Kappa Curve has Double Cusp at Origin

Theorem

Let $\KK$ be a kappa curve expressed in Cartesian coordinates as:

$x^4 + x^2 y^2 = a^2 y^2$

$\KK$ has a double cusp at the origin.

This double cusp is a double cusp of the first kind.

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

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): kappa curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): kappa curve