Definition:Brachistochrone

Definition

Let a point $A$ be joined by a wire to a lower point $B$.

Let the wire be allowed to be bent into whatever shape is required.

Let a bead be released at $A$ to slide down without friction to $B$.

The shape of the wire so that the bead takes least time to descend from $A$ to $B$ is called the brachistochrone.

Also see

• Brachistochrone is Cycloid

Linguistic Note

The word brachistochrone comes from the Greek βράχιστος χρόνος (brakhistos khrónos), which means shortest time.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 6$: The Brachistochrone. Fermat and the Bernoullis
• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.2$: Examples
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): brachistochrone
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): brachistochrone
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): brachistochrone