geometry - How to find the parametric equation of a cycloid ...
"A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line." - Wikipedia. In many calculus books I have, the cycloid, in parametric form, is used in examples to find arc length of parametric equations. This is …
Finding the equation for a (inverted) cycloid given two points
A cycloid can also be interpreted the equation of motion of a point in a rolling-circle. You can check here if you are not convinced. Or even prove it mathematically.
What's up with the cycloid-shaped pot in Melville's Moby Dick?
It was in the left hand try-pot of the Pequod [the whaling ship of Captain Ahab], with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time.
calculus - Finding the area under one arch of cycloid
Jan 28, 2022 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Is it possible to express a cycloid in polar coordinates
The parametric equations for a cycloid of radius 1 centered at the pole are $$ x(t) = t - \pi - \sin t \\ y(t) = \pm (1- \cos t) $$ where the plus sign is a cycloid above the x-axis and the minus sign a cycloid below the x-axis.
intuition - Proof of the Cycloid Parametric Equation - Mathematics ...
Mar 5, 2024 · Here we establish that the distance PT is equal to the distance OT, which then (alongside other steps) allows us to derive the parametric equation of the cycloid. Every video or written proof I have seen on the proof for deriving the parametric curve consider this step to be "intuitive", but this does not strike to me as intuitive at all.
calculus - Surface area by the revolution of cycloid - Mathematics ...
Oct 5, 2016 · Surface area by the revolution of cycloid. Ask Question Asked 8 years, 3 months ago.
geometry - Equation of various cycloids: when it is regular ...
Jul 29, 2021 · This is an exercise from a book on Differential Geometry. Let a disc of radius 1 roll on the x-axis in the x–y plane.
Newest 'cycloid' Questions - Mathematics Stack Exchange
Dec 19, 2024 · Ceva Cycloid polar coordinates form is: $$ r = 1 + 2\cos(2\phi) $$ I found that the relation between polar ...
integration - Rotating cycloid - Mathematics Stack Exchange
Jun 1, 2017 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.