func (G16Helix) GoldenPhaseOffset(k int) float64 · z_k(θ)

Read the equation

This relation defines z_k(θ) in the source section “func (G16Helix) GoldenPhaseOffset(k int) float64 · z_k(θ)”. It specifies the displayed relationship between the named quantities or parameters. 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 z_k(θ) as the quantity being defined or updated by this relation.

2. Substitute the source-defined variables or recorded values and follow the displayed arithmetic and indexing exactly.

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

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
	return HelixPoint{
		X: HelixRadius * math.Cos(phase),
		Y: HelixRadius * math.Sin(phase),
		Z: (Pitch/(2.0*math.Pi))*theta + h.VerticalOffset(k),
	}
}

// PointGolden returns point with golden ratio phase adjustment

z_k(θ) = (p/2π)·θ + δ_k

Related builds

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