# Definition:Brachistochrone

## Contents

## 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**.

## Linguistic Note

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

## Also see

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1.6$: The Brachistochrone. Fermat and the Bernoullis - 1975: W.A. Sutherland:
*Introduction to Metric and Topological Spaces*... (previous) ... (next): $2.2$: Examples