Dentist Finds Hidden Triangle in da Vinci’s Vitruvian Man — Linking Art, Anatomy and Geometry

A London dentist has identified a previously overlooked geometric element in Leonardo da Vinci’s iconic 1490 drawing, the Vitruvian Man: an equilateral triangle tucked between the figure’s legs whose apex aligns with the navel.

Leonardo’s drawing was inspired by the Roman architect Vitruvius, who argued in De architectura that the ideal human body can be proportionally inscribed in both a circle and a square, using the navel as a central point. Vitruvius described how, when a man lies with limbs extended and compasses centered on the navel, his fingers and toes reach the circumference of a circle; he also explained how the span of outstretched arms can equal the height, producing a square.

Dr. Rory Mac Sweeney, a dentist based in London, published an analysis in the Journal of Mathematics and Arts arguing that Leonardo’s composition also contains an equilateral triangle whose peak meets the navel. Sweeney notes the triangle corresponds to Bonwill’s triangle, a concept in dental anatomy defined by the contact point of the mandibular central incisors and the two mandibular condyles.

Bonwill’s triangle traces to Dr. William Bonwill’s 1864 work on tooth articulation. After studying thousands of dentures and skulls, Bonwill proposed that many optimal dental arches conform to an equilateral-triangle-based geometry — a practical principle in prosthodontics and occlusion.

Sweeney extends the observation beyond dentistry. He shows that if five additional equilateral triangles of the same size are drawn radiating from the navel, they form a hexagonal pattern that underlies a ratio of roughly 1.64 — a tetrahedral ratio — between the side of the square and the radius of the circle. He argues this relationship reflects spatial arrangements seen in efficient biological and synthetic architectures.

To reinforce the broader geometric resonance, Sweeney compares these proportions to Buckminster Fuller’s Isotropic Vector Matrix (1975), suggesting that the relationships connecting crystal geometry, biological form and coordinate systems may also be implicit in human proportions as rendered by Leonardo.

Whether Leonardo intentionally encoded this triangle or whether a modern viewer projects contemporary knowledge onto a Renaissance drawing, the discovery highlights how art invites multiple readings: what the artist put on paper and what a viewer brings to it can both reveal new layers of meaning.

Key points: an equilateral triangle aligns with the Vitruvian navel; it corresponds to Bonwill’s dental triangle; repeated triangles suggest a hexagonal/tetrahedral ratio (~1.64); and these relationships echo later geometric systems such as Fuller’s matrix.