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Common Spirals


General parametric equation:

x(θ) = r(θcos(θ)

y(θ) = r(θsin(θ)

The radius r(θ) if different for each type of curve:

Archimedes spiral - r(θ) = θ

Fermat spiral - r(θ) = √θ

Logarithmic spiral - r(θ) = e(a·θ)

Golden spiral - r(θ) = φ(2/π·θ)

Hyperbolic spiral - r(θ) = 1/θ

Lituus - r(θ) = 1/√θ

 

Tip: Click "Calculate" to see the respective plot.


Substitute