Astadium is a two-dimensionalgeometric shape constructed of arectangle withsemicircles at a pair of opposite sides.^[1]The same shape is known also as apill shape,^[2]discorectangle,^[3]obround,^[4][5] orsausage body.^[6]

The shape is based on astadium, a place used forathletics andhorse racing tracks.

A stadium may be constructed as theMinkowski sum of adisk and aline segment.^[6] Alternatively, it is theneighborhood of points within a given distance from a line segment.A stadium is a type ofoval. However, unlike some other ovals such as theellipses, it is not analgebraic curve because different parts of its boundary are defined by different equations.

Theperimeter of a stadium is calculated by the formula${\displaystyle P=2(\pi r+a)}$ wherea is the length of the straight sides andr is the radius of the semicircles. With the same parameters, thearea of the stadium is${\displaystyle A=\pi r^2+2ra=r(\pi r+2a)}$.^[7]

When this shape is used in the study ofdynamical billiards, it is called theBunimovich stadium.Leonid Bunimovich used this shape to show that it is possible for billiard tracks to exhibitchaotic behavior (positiveLyapunov exponent and exponential divergence of paths) even within a convex billiard table.^[8]

Acapsule is produced by revolving a stadium around theline of symmetry thatbisects the semicircles.

• Weisstein, Eric W."Stadium".MathWorld.

• Piecewise-circular curves

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