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Stadium (geometry)

A stadium is a two-dimensional geometric shape constructed of a rectangle with semicircles at a pair of opposite sides. The same shape is known also as a pill shape, discorectangle, obround,, racetrack or sausage body.

Formulas
The perimeter of a stadium is calculated by the formula P = 2 (\pi r+a) where a is the length of the straight sides and r is the radius of the semicircles. With the same parameters, the area of the stadium is A = \pi r^2 + 2ra = r(\pi r + 2a). ==Bunimovich stadium==
Bunimovich stadium
When this shape is used in the study of dynamical billiards, it is called the Bunimovich stadium. Leonid Bunimovich used this shape to show that it is possible for billiard tracks to exhibit chaotic behavior (positive Lyapunov exponent and exponential divergence of paths) even within a convex billiard table. ==Related shapes==
Related shapes
A capsule is produced by revolving a stadium around the line of symmetry that bisects the semicircles. ==References==
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