Leonardo’s Vitruvian man.

This construction, which I use to apply proportions to the violas, was arrived at by working workshop requirements and independently of any reference to Leonardo’s drawing. I view the similarities between the two constructions as highlighting the idea that basic geometric constructions can, and were, be applied to different practical applications.