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Universal Helical Geometry: Spherical Coordinates, Earth Rotation, and DNA Topology

This paper derives the complete transformation of a standard helix r(t) = (R cost, R sin t, ct) from Cartesian to spherical coordinates (r, θ, φ), providing explicit formulas for r(t), θ(t), φ(t), and their derivatives. We establish the constant angular velocity θ(t) = 1 through rigorous calculation using the two-argument arctangent and Cartesian velocity components. The analysis reveals the helix’s uniform rotation about the z-axis with monotonic polar angle evolution, connecting to Cuculescu’s [1] geometric constructions of helical motion on developable surfaces.

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Rotation, and DNA Topology

1946-LA-602-Konopinski-Marvin-Teller-Ignition-fo-the-Atmsophere

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NKBIP-01: Curated Publications Specification

The specification for curated publications: ordered, optionally-hierarchical assemblies of Nostr events. Publications provide a standard way to organize and present related content, similar to how books organize chapters or journals organize articles.

Section of Eiffel Tower's Original Staircase to be Auctioned

A 14-step segment of the Eiffel Tower's original spiral staircase will be auctioned in Paris. The 2.75-meter-high steel piece, which once connected the tower's second and third floors, has been privately owned for over 40 years and is estimated to sell for between 120,000 and 150,000 euros.

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