New research claims that the Vitruvian Man is not just a beautiful sketch from the Renaissance, but the outcome of a rigorous geometric construction based on a forgotten system of measurements centred on the number 120.
A 2,000-year-old challenge hidden in a drawing
The story starts long before Leonardo. In the first century BCE, the Roman architect Vitruvius wrote that a well-proportioned human body could fit perfectly inside both a circle and a square. The navel, he said, should be the centre of the circle, while the body’s height should equal its arm span, defining the square.
This created a clear geometric puzzle. If the navel is the centre of the circle, the centre of the square cannot sit in exactly the same place without stretching or compressing the body. For centuries, this contradiction remained more a philosophical idea than a technical problem.
Medieval artists dealt with it symbolically rather than mathematically. Only in the 15th century did engineers and draftsmen start to wrestle with the geometry. Figures drawn by Taccola and Francesco di Giorgio Martini show bodies attempting to match Vitruvius’s rules, but the limbs look misaligned or stiff, exposing the difficulty of the construction.
Leonardo’s bold move: shifting the centre of the circle
Around 1490, Leonardo picked up Vitruvius’s challenge with a different ambition. He did not just want to illustrate the ancient text. He wanted to solve its internal contradiction.
Recent work by Jean-Charles Pomerol, emeritus professor at Sorbonne University, and independent Leonardo specialist Nathalie Popis, argues that the key lies in a subtle but radical decision: Leonardo moves the centre of the circle down from the navel to the pubis.
By relocating the centre to the pubis, Leonardo changes the entire geometry of the figure while keeping the body believable.
In the famous version with outstretched arms and spread legs, the body is in a so‑called dynamic position. The centre of gravity drops lower, towards the pelvis. Setting the circle’s centre at the pubis makes the figure mechanically more stable, closer to how an actual body balances when limbs open outward.
In the second posture, the one matching the square, the man stands upright with legs together and arms horizontal. Here, the height equals the arm span, just as Vitruvius described. Leonardo, who measured real bodies and dissected cadavers, knew this relation was broadly valid in nature.
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Pomerol and Popis show that these two different postures are not a visual trick. They are a deliberate strategy: one position solves the square, the other solves the circle. Together, they answer the Vitruvian puzzle without distorting human anatomy.
Geometry that moves with the body
This dual posture turns the Vitruvian Man into more than a frozen diagram. It reflects how the body shifts when arms and legs move, how weight transfers through joints, and how balance adjusts with posture.
The drawing is not a mystical symbol; it is a compact study of gravity, equilibrium and human movement.
Leonardo’s choice lines up with principles already laid out by Archimedes about balance and centres of mass. In modern terms, the drawing encodes a primitive biomechanics lesson inside a single sheet of paper.
The secret grid: why the number 120 matters
The study goes beyond centres and circles. It argues that Leonardo built the entire figure on a hidden measuring grid based on the number 120.
Why 120? Because it is what mathematicians call a “highly composite” number: it can be divided exactly by 2, 3, 4, 5, 6, 8, 10 and 12. That makes it ideal for expressing simple fractions without decimals, a useful feature when you are drawing with a pen, not a calculator.
Every major segment of the Vitruvian body can be expressed as a clean fraction of 120, forming a tightly organised network of proportions.
According to Pomerol and Popis, Leonardo assigns 120 units to the full height of the man, then breaks this down into parts that match observed anatomy:
- distance from pubis to top of the head: 60 units
- length of the hand: 13 units
- length of the foot: 17 units
On their own, these numbers might look arbitrary. Together, they form a grid with consistent relations between vertical and horizontal segments. The forearm aligns proportionally with the foot. The torso segments match clear fractional rules. Each measurement refers back to the same master unit.
A link to ancient calculation traditions
This logic echoes much older numerical habits. Ancient scholars often worked with base‑60 systems. We still use this today when we split hours into 60 minutes, or circles into 360 degrees. The number 120, as double 60 and product of the first five integers (1×2×3×4×5), fits naturally into that tradition.
For Pythagorean thinkers, numbers like these were not just convenient. They signalled an underlying order in nature. Leonardo, steeped in classical sources, appears to revive that mindset, but applies it to measured flesh and bone rather than abstract harmony.
| Body element | Proportional value (out of 120) | Implied idea |
|---|---|---|
| Total height | 120 | Master reference for all other parts |
| Pubis to top of head | 60 | Half the total height, anchoring the torso |
| Hand | 13 | Small but structurally linked to other limbs |
| Foot | 17 | Supports balance and mirrors forearm length |
The researchers argue that this framework does not warp the figure just to fit pretty numbers. Instead, Leonardo starts with observation, then chooses a number system flexible enough to match what he sees.
A rare fusion of ancient maths and hands-on anatomy
Leonardo’s notebooks show how deeply he engaged with Greek mathematics. Euclid’s geometry, Pythagorean number philosophy and Archimedean mechanics all feed into his work.
Yet he does something unusual for his time: he checks these theories against direct observation. Between 1506 and 1513 he systematically dissected human bodies, measuring bones, noting how muscles attach, and tracing the way weight passes through the skeleton.
For Leonardo, authority was not enough; a claim about proportion had to withstand the test of the knife and the ruler.
The Vitruvian Man, seen through the lens of the new study, stands at this crossroads. Axes, angles and centres are laid out with mathematical discipline. At the same time, details of the torso, limbs and joints show a careful respect for real anatomy.
From symbol to scientific diagram
Pomerol and Popis insist that the drawing should not be reduced to a cultural logo of the Renaissance or a vague emblem of “humanity at the centre of the universe”. It functions as a compact scientific diagram: an attempt to express, on one sheet, how numbers, geometry and living bodies can fit together.
The use of two postures, one for the square and one for the circle, shows that Leonardo is willing to bend the textual rule in order to keep physical plausibility. The text of Vitruvius is treated as a starting point, not a rigid script.
Why this matters for today’s readers
For anyone working with the human body today—designers, physiotherapists, 3D modellers, sports scientists—the study offers a reminder: proportions are rarely arbitrary. Good models often rest on simple, repeatable ratios, just as Leonardo set up with his grid of 120 units.
Imagine designing a virtual character for a video game. Instead of eyeballing each limb, you could define a base unit—say the total height—then express hand, forearm or foot length as stable fractions. The result feels more natural because relationships stay consistent, just as in the Vitruvian construction.
The approach can also help in teaching geometry. Using the Vitruvian Man as a case study, pupils can experiment with circles, squares, centres of gravity and ratios, then test these ideas by sketching or with simple digital tools. It turns an iconic image into a working laboratory for concepts that often feel abstract on the blackboard.
Key notions behind the Vitruvian riddle
Several notions underpin the new interpretation and are worth keeping in mind:
- Proportion: the relation between different parts of a whole, often expressed as simple ratios such as 1:2 or 5:8.
- Centre of gravity: the point where the weight of a body can be thought to act; moving limbs shifts this point.
- Highly divisible numbers: integers like 60 or 120 that can be split into many equal parts without fractions, ideal for measurement schemes.
- Dynamic posture: a position where limbs are not aligned with the main axes, forcing geometry to adapt to movement.
The new study on Leonardo’s drawing suggests that when we look at the Vitruvian Man, we are not just seeing a Renaissance fantasy of perfection. We are also looking at a careful attempt to give a precise geometric answer to a 2,000‑year‑old question, one unit out of 120 at a time.