Leonardo da Vinci, the renowned Italian polymath celebrated for his creation of the Mona Lisa, possessed a profound geometric comprehension that significantly predated contemporary understanding.
In the crafting of the Vitruvian Man in 1490—a seminal illustration depicting the ‘ideal’ human form—it is posited that the Renaissance master may have drawn upon a mathematical proportion that was not formally codified until well into the 19th century.
This artwork stands as one of history’s most recognizable images, yet for over five centuries, the rationale behind da Vinci’s specific choices for limb proportions remained elusive.
As elucidated in a recent publication issued last year, a London-based dental professional believes he has finally resolved this enduring enigma.
A comprehensive summary is provided in the video below:
Rory Mac Sweeney identified a pivotal, concealed element within the lower pelvic region of the Vitruvian Man: an equilateral triangle, which he suggests could illuminate “one of the most scrutinized yet enigmatic works in the annals of art history.”
The conceptual framework for the Vitruvian Man is partly derived from the treatises of Vitruvius, a Roman architect, who advocated for the notion that the perfect human physique could be inscribed within both a circle and a square simultaneously.
Da Vinci’s detailed sketch employs a square to meticulously frame a ‘cruciform stance,’ characterized by outstretched arms and adducted legs. Concurrently, a circle encompasses a pose where the arms are elevated and the legs are spread apart.
A prevalent hypothesis posits that da Vinci based the Vitruvian Man’s proportions on the Golden Ratio Theory; however, the actual measurements exhibit a divergence from this principle.
According to Mac Sweeney, “the resolution to this geometric quandary has been conspicuously present all along.”
“When one spreads their legs… and elevates their arms to the extent that their fingertips align with the apex of the head… the inter-leg space forms an equilateral triangle,” da Vinci documented in his preparatory notes for the Vitruvian Man.
Upon performing calculations concerning this triangular formation, Mac Sweeney ascertained that the separation of the figure’s feet and the distance to his navel established a ratio approximating 1.64 to 1.65.
This value is remarkably proximate to the tetrahedral ratio of 1.633—a geometric configuration distinguished by its inherent balance, which was officially defined in 1917.
This ratio is instrumental in determining the most efficient method for packing spherical objects. For instance, when four spheres are arranged in the tightest possible configuration to form a pyramidal structure, the ratio between the height of their centers and the diameter of their base is 1.633.
It is plausible that Mac Sweeney recognized the significance of this numerical value due to a comparable triangular principle employed in dentistry since 1864.
When applied to the structure of the human jaw, the Bonwill triangle delineates the optimal positioning for its functional efficacy. Its inherent ratio also measures 1.633.
Mac Sweeney perceives this correlation as more than mere coincidence.
Analogous to minerals, crystalline structures, and other naturally occurring biological aggregation systems, Mac Sweeney hypothesizes that the human jaw naturally organizes itself around tetrahedral geometries, thereby maximizing mechanical efficiency.
If this tetrahedral ratio is indeed replicated across the human physique, Mac Sweeney hypothesizes that it stems from the principle that “human anatomy has evolved in accordance with geometric frameworks that govern optimal spatial arrangement throughout the cosmos.”
Should Mac Sweeney’s assertions prove accurate, it suggests that Leonardo da Vinci may have inadvertently discovered a universal principle during his creation of the Vitruvian Man.
“The identical geometric interrelationships observed in maximally efficient crystalline formations, biological edifices, and Fuller’s coordinate systems appear to be embedded within human proportions,” Mac Sweeney elaborates, “implying that Leonardo intuitively grasped fundamental truths pertaining to the mathematical essence of existence itself.”
The degree to which the scientific community will endorse Mac Sweeney’s findings remains to be determined, but the very fact that da Vinci made explicit mention of the equilateral triangle in his notes underscores the significance of the area between the Vitruvian Man’s legs.
This research was formally presented in the Journal of Mathematics and the Arts.
