Leonardo da Vinci The renowned Italian multi-talented individual known for painting the Mona Lisa possessed an advanced grasp of geometry far beyond his era.
To draw the Vitruvian Man in 1490 - a depiction of the "perfect" human physique - A person from the Renaissance era might have used a mathematical proportion that was officially recognized only in the 19th century.
One of the most famous pictures ever taken, but for over 500 years, people couldn't understand why Leonardo da Vinci used those particular measurements for the arms and legs.
A dental professional from London believes he has finally uncovered the answer to the enigma.
Related: Four Methods That Demonstrated Leonardo da Vinci's Advanced Thinking for His Era
Rory Mac Sweeney has uncovered a significant concealed element, located in the area of the Vitruvian Man's groin: an equilateral triangle that he thinks could clarify the phrase "one of the most studied but enigmatic pieces in the history of art."
The Vitruvian Man draws inspiration from the works of Roman architect Vitruvius who claimed that the ideal human body could be contained within a circle and a square.
Leonardo da Vinci's sketch employs a square to accurately enclose a 'cross-shaped' position, with limbs extended outward and feet together. In contrast, the circle surrounds a stance where the arms are lifted upward and the legs are apart.
A common interpretation is that da Vinci selected the measurements of the Vitruvian Man according to the principles of... Golden Ratio Theory but the dimensions aren't entirely consistent.
According To Mac Sweeney, "the answer to this geometrical puzzle has been visible all along."
"If you spread your legs apart... and lift your arms so that your outstretched fingertips reach the level of the top of your head... the area between your legs will form an equilateral triangle," Leonardo da Vinci wrote in his annotations for the Vitruvian Man.
After performing calculations on this triangle, Mac Sweeney discovered that the distance between the man's feet and the height of his belly button resulted in a ratio approximately ranging from 1.64 to 1.65.
This is nearly equal to the tetrahedral ratio of 1.633 — an exceptionally stable shape, formally recognized in 1917.
The ratio helps determine the most efficient method of arranging spheres. For example, when four spheres are packed together as tightly as possible in a pyramidal formation, the ratio of height to base measured from their centers equals 1.633.
Maybe Mac Sweeney understood the importance of that figure due to a comparable triangular concept applied in dental practice.
Conceived within the human jaw, Bonwill's triangle It determines the ideal placement for jaw functionality, having been utilized since 1864. Its proportion is also 1.633.
Mac Sweeney believes this isn't just chance.
Just like minerals, crystals, and various natural packaging structures seen in biology, Mac Sweeney believes the human jaw inherently forms around tetrahedral shapes, which enhance mechanical effectiveness.
If the tetrahedral proportion is continually present around our bodies, Mac Sweeney thinks That is due to the fact that "human anatomy has developed following geometric laws that dictate efficient space arrangement across the universe."
If Mac Sweeney is correct, Leonardo da Vinci might have uncovered a fundamental law while sketching the Vitruvian Man.
Similar geometric patterns found in ideal crystal formations, living organisms' designs, and Fuller's coordinate frameworks appear to be present within the dimensions of the human body, writes Mac Sweeney, "indicating that Leonardo grasped essential insights regarding the mathematical essence of reality."
It is uncertain whether other scientists support Mac Sweeney's views, yet the fact that Da Vinci referenced the equilateral triangle in his writings implies that the element located between the Vitruvian Man's legs holds significance.
The research was released in the Journal of Mathematical Artistry .