Equiangular spiral

Plane Curves

Description

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

Mapping

\left\{x\to a e^{b t} \cos (t),y\to a e^{b t} \sin (t)\right\}
$<mrow> <mo>{</mo> <mrow> <mrow> <mi>x</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>t</mi> </mrow> </msup> <mo>&#8290;</mo> <mrow> <mi>cos</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>y</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>t</mi> </mrow> </msup> <mo>&#8290;</mo> <mrow> <mi>sin</mi> <mo>&#8289;</mo> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mrow> </mrow> <mo>}</mo> </mrow>$
{x -> a*E^(b*t)*Cos[t], y -> a*E^(b*t)*Sin[t]}
[x = a*exp(b*t)*cos(t), y = a*exp(b*t)*sin(t)]

Constants

\{a,b\}
$<mrow> <mo>{</mo> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> </mrow> <mo>}</mo> </mrow>$
{a, b}
[a, b]

Cite this as:

Plane Curves: Equiangular spiral from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/PlaneCurves/Equiangular-Spiral.php