Normal to Cycloid passes through Bottom of Generating Circle/Proof 1
Jump to navigation
Jump to search
Theorem
Let $C$ be a cycloid generated by the equations:
- $x = a \paren {\theta - \sin \theta}$
- $y = a \paren {1 - \cos \theta}$
Then the normal to $C$ at a point $P$ on $C$ passes through the bottom of the generating circle of $C$.
Proof
From Normal to Cycloid, the equation for the normal to $C$ at a point $P = \tuple {x, y}$ is given by:
This theorem requires a proof. In particular: We don't even have the definition of a normal to a curve posted up yet, so there's a long way to go here. 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
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.21$: The Cycloid: Problem $3$