Tautochrone problem
The tautochrone problem is the problem set by Johann Bernoulli for his older brother, Jakob. Jakob did solve the problem by creating the calculus of variations. The problem is as follows:
- what shape must you bend a piece of wire such that a frictionless bead placed at any point along it will always reach the lowest point of the wire in the same amount of time?
Another form of the problem asks:
- what shape do you need to bend a piece of wire into so that a frictionless bead can slide down from one point to any other in the least amount of time?
The solution is in fact an upside down cycloid. This answer was first discovered by Huygens in 1673.
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