The tautochrone curve has the property that a ball placed anywhere on it will take the same amount of time to slide to the bottom, regardless of starting position.
Notes on verification
Well-established mathematical/physics result, confirmed by Wikipedia and multiple independent educational sources; consistent with classical mechanics theory (Huygens' discovery). [tier=unverified indep_score=0.3 clusters=3 claim_tier=notable] [rescored 2026-09-15: curated origin-host map (PR #65); unclassified hosts no longer scored as aggregators]
Sources
- List of mathematics history topics (wikipedia)
- https://www.johndcook.com/blog/2011/10/15/tautochrone/ (corroboration)
- https://www.worldwidewords.org/ww-tau1.html (corroboration)
- https://handwiki.org/wiki/Physics:Tautochrone_curve (corroboration)