1. The curve of fastest descent between two points; the path along which an object sliding without friction under gravity alone will travel from one point to another in the shortest time.
Usage: mathematics; physics; technical term

Examples

• The brachistochrone problem was famously solved by Johann Bernoulli in the 17th century.
• A ball rolling down a brachistochrone curve reaches the bottom faster than one rolling down a straight incline.
• The shape of a brachistochrone is a cycloid, not a straight line.
• Physicists use the brachistochrone to illustrate principles of optimization and calculus of variations.
• The brachistochrone demonstrates that the shortest path is not always the fastest path.