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Definition: One of the famous problems in the history of mathematics is the brachistochrone problem: to find the curve along which a particle will slide without friction in the minimum time from one given point P to another Q, the second point being lower than the first but not directly beneath it. The word "brachistochrone" comes from the Greek words brachistos, meaning shortest, and chronos, meaning time.
Source: Elementary Differential Equations and Boundary Value Problems - William Boyce & Richard DiPrima