image of Equiangular spiral

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°.

Object definitions

Mapping

Mapping of Equiangular spiral
\left\{x\to a e^{b t} \cos (t),y\to a e^{b t} \sin (t)\right\}
<math> <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> </math>
{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

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

Cite this as:

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

Terms of use:

You can use the contents of DG Library pages for education, research, professional needs and enjoyment.
If you use this library, please, cite DG Library as the source of the data.

Pages of DG Library may not be copied, mirrored, redistributed, printed, or reproduced in bulk without permission. Usage for any commercial purposes without permission is prohibited.
 

DG Library is database of over 580 objects for differential geometry and its applications. Read more...

  • Share via email
  • Share via Twitter
  • Share via Facebook