page_title: Brachistochrone curve
hierarchical_section_title: Brachistochrone curve
caption_attribution_description: English: comparison of speed on curves Français&#160;: comparaison des vitesse sur diverses courbes
context_page_description: A Brachistochrone curve is the fastest path for a ball to roll between two points that are at different heights. A ball can roll along the curve faster than a straight line between the points.
  The curve will always be the quickest route regardless of how strong gravity is or how heavy the object is. However, it might not be the quickest if there is friction.
  The curve can be found using calculus of variations and optimal control.
context_section_description: A Brachistochrone curve is the fastest path for a ball to roll between two points that are at different heights. A ball can roll along the curve faster than a straight line between the points.
  The curve will always be the quickest route regardless of how strong gravity is or how heavy the object is. However, it might not be the quickest if there is friction.
  The curve can be found using calculus of variations and optimal control.
caption: The ball on the red Brachistochrone curve reaches the other side before the other two balls.