= Translation surface (differential geometry)
{wiki=Translation_surface_(differential_geometry)}
In differential geometry, a **translation surface** is a type of surface that can be constructed by translating a polygon in the Euclidean plane. The concept is closely related to flat surfaces and is prevalent in the study of flat geometry, especially in the context of billiards, dynamical systems, and algebraic geometry. \#\#\# Definition A translation surface is defined as a two-dimensional surface that is locally Euclidean and has a flat metric.
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