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 
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)