PHYSICS VASE N°2 — Curved Manifold Resonance

PHYSICS VASE N°2 — Curved Manifold Resonance

Limited Edition Research Series (2/50)
Published by 3D Print Official

Inspired by:

Nikolai Lobachevsky

and the geometry of non-Euclidean surfaces

Abstract

Physics Vase N°2 explores harmonic modulation on a hyperbolic surface, translating non-Euclidean geometric principles into additive manufactured form.

The underlying radial structure follows the equation of a rotational hyperboloid:

a surface historically connected to the foundations of hyperbolic geometry developed by Nikolai Lobachevsky.

Superimposed cylindrical harmonics introduce separable radial and axial oscillations across a curved manifold, generating a standing interference pattern embedded within a negatively curved geometry.

The result is a parametric structure where curvature and resonance coexist.

Physical Attributes Encoded

• Hyperbolic curvature
• Non-Euclidean geometric structure
• Harmonic interference
• Cylindrical separation of variables
• Structural ruled-surface efficiency

Hyperbolic geometry predates relativity, but later became essential for understanding curved spacetime in Albert Einstein’s field equations.

Research Continuation

This piece represents the second study within a 50-object exploration of physics-derived computational forms.

The theoretical foundation of Physics Vase N°3 will be derived from proposals submitted in the discussion.

Community engagement and scholarly participation inform the direction of subsequent editions.