The brachistochrone problem revisited: a numerical solution via non-linear root-finding

Abstract

We revisit the famous brachistochrone problem – determining the shape of the frictionless slide connecting two points at different altitudes which allows a particle to travel under gravity in the shortest possible time – and discuss a modest numerical solution which employs – and hence could enrich the teaching of – iterative root-finding methods.

Keywords:

• Brachistochrone
• Snell's law
• numerical solution
• root-finding

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The first author found these to be suitable means for not only objective assessment but also students' enhancement of various transferable skills.