Some 500 years ago, Leonardo da Vinci sketched what he believed was the perfectly proportioned male body.

The drawing, called the Vitruvian Man, is one of the most famous anatomical drawings in the world.

The complex interplay of art, mathematics and human anatomy has puzzled scientists for hundreds of years.

But now, a London-based dentist claims to have worked out the secret to how da Vinci perfectly placed the human figure inside a circle and a square.

Dr Rory Mac Sweeney, a qualified dentist with a degree in genetics, says the key to unlocking the drawing's geometric code lies in the use of an 'equilateral triangle' between the man's legs, mentioned in manuscript notes that accompany the drawing.

The researcher discovered this isn't just a random shape – and in fact reflects the same design blueprint frequently found in nature.

Analysis reveals this shape corresponds to Bonwill's triangle, an imaginary equilateral triangle in dental anatomy that governs the optimal performance of the human jaw.

This suggests da Vinci understood the ideal design of the human body centuries before modern science, Dr Sweeney said.

When this triangle is used to construct the drawing it produces a specific ratio between the size of the square and the circle.

Dr Sweeney has discovered that this ratio – 1.64 – is almost identical to a 'special blueprint number' – 1.6333 – that appears over and over again in nature for building the strongest, most efficient structures.

This same number is found in the geometry of a perfectly functioning human jaw, the unique proportions of the human skull, the atomic structure of super-strong crystals and the tightest way to pack spheres.

'We've all been looking for a complicated answer, but the key was in Leonardo's own words,' Dr Sweeney, who graduated from the School of Dental Science at Trinity College in Dublin, said.

'He was pointing to this triangle all along. What's truly amazing is that this one drawing encapsulates a universal rule of design.

'It shows that the same "blueprint" nature uses for efficient design is at work in the ideal human body.

'Leonardo knew, or sensed, that our bodies are built with the same mathematical elegance as the universe around us.'

According to the dentist, the discovery is significant because it shows that Vitruvian Man is far more than just a beautiful piece of art. 

Instead, it is the work of 'scientific genius that was centuries ahead of its time', he said.

The pen-and-ink drawing of the nude male in two different poses, with arms and legs enclosed within a circle and square, was created by the Renaissance polymath around 1490.

It was partly influenced by the writings of Roman architect Marcus Vitruvius Pollio, who believed the human body has harmonious proportions.

He proposed that a human figure could fit perfectly inside a circle and a square but provided no mathematical framework for achieving this geometric relationship.

Da Vinci, who solved the puzzle, never explicitly explained how. For the last 500 years scientists have come up with numerous theories and ideas but none have matched the actual measurements.

The study, published in the Journal of Mathematics and the Arts, reads: 'For over 500 years, Leonardo da Vinci's geometric system for establishing the precise relationship between the circle and square in his Vitruvian Man drawing has remained a mystery.

'This paper demonstrates that Leonardo's explicit textual reference to "an equilateral triangle" between the figure's legs provides his construction method and reveals the anatomical foundation for his proportional choices.

'The analysis shows that Leonardo's equilateral triangle corresponds to Bonwill's triangle in dental anatomy—the foundational geometric relationship governing optimal human jaw function.'

It concludes: 'The findings position Vitruvian Man as both artistic masterpiece and prescient scientific hypothesis about the mathematical relationships governing ideal human proportional design.'

Scientists have previously compared the Vitruvian Man with nearly 64,000 physically fit men and women and discovered da Vinci was close to anatomical measurements of the modern-day humans.

The team found the groin height, shoulder width and thigh length of today's measurements were 10 percent within those of the Vitruvian Man.

However, the head height, arm span, chest and knee height are slightly more than da Vinci's estimates.