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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, Îļ, φ), providing explicit formulas for r(t), Îļ(t), φ(t), and their derivatives. We establish the constant angular velocity Îļ(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

Two mathematicians at lunch, trying to understand modern AI

Two accomplished mathematicians sit down for coffee and try to understand the modern AI paradigm. No panic. No hype. No pitch deck. Just proof-minded people watching an industry confuse probability with intelligence, benchmarks with truth, and agents with accountability. A light-hearted conversation about the clown show — and why the future belongs to systems that can prove behaviour under pressure. #ECAI #DamageBDD #AI #Mathematics #DeterministicAI #FormalVerification #Cryptography #EllipticCurves #BDD #Verification #TechLeadership #SoftwareEngineering #Nostr #LinkedIn

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Introducing: Devstral 2 and Mistral Vibe CLI.

Today, we're releasing Devstral 2—our next-generation coding model family available in two sizes: Devstral 2 (123B) and Devstral Small 2 (24B). Devstral 2 ships under a modified MIT license, while Devstral Small 2 uses Apache 2.0. Both are open-source and permissively licensed to accelerate distributed intelligence.

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Chili oil

Crispy garlic-shallot chili oil with umami depth

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Digging low-level : Bitwise Operation āļ—āļģāļ‡āļēāļ™āļ­āļĒāđˆāļēāļ‡āđ„āļĢ?

Bitwise Operations āđ€āļ›āđ‡āļ™āđ€āļ„āļĢāļ·āđˆāļ­āļ‡āļĄāļ·āļ­āļ—āļĩāđˆāļ—āļĢāļ‡āļžāļĨāļąāļ‡āļŠāļģāļŦāļĢāļąāļšāļ™āļąāļāļžāļąāļ’āļ™āļēāļ—āļĩāđˆāļ•āđ‰āļ­āļ‡āļāļēāļĢāļ›āļĢāļ°āļŠāļīāļ—āļ˜āļīāļ āļēāļžāļŠāļđāļ‡āđāļĨāļ°āļāļēāļĢāļ„āļ§āļšāļ„āļļāļĄāļĢāļ°āļ”āļąāļšāļšāļīāļ• āđ‚āļ”āļĒāđ€āļ‰āļžāļēāļ°āđƒāļ™āļāļēāļĢāļžāļąāļ’āļ™āļēāļĢāļ°āļšāļšāļĢāļ°āļ”āļąāļš low-level āđāļĨāļ°āļāļēāļĢāļ—āļģāļ‡āļēāļ™āļāļąāļšāļŪāļēāļĢāđŒāļ”āđāļ§āļĢāđŒāđ‚āļ”āļĒāļ•āļĢāļ‡

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