Evolute of Ellipse
Jump to navigation
Jump to search
Theorem
Let $E$ be an ellipse embedded in a Cartesian plane with the equation:
- $\dfrac {x^2} {a^2} + \dfrac {y^2} {b^2} = 1$
Cartesian Form
The evolute of $E$ is given by the Cartesian equation:
- $\paren {a x}^{2 / 3} + \paren {b y}^{2 / 3} = \paren {a^2 - b^2}^{2 / 3}$
Parametric Form
The evolute of $E$ can be expressed using the parametric equation:
- $\begin {cases} a x = \paren {a^2 - b^2} \cos^3 \theta \\ b y = \paren {a^2 - b^2} \sin^3 \theta \end {cases}$
Proof
This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- Weisstein, Eric W. "Ellipse Evolute." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EllipseEvolute.html