Exploring the geometry of equilibrium
Introduction
I’m a London-based dental surgeon and independent researcher investigating scale-invariant geometric principles that govern optimal spatial organization.
My research reveals how the tetrahedral ratio √(8/3) ≈ 1.633 appears across seemingly unrelated domains: hexagonal close-packed crystals, optimal human jaw architecture, Fuller’s tensegrity structures, and Leonardo da Vinci’s Vitruvian Man. This mathematical convergence points to a universal principle—when systems optimize for structural efficiency, they converge on the same geometric solution.
By connecting Renaissance geometry, crystallography, and biological architecture, this work demonstrates how form follows fundamental geometric necessity.
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“A London dentist may have cracked Leonardo’s geometric code.”
“An elegant mathematical bridge between anatomy and art.”
Decoding Vitruvian Man: The 500-Year-Old Mystery
For over five centuries, scholars have debated how Leonardo determined the precise relationship between the circle and square in his iconic Vitruvian Man. The hint was, it appears, was hidden in plain sight – Leonardo’s own words on the drawing specify “the space between the legs will be an equilateral triangle.”
This seemingly simple geometric constraint makes Vitruvius’s ancient problem mathematically determinate—yielding a unique solution: √(8/3) ≈ 1.633. Leonardo’s measured proportions (1.64-1.65) match this theoretical value within 1% tolerance.
But here’s what makes this extraordinary: this same ratio governs optimal human jaw function. The equilateral triangle Leonardo specified in 1490 corresponds precisely to Bonwill’s triangle—the geometric foundation of dental occlusion, not formally established until 1864.
Leonardo wasn’t creating idealized proportions. He was documenting geometric principles that biological systems instantiate through functional optimization.
“Vitruvian Man is more than a study of proportion—it’s a proof of geometric necessity.”
my latest book
The Paradox of Lucid Dreaming
Conscious Exploration
Experience the sights, sounds, and secrets of an ancient empire brought vividly to life.
Scientific Insight
Dr. Rory Mac Sweeney combines decades of research and firsthand experience to explain the mechanics of lucid dreaming and its connection to human evolution.
Philosophical Depth
Each chapter dives into consciousness, creativity, and perception—inviting readers to question what it means to be awake, aware, and alive.
Evidence-Based Research
Grounded in scientific method and supported by real-world data, the book makes complex psychological concepts accessible to all readers.
Transformational Practice
Beyond theory, The Paradox of Lucid Dreaming provides practical techniques for mastering awareness in both dream and waking life, helping you reach higher states of clarity and purpose.
The Intersection of Science & Spirit
A compelling fusion of logic and intuition, The Paradox of Lucid Dreaming bridges measurable science with the infinite mysteries of the soul.
