image of Equiangular spiral (polar)

Equiangular spiral (polar)

Plane Curves


The Equiangular spiral (polar), also called logarithmic spiral, growth spiral or Bernoulli spiral, describes a family of spirals of one parameter. A special case of the Equiangular spiral (polar) is the circle curve, where the constant angle is 90°.

Object definitions


Mapping of Equiangular spiral (polar)
\left\{r\to a e^{b \theta },\phi \to \theta \right\}
<math> <mrow> <mo>{</mo> <mrow> <mrow> <mi>r</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>a</mi> <mo>&#8290;</mo> <msup> <mi>&#8519;</mi> <mrow> <mi>b</mi> <mo>&#8290;</mo> <mi>&#952;</mi> </mrow> </msup> </mrow> </mrow> <mo>,</mo> <mrow> <mi>&#981;</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mi>&#952;</mi> </mrow> </mrow> <mo>}</mo> </mrow> </math>
{r -> a*E^(b*\[Theta]), \[Phi] -> \[Theta]}
[r = a*exp(b*theta), phi = theta]


Constants of Equiangular spiral (polar)
<math> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> </mrow> <mo>}</mo> </mrow> </math>
{a, b}
[a, b]

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Plane Curves: Equiangular spiral (polar) from Differential Geometry Library.

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