ABOUT DR. RORY Mac Sweeney
Dentist. Anatomist. Geometric detective.
Biography
Dr Rory Mac Sweeney is a London-based dental surgeon and independent researcher. His background spans craniofacial anatomy and a long involvement in competitive sport karate, where he developed a practical feel for balance, structure, and how the body organises efficient movement.
That combination — clinical training in human structure alongside a movement practitioner’s sense of proportion — shaped the question behind his research: whether the proportions of Leonardo da Vinci’s Vitruvian Man can be accounted for geometrically.
His 2025 paper in the Journal of Mathematics and the Arts sets out the ratio √(8/3) ≈ 1.633 — which arises exactly in tetrahedral geometry and hexagonal close-packed crystals — and argues it offers a candidate account of the drawing’s proportions, reachable with compass and straightedge alone. He continues to explore where the same ratio may be relevant in craniofacial and dental architecture.
Academic & Clinical Foundations
- Doctor of Dental Surgery, London
- Research in craniofacial geometry and proportional systems
- Contributor to interdisciplinary dialogue between art history, mathematics, and biological form
Public Recognition
“The Dentist Who Solved the Vitruvian Man Mystery” — The Independent
“Mac Sweeney’s 1.633 ratio is an elegant structural solution bridging art and anatomy.” — Oral Health Group
The Vision
For over five centuries, Leonardo da Vinci’s Vitruvian Man has inspired artists and scientists alike. There has been much speculation as to the meaning of the drawing…
My research suggests Leonardo’s drawing ideal human proportions reveals a hidden structure of balance—what modern geometry calls the Vector Equilibrium, the perfect state where all forces are equal and in harmony.
The Geometry of Balance
The Vector Equilibrium
In this structure, every edge, radius, and angle is equal.
It represents total balance—the zero point between motion and rest.
Nature builds from this state: atoms, crystals, and even living forms follow its geometry.
The Flower of Life
Leonardo sketched this pattern in his notebooks.
Six circles surrounding a seventh form a perfect hexagon, the blueprint for the Vector Equilibrium in two dimensions.
It is the same symmetry seen in snowflakes, honeycombs, and the seeds of a sunflower.
Leonardo’s Geometry
Leonardo left a simple clue on Vitruvian Man:
“the space between the legs will be an equilateral triangle.”
That triangle generates the hexagonal symmetry behind the circle.
The square defines orthogonal symmetry, the geometry of architecture.
Where the triangle’s logic meets the square’s order, a universal proportion appears—the geometry of balance itself.
The Human Connection
The same geometric ratio appears within human anatomy.
The arcs of the skull, the curve of the bite, and the mechanics of the jaw all express this same equilibrium.
Leonardo’s geometry wasn’t artistic ornament—it mirrors the structure of life itself.
A Universal Pattern
From Leonardo’s drawings
→ to Fuller’s Vector Equilibrium
→ to the atomic lattice of matter—
the same pattern repeats across scales.
Geometry, art, anatomy, and physics are all speaking one language: equilibrium.
Explore the Work
Leonardo’s Complementary Ratios (2025) – Journal of Mathematics and the Arts
Vitruvian Man: A Modern Anatomical Analysis (2025)
Lecture Series: The Geometry of Balance — London 2026