Can a path that gets closer to its target at every step still be
infinitely long? Yes, on an Archimedean spiral. I derive the
closed-form arc length, show L → ∞ as the radial step
m → 0⁺, and connect the result to gradient descent: improving
the loss at every step doesn't bound the length of the path.
Always closer, never arriving. Make m smaller and watch
the distance walked grow like πR²/m.
BlogDec 2024 – Apr 2025 · Medium
Efficient Fibonacci computation: Édouard Lucas's Pascal-triangle method
Lucas's combinatorial formula gives the exact nth Fibonacci
number without recursion, by summing a shallow diagonal of Pascal's
triangle. I compare its cost with matrix exponentiation, Binet's
formula and naive recursion, and show it suits resource-constrained
environments.