Equiangular spiral (polar)
Plane Curves
Description
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
- TeX
- MathML
- Mathematica input
- Maple input
\left\{r\to a e^{b \theta },\phi \to \theta \right\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mrow>
<mi>r</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<msup>
<mi>ⅇ</mi>
<mrow>
<mi>b</mi>
<mo>⁢</mo>
<mi>θ</mi>
</mrow>
</msup>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>ϕ</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mi>θ</mi>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
</math>
{r -> a*E^(b*\[Theta]), \[Phi] -> \[Theta]}
[r = a*exp(b*theta), phi = theta]
Constants
- TeX
- MathML
- Mathematica input
- Maple input
\{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 (polar) from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/PlaneCurves/Equiangular-Spiral-Polar.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...
