Why even after 500 years of his death, do we still admire Leonardo da Vinci’s varied accomplishments in painting, architecture, and mathematics? Because he is truly the “Supreme Genius of the Ages.”

His paintings: The Mona Lisa, The Last Supper, and Vitruvian Man are some of the iconic images in the history of western art. These drawings are such an extraordinary legacy; they made the thirst for knowledge so visual.

Leonardo was the authentic interpretation of a polymath renaissance man. Apart from being a visionary painter, he was an engineer, anatomist, and chronicler of science.

Although he had a minimal impact on the science and technology of his time, today, we have enough pieces from the ‘Leonardo Puzzle’ to actually see how ahead of his time he was in many ways — and in fact, we’re still learning from him.

To comprehend his scientific brilliance and innovative mind, let’s observe his iconic painting “The Vitruvian Man,” which beautifully signifies Leo’s ability to observe the world and meticulously record thoughts in beautiful illustrations.

What is Vitruvian Man?

Vitruvian man is a sketch drawn in 1480 with pen and ink on paper that redefined beauty and changed the landscape of art during the Renaissance era. It is the picture of the naked man standing inside a square and a circle that beautifully depicts the unique intersection of art and mathematics — at which Leonardo spent most of his time throughout his life.

The sketch “Vitruvian Man” references the first-century BCE Roman architect and civil engineer Marcus Vitruvius Pollio.

According to Marcus,

“The navel is the center of the human body, and if one takes a compass and places the fixed point on the navel, a circle can be drawn perfectly around the body.”

He further added that:

“The arm span and height have a nearly perfect correspondence in the human body, thus placing the body perfectly inside a square as well.”

Both Vitruvius and Leonardo saw real implications in the alignment between anatomy and geography.

This concept was tied in with the problem of “squaring the circle,” (finding a procedure to hand-draw a circle and square of equal area) proposed by ancient geometers.

Leonardo used Vitruvian Man in his sketch to find the solution with the interesting proportions of the human body.

His solution with Vitruvian Man gives us a unique vision into the human body — one that’s obsessively symmetrical, deceptively simple, but extraordinarily beautiful.

How does the Vitruvian Man relate to math?

Man is the symbol of God’s supreme creation, the ultimate expression of the cosmos itself. Da Vinci painted a nude man standing inside a square and circle with arms and legs wide open in two different positions to find the underlying mathematics in his drawing.

The measurements of man in nature are distributed in a manner that:

The size of a palm is = four fingers (1:4)

A cubit is = 6 palms (1:6)

Foot is = 4 palms (1: 4)

4 cubits make a man =24 palms (6 x 4) if legs are wide open (1:24)

The head is lowered by 1/14 of height if hands are raised enough that the extended fingers touch the line of the top of the head.

Remember that the center of the extended limbs will be the navel, and space between the legs will be an equilateral triangle, and the length of a man’s outspread arms is equal to his height.

Da Vinci demonstrated the beauty and simplicity of proportions with simple dimensions. To square a circle with the same area, Leonardo tried his best by using the proportions of his body.

To calculate the area of a circle, we have a formula:

The circle has a radius of 2 with its center at the navel.

The Area of the square is:

A square has a base of 4 cubits and a height of 4 cubits.

To take the area of a circle and create a square with an equal area(squaring a circle), Vinci took the navel of the human body as the center of the circle. He then placed the man’s body perfectly inside a square as Vitruvius claimed — the arm span and height have a nearly perfect correspondence in the human body.

Leonardo considered the area of the human body to be equal to the areas of squares and circles as the man’s body perfectly fits both shapes.

Around the time Leonardo sketched the Vitruvian Man, however, a Neoplatonist named Pico Della Mirandola had a different idea.

He claimed that:

humans have a mortal body accompanied by an immortal soul; they divide the universe nicely in half. They have a unique ability to take any position they want as God made them capable of comprehending the beautiful universe HE had created. God has placed mankind at the center of the universe with the ability to take whatever form he likes.

With this concept, Leonardo tried to change the man’s position as long as he can fill the irreconcilable areas of a circle and a square.

However, Leonardo wasn’t utterly successful in solving this problem due to the irrational nature of pi, he did get extremely close!

He also described the model body in the following fractions:

• From the hairline to the base of the chin is 1/10 of the height of a man

• From beneath the chin to the head’s top is 1/8 of the height

• From over the chest to the hairline is 1/7 of the height

• From above the chest to the head’s top is 1/6 of the height

• The maximum width of the shoulders is 1/4 of the height

• From the breasts to the head’s top is 1/4 of the height

• The distance from the elbow to the hand’s tip is 1/4 of the height

• The distance from the elbow to the armpit is 1/8 of the height

• The length of a hand is 1/10 of the height of a man

Parting Thoughts

If geometry is the language with which God has written the universe, then Vitruvian Man seems to declare that we can exist within all its elements.

Vitruvian Man is not just a beautiful work of art; it was also Leonardo da Vinci’s attempt to solve the geometric problem that had been frustrating mathematicians since the days of Pythagoras.

Leonardo da Vinci practiced his love of mathematics in everything he did. His artistic works of surpassing beauty proved once and for all that mathematics truly is the universal language.

Originally published at Medium