A stadium is a two-dimensional
geometric shape constructed of a
rectangle with
semicircles at a pair of opposite sides.[1]
The same shape is known also as a pill shape,[2]discorectangle,[3]obround,[4][5] or sausage body.[6]
A stadium may be constructed as the
Minkowski sum of a
disk and a
line segment.[6] Alternatively, it is the
neighborhood of points within a given distance from a line segment.
A stadium is a type of
oval. However, unlike some other ovals such as the
ellipses, it is not an
algebraic curve because different parts of its boundary are defined by different equations.
Formulas
The
perimeter of a stadium is calculated by the formula 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 .[7]
^O'Hara, Michael J.; O'Leary, Dianne P. (April 2008). "Adiabatic theorem in the presence of noise". Physical Review A. 77 (4). American Physical Society (APS): 042319-1–042319-20.
arXiv:0801.3872.
doi:
10.1103/physreva.77.042319.