Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture

Geometry of the tracks left by a bicycle is closely related with the so-called Prytz planimeter and with linear fractional transformations of the complex plane. We describe these relations, along with the history of the problem, and give a proof of a conjecture made by Menzin in 1906.