Event № 481
A bicycle is a fascinating object, from many points of views, both practical and theoretical. In this talk I will concentrate, mostly, on the geometry of bicycle tracks. At first sight, the pair of front and back wheel tracks left by a passing bike on a sandy or muddy terrain seems like a random pair of curves. This is not the case. For example, one can usually distinguish between the front and back wheel tracks, and even the direction at which these were traversed, based solely on their shapes. Another example: If the front wheel traverses a closed path, then, typically, the back track does not closes up, by an amount related to the area enclosed by the front track and the bicycle length (this fact was used to build an area measuring device, now obsolete, called the Hatchet planimeter). Recently, the subject has attracted attention due to newly discovered relations with the theory of completely integrable systems.