A cycloid; the curve of fastest descent between two points.
The curve upon which a body moves in the least possible time from one given point to another.
It was almost a dramatic scene that day when he leaped from his chair and scrawled the equation of the "brachistochrone" on the blackboard in a handwriting that no mortal man could decipher.
The brachistochrone curve that gives the minimum travel time is determined by using the calculus of variations to find the best compromise between the shortest path – i.e., a straight slope – and the path that gives the maximum initial acceleration, i.e., a vertical drop followed by a short bend followed by a horizontal path.
Another is the famous brachistochrone problem in which a ball rolls down a curve a cycloid that gives the minimum time of travel.
Finally, the cycloid is also said to be the brachistochrone (from the Greek brakhistos, or shortest, and khronos, or time) because it is the path of an object falling freely from the ﬁxed point A to the ﬁxed point B in the shortest possible time.
DFW's Sentence The closest conventional analogue I could derive for this figure was a cycloid, L'Hopital's solution to Bernoulli's famous brachistochrone problem, the curve traced by a fixed point on the circumference of a circle rolling along a straight line.
The word 'brachistochrone' comes from Ancient Greek roots meaning "shortest" and "time".