Vitruvian Man

(Leonardo da Vinci, 1490, Gallerie dell'Accademia, Venice)

The Vitruvian Man, considered the symbol of Renaissance art, is probably the most famous drawing created by Leonardo da Vinci (1452 – 1519).

This work, done in pen and ink on paper, is based on the study of the ideal proportions of the human body. In the upper and lower part of the drawing there are two explanatory texts of the work, which refer to the "De Architectura" of Vitruvius, Roman architect and writer, active in the second half of the 1st century b.C. The "De Architectura" was written by Vitruvius probably around 15 b.C. and it was dedicated to the emperor Augustus. The treatise, despite having architecture as its main topic, spoke of the human body and its perfect geometric proportions.

Vitruvius presents “De Architectura” to Augustus (1654 print).

Leonardo Da Vinci, in his dual capacity as scientist and artist, was very fascinated by human anatomy, so much so that he delved into the aspect concerning the golden section in his anatomical studies.

Leonardo da Vinci inscribes the Vitruvian Man in the geometric figures of the circle and the square, which Plato considered perfect figures and which Leonardo da Vinci related to each other, following the rules of the golden section. Observing the drawing, it can be noted that the opening of the man's arms is equal to the side of the square, while the navel represents the center of the circle but not that of the square, which instead has the man's pubis in the center; tracing a segment passing through the navel and parallel to the opening of the arms, 2 golden rectangles are identified.

Modulor

(Le Corbusier)

The word “Modulor” derives from the contraction of the French words module (module) and nombre d'or (golden number); it is a system of units of measurement that the Franco-Swiss architect Le Corbusier (1887 – 1965), pseudonym of Charles-Édouard Jeanneret-Gris, created in 1945, applying the golden section to the dimensions of the human body. The two dimensional scales (the blue series and the red series) of which the Modulor is composed are based on the Fibonacci sequence.

Modulor finds its cultural roots in classical Greece and Renaissance artists. In fact, Le Corbusier developed this measurement system in the wake of Vitruvius' treatises and the works of the architect Leon Battista Alberti (1404 – 1472). The goal was to find geometric and mathematical proportions related to the human body and to use this knowledge to improve the aesthetics and the functionality of the architecture.

Le Corbusier published the first edition of Modulor in 1948 and he proposed it in 1949 as a system to be used to size buildings and interior furnishings.

The graphical representation of Modulor is a stylized human figure with one arm raised, standing inside a square. This figure provides three measurements which, in a man of average height, correspond to:

• 113 cm - height from ground to navel;

• 70 cm - distance between the navel and the top of the head;

• 43 cm - distance between the top of the head and the fingertips of the raised hand.

These three measurements are in golden ratio and follow the principle of the Fibonacci sequence; in particular:

• 43 + 70 = 113;

• 113 + 70 = 183;

• 113 + 70 + 43 = 226.

Furthermore, the measures 113, 183, 226, which characterize the occupation of the space by a standing man six feet tall, represent:

• 113 cm - height from ground to navel (as already highlighted);

• 183 cm - height of the average man;

• 226 cm - height of the man with his arm raised.

Le Corbusier applied for the first time the proportions of the Modulor in the project of the Unité d'Habitation in Marseille (1945 – 1952).

It can be said that Modulor is a sort of manual that Le Corbusier would have wanted on the table of every architect and on the walls of every construction site.

The human body and the golden ratio

Drawing of the proportions of the human body

(early 19th century)

Different parts of the human body, such as the arms, fingers and height, respect the "Divine Proportion". In particular, the harmony and sense of beauty are greater if the ratios between the measurements of the human body approach the value of the golden ratio.

For example, the human face can be completely decomposed into a grid with rectangles whose sides are in the golden ratio and in a beautiful face it is equal to φ:

• the ratio of height to width of the face;

• the ratio of height to width of the nose;

• the ratio of length to height of the profile of the mouth.

Golden ratios are also those between the phalanges of the middle and ring finger:

It should be added that the Fibonacci sequence, related to the golden number φ, appear also in the DNA chain. In fact, for each complete cycle of the spiral double helix of the DNA, the sizes:

• 21 Angstrom (2.1 nm) – width;

• 34 Angstrom (3.4 nm) – length;

are numbers belonging to the Fibonacci sequence and their ratio, which is 1.6190476..., approximates very well the golden number φ = 1.6180339...: