The tautochrone curve has fascinated me since I first heard about it and I want to share it with my Calculus class as an end of the year project. I think something similar to this (Demonstrating that a cycloid solves the Tautochrone Problem) would suffice. I don't completely understand it myself, so that is a little bit of a problem. It is an AP calculus BC course in high school, so the kids are for the most part unmotivated and I want to help them realize how cool it can be. I don't need anything super complicated, just something simple enough for high schoolers with Calulus 2 under their belt to understand. Thank you so much!
2026-04-02 02:13:02.1775095982
I need some help understanding proofs for an upside-down cycloid being the tautochrone curve. Could someone show me or point me to a simple proof?
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As I recall, Polya's "Mathematics and Plausible Reasoning, vol 1" has a good discussion of this. Look in chapter 9, "Physical Mathematics."