The Vitruvian Man and the logo of Mind of Dave

Leonardo's Blend of Math and Art

Created by Leonardo da Vinci around the year 1487, the Vitruvian Man is a beautiful combination of science and art that at the same time demonstrates Leonardo's deep understanding of proportion. It depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square.

Leonardo's seemingly simple drawing created in pen and ink on paper is da Vinci's attempt to answer an age-old geometric problem. The notes accompanying the drawing, sometimes called the Canon of Proportions or the Proportions of Man, elaborately outline the significant concepts and interpretation of the drawing in geometric form. The drawing is also believed to be the philosophical solution to the nature of man and an analogy for the workings of the universe.

The work and the accompanying text were based on the famous treatise on architecture by the famed architect, Vitruvius Pollio. Vitruvius believed that the principles governing the representation of the human form also applied to temple architecture in terms of weight, symmetry and proportion. He provides numerous observations about the proportions of the human body, including that the navel is the center of the human body, which can be used as a fixed point to draw a perfect circle around the body, that the height of a man was nearly equal to his arm span and that a sketch of a body with arms outstretched could perfectly be placed inside a square. This claim that a human body could fit into both a circle and a square captivated da Vinci greatly. Many of his contemporaries struggled to render this idea in visual form.

Another concept that also fascinated da Vinci was the mathematical problem of squaring a circle. The area of a circle or square could be easily calculated individually, but the real challenge laid in constructing a square with the same area as a given circle using a compass and a straightedge.

The Geometry of The Vitruvian Man

A man of science and art, Leonardo da Vinci created a drawing which, unlike those of all the other artists, was meticulously done. The innovative part which distinguishes it from earlier illustrations is that he separated the center of the two postures one for the circle centered at the navel and the other for the square at the genitals. It is believed that this solution was first put forth by Giacomo Andrea, Leonardo's dear friend and an expert on Vitruvius. There's some debate about whether the pair worked in tandem, but nevertheless, historians agree Leonardo perfected flaws in its execution where Giacomo failed.

The notes accompanying Leonardo's drawing clearly elaborate on the classical architecture concepts by Vitruvius, as well as Leonardo’s observations on proportions and geometry. Fascinated by the ideal proportions of the human body, he applied the concept of the golden ratio to his design. His notes include:

If you open the legs so as to reduce the stature by one-fourteenth and open and raise the arms so that the middle fingers touch the level of top of the head, know that the centre of the extremities of the outspread limbs will be in the navel, and the space between the legs will make an equilateral triangle.

Vitruvian Man prototype by Giacomo Andrea de Ferrara, 1490 or earlier. Captions, via Creative Commons

Man as the Center of the Universe

Leonardo da Vinci was concerned with not only finding the ratios of man but of all creation. In a notebook from 1492, Leonardo wrote:

By the ancients man has been called the world in miniature; and certainly this name is well bestowed, because, inasmuch as man is composed of earth, water, air and fire, his body resembles that of the earth.

Envisioned as a cosmografia del minor mondo (cosmography of the microcosm), the Vitruvian Man represents a cornerstone of Leonardo's attempts to relate man to nature. Since ancient times, the circle connoted things divine and cosmic. It has the perfect shape where all of its points on its circumference are equidistant from the center. The square is the symbol for the earth, for all physical manifestation, and for our orientation on earth via the four directions, four seasons and four elements. Fitting within a circle, humans were a reflection of the celestial. Fitting within a square, humans were also a reflection of the Earth. Symbolizing different aspects of the universe, humans could bridge the gap between the terrestrial and the divine.

In an attempt to find a relationship between spirit and matter, between God and man, Da Vinci correlated the symmetry of human anatomy to the symmetry of the universe, giving it a literally universal application. The individual with the natural geometric perfection, fills the universe itself, being in cohesion with, simultaneously creating one within himself.

Throughout history, Leonardo's image has been recurrently used to illustrate the Renaissance idea of man as a symbolic microcosm, thus praising his role as the center of the universe. A fine example of Leonardo's constantly inquiring mind, the Vitruvian Man continues to fascinate artists, mathematicians and philosophers alike.