For ten points, name this mathematical object that is the curve such that a massive point falling under gravity will reach the bottom of the curve at the same time no matter where it starts on the curve, and is a cycloid.
The solution to the problem of this name was first published in 1673's Horologium oscillatorium. In that work, Christian Huygens utilized the idea of a functional to discover that the only curve satisfying the definition of this is the curve traced when a point on the edge of a wheel rolls along a surface. For ten points, name this mathematical object that is the curve such that a massive point falling under gravity will reach the bottom of the curve at the same time no matter where it starts on the curve, and is a cycloid.
The solution to the problem of this name was first published in 1673's Horologium oscillatorium.
tautochrone (prompt on “cycloid” before the end)