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

Historical Note

The brachistochrone was investigated by Jacob Bernoulli, using the techniques of calculus.

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