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and the geometry of non-Euclidean surfaces

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.

• 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.

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.

Vote for the theory you’d like to see brought to life! Share your choice in the comments, and let’s unveil Vase 3 together!