Part 2/6:
Bernoulli's insight was to draw a connection between this mechanical problem and the behavior of light. He realized that the path of fastest descent is analogous to the path of light as it refracts between media of different densities, obeying Snell's Law. This led him to the solution of a cycloid - the curve traced by a point on the rim of a rolling wheel.
The Principle of Least Time
The connection to light was no accident. Over a century earlier, the mathematician Pierre Fermat had proposed that light always takes the path of least time between two points. This "principle of least time" could explain the phenomenon of refraction.