Epicycloid whose Ratio of Generating Circle Radii is Rational is Closed Curve

Theorem

Consider the epicycloid $E$ generated by a epicycle $C_1$ of radius $b$ rolling within a deferent $C_2$ of radius $a$.

Let $k = \dfrac a b$ be a rational number.

Then $E$ is a closed curve.

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): epicycloid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): epicycloid