Chord Hopper vs Helix Walker

Pure chord jumps between primes vs continuous helix travel

A (helix): total arc = (p_N − p₁) × √2 | B (chord hopper): total = Σ √(2 − 2cos(g_n) + g_n²) | R(N) = B / A

Primes 2000

Ratio R(N) = B / A

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A — Helix Walker

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continuous arc length

B — Chord Hopper

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sum of straight jumps

Shortcut

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distance saved by hopping

R(N) = Σ chords / helix arc — does it converge?

Local chord / arc ratio per gap (colored by gap size)

Analyzing convergence...