Leonardo Da Vinci’s *Vitruvian Man *is one of the world’s most recognizable images — but what does it really mean?

Well, this seemingly simple notebook sketch attempted to do the impossible: to understand Man’s place in the universe.

Today, we explore how it solved an unsolvable problem from ancient times, and set culture on a new course for centuries to come…

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**A Metaphysical Math Riddle**

The Renaissance was a collision between the grandeur of classical antiquity and the theological richness of Christendom.

The combination of the two gave rise to some of history’s greatest paintings, music, and buildings, but it also created some philosophical snags that troubled genius minds for generations. One of those snags was the problem of “squaring the circle.”

In mathematical terms, the problem is simple enough: is it possible to draw a square and circle with the same area, using only a compass and a straightedge?

Metaphysically, however, the problem went far deeper.

The shape of the square was long associated with the physical world — its four sides and corners were reflected in the four cardinal directions, four seasons of the year, and the traditional four elements that comprise the cosmos.

The circle, lacking a beginning or end, represented infinity, or the divine world. Renaissance art and architecture drew on the interplay between these two shapes to symbolize the union of Heaven and Earth.

On the level of mathematics, the ancient riddle was about figuring out how to unite two geometrical shapes. But on a deeper level, it asked a far more important question — can the physical world ever be fully united to the divine?

**Insight from Ancient Times**

Renaissance thinkers who wrestled with this question finally struck gold when, in 1416, an ancient text was rediscovered…

*De Architectura *was the masterwork of a Roman architect named Vitruvius. In it, he explains the principles that classical architects used to incorporate the patterns of nature into their buildings, from the proportions of rooms to the slopes of roofs. Vitruvius gave Renaissance architects a blueprint for achieving the symmetry, proportion, and geometry that would connect their buildings with God’s creation.

Most astonishingly, Vitruvius revealed that a building’s ideal proportions could be found in plain sight — in the proportions of the human body.

Vitruvius reasoned that the outstretched limbs of a perfectly proportioned man could create the foundation points of a circle and a square that would harmonize with one another:

For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.

Several thinkers attempted to make sense of this before Leonardo did. One architect tried to draw Vitruvius' description, and another measured a man against a church floor plan…

Vitruvius’ insights into proportions ultimately allowed his readers to construct palaces, cathedrals, and other works of art that still dazzle the world, but they also provided the key to “squaring the circle” — although it would take a genius, unconventional mind to fully crack the code.

That’s where Leonardo steps in.

**A New Solution**

Squaring the circle is, mathematically speaking, impossible (due to the nature of *pi*, being an irrational number).

However, Leonardo’s genius wasn’t limited to mathematics, and he understood that this age-old problem was about more than just math. While the Renaissance was grappling with the question of humanity’s place in the cosmos, this ancient riddle taunted its thinkers with the concern that the physical realm could never be fully joined to the heavenly one — thus leaving humanity forever separated from the divine.

Drawing on his creativity, Da Vinci came up with an image that solved the problem even more elegantly than a mathematical formula — the Vitruvian Man.