Equation of Circular Helix/Parametric Form

Theorem

Let $\HH$ be a circular helix embedded in Cartesian $3$-space whose axis coincides with the $z$-axis.

$\HH$ can be described by the parametric equation:

$\begin{cases}

x & = a \cos t \\ y & = a \sin t \\ z & = b t \\ \end{cases}$ where $t$ is the parameter.

Proof

This theorem requires a proof. In particular: It needs to be proved that the tangent to $\HH$ is at a constant angle to the $z$-axis 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): helix
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): helix