"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 …

Mar 29, 2015 · As for the change of variable induced by the parametrisation of the cycloid, this comes from the very definition of the differential: $$\mathrm d\mkern1.5mu x=x'(t)\,\mathrm d\mkern1.5mu t.$$ Share Cite

Aug 7, 2015 · The other, smaller cycloid is being generated by a related mechanism: it is the envelope of the diameter of the rolling circle! Skipping the details, it can be shown that if the larger cycloid has the parametric equation $\left(t-\sin t\quad 1-\cos t\right)^\top$ the smaller cycloid has the corresponding equation $\left(\frac{2t-\sin 2t}{2 ...

Oct 5, 2016 · Surface area by the revolution of cycloid. Ask Question Asked 8 years, 5 months ago.

Aug 17, 2014 · My lecturer proposed a question to particular result regarding the curvature of a Cycloid (generated by circle of radius 1) at its cusps. Having left it as an open problem, I thought it'd be interesting to share it here and find a hopeful answer that I can share with him.

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Jun 10, 2019 · In the Wikipedia article about the tautochrone curve, there is a proof of the fact that the tautochrone curve must be a cycloid. The proof starts with the following statement: One way the curve ...

Aug 8, 2020 · $\begingroup$ The exact problem is that if I have a point on the rim of a circle of radius R that is at point (0,0) at t = 0.

Aug 8, 2017 · This is an old post, but there will still be people wanting to know how the parametric equations of the cycloid were obtained from the solution to the DE. Historically, the people who solved this problem already knew that the answer was the cycloid, so they knew the parametric equations, so they just had to show that they satisfied the DE.

Mar 13, 2021 · 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.