Project III (MATH3382) 2016-17

Billiards

Anna Felikson

Description:

A mathematical billiard is in idealisation of a well-known game, where balls are moving along straight lines on a table, reflecting from the boundaries of the table so that the angle of incidence is equal to the angle of reflection. Some simple questions one could ask about billiards are: if a ball starts from a given point to a given direction, will it ever come back to this point? are there periodic trajectories? how does this depend on the shape of the table? can one work with billiards in geometries other than Euclidean one? These questions may bring us to many different areas of mathematics, such as dynamical systems, reflection groups, geometry of surfaces.

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Prerequisites/Corequisites: taking Geometry III/IV would help.

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Resources:

One can look at MathWorld page for billiards.
The wikipedia page for Dynamical billiards is a bit on more technical side.
One can start the reading from Geometry and Billiards book by Serge Tabachnikov.

More reading on billiards can be found here.

email: Anna Felikson

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