func (G16Helix) VerticalOffset(k int) float64 · GoldenPhaseOffset returns θ_k

Read the equation

This relation defines GoldenPhaseOffset returns θ_k in the source section “func (G16Helix) VerticalOffset(k int) float64 · GoldenPhaseOffset returns θ_k”. Uses a remainder or modular operation, retaining the numeric representation used in the source. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read GoldenPhaseOffset returns θ_k as the quantity being defined or updated by this relation.

2. Uses a remainder or modular operation, retaining the numeric representation used in the source.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

type G16Helix struct{}

// VerticalOffset returns δ_k = k·h/16
func (G16Helix) VerticalOffset(k int) float64 {
	return float64(k) * RisePerBP / NumStrands
}

// GoldenPhaseOffset returns θ_k = 2πk·φ⁻¹ mod 2π
func (G16Helix) GoldenPhaseOffset(k int) float64 {
	return math.Mod(2.0*math.Pi*float64(k)*PHIInv, 2.0*math.Pi)
}

// Point returns point on strand k at parameter θ
// x_k(θ) = r·cos(θ + 2πk/16)
// y_k(θ) = r·sin(θ + 2πk/16)
// z_k(θ) = (p/2π)·θ + δ_k
func (h G16Helix) Point(k int, theta float64) HelixPoint {
	phase := theta + 2.0*math.Pi*float64(k)/NumStrands

GoldenPhaseOffset returns θ_k = 2πk·φ⁻¹ mod 2π

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